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Investigation of a robust tendon-sheath mechanism for flexible membrane wing application in mini-UAV
Mechanical Systems and Signal Processing 85 (2017) 252–266
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Investigation of a robust tendon-sheath mechanism for flexible membrane wing application in mini-UAV Shian Lee a, Tegoeh Tjahjowidodo a,n, Hsuchew Lee b, Benedict Lai a a School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, North Spine (N3), Singapore 639798, Singapore b Dept. of Mechanical and Manufacturing Engineering, University of Calgary, 2500 University Drive N.W., Calgary, Canada T2N 1N4
a r t i c l e in f o
abstract
Article history: Received 15 March 2016 Received in revised form 8 August 2016 Accepted 11 August 2016
Two inherent issues manifest themselves in flying mini-unmanned aerial vehicles (miniUAV) in the dense area at tropical climate regions, namely disturbances from gusty winds and limited space for deployment tasks. Flexible membrane wing (FMW) UAVs are seen to be potentials to mitigate these problems. FMWs are adaptable to gusty airflow as the wings are able to flex according to the gust load to reduce the effective angle-of-attack, thus, reducing the aerodynamic loads on the wing. On the other hand, the flexible structure is allowing the UAV to fold in a compact package, and later on, the mini-UAV can be deployed instantly from the storage tube, e.g. through a catapult mechanism. This paper discusses the development of an FMW UAV actuated by a tendon-sheath mechanism (TSM). This approach allows the wing to morph to generate a rolling moment, while still allowing the wing to fold. Dynamic characteristics of the mechanism that exhibits the strong nonlinear phenomenon of friction on TSM are modeled and compensated for. A feed-forward controller was implemented based on the identified nonlinear behavior to control the warping position of the wing. The proposed strategy is validated experimentally in a wind tunnel facility by creating a gusty environment that is imitating a realistic gusty condition based upon the results of computational fluid dynamics (CFD) simulation. The results demonstrate a stable and robust wing-warping actuation, even in gusty conditions. Accurate wing-warping can be achieved via the TSM, while also allowing the wings to fold. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Drone UAV CFD Gust Flexible membrane wing Control and identification Tendon-sheath Wing-warping Bouc–Wen
1. Introduction Mini-unmanned aerial vehicles (UAV), also known as drones, can be deployed for various purposes, for example, surveillance missions or payload delivery, therefore sparking an increasing amount of research interest. The mini-UAVs can be separated into two main categories, which are the fixed wings and the rotary wings. The difference in performance between these two is significant [1]. Fixed wings are more suitable for example for border patrol missions as the aircraft will be able to handle longer flight time and carry more payload. The mini-UAV discussed in this paper will solely be a fixed wing. Mini-UAVs are extremely stealthy, and are usually defined as a UAV light and small enough to be carried and operated by a single human operator. However, due to the small weight and moment of inertia, they are also very susceptible to gusts n
Corresponding author. E-mail address: [email protected] (T. Tjahjowidodo).
http://dx.doi.org/10.1016/j.ymssp.2016.08.014 0888-3270/& 2016 Elsevier Ltd. All rights reserved.
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and thus becomes a challenging vehicle to pilot. Gusty environments, especially in tropical climates with frequent thunderstorms [2] pose a huge challenge to these aircraft. Huge control surfaces and fins and an onboard autopilot are the conventional methods to help increase the control authority and stability of the mini-UAVS. Quick deployment and easy storage of the mini-UAV are also critical for a surveillance mission. Usual fixed wing mini-UAVs may take up a lot of space as the wingspan can reach up to more than 1 m. In typical operations, the operator will have to disassemble the mini-UAV for transportation and then assemble it again for deployment. This will expose the operator to dangerous elements, as well as cause a delay which might allow the surveillance target to exit the surveillance area before the mini-UAV is ready. For the purpose of quick deployment and easier storage, the foldable wing is one of the solutions. Research on flexible wings for fighter aircraft already exists [3], but recently there is an increasing number of works being done specifically for mini-UAVs. FMW by [4] has paved a way for the work in this paper. Being able to deploy immediately without any installation or assembly is one of the advantages of the FMW mini-UAV. By folding the wings around the fuselage for storage and transportation, the mini-UAV can also be launched directly from the storage tube, which has been shown by Prioria Robotics Maveric UAV from Florida. Adaptive washout, a phenomenon which occurs in the FMW, allows the FMW mini-UAV to handle higher angle of attack, delay stall response and dampen gust disturbances as well [4]. The ease of repair of the FMW is also a very valuable feature. A damaged wing can be repaired fairly quickly and easily by applying some adhesive on the damaged area. Developed by the University of Florida, the FMW is fabricated by curing layers of prepreg carbon fiber [4]. It is impossible to install a servo and actuate a conventional aileron on the wing as the wing is very thin and flexible, thereby rendering the very little amount of roll control. This is a major drawback of the FMW. In [5], the FMW is warped to increase the roll control authority. Various wing-warping methods have been tried, but most are not suitable as the wing is constrained span-wise and becomes unfoldable. In this research, the application of a tendon-sheath mechanism (TSM)to actuate the FMW is investigated. The inspiration for this research originated from the mechanism of a flexible endoscopic system that uses tendon-sheath as the mechanism for actuation [6,7]. The actuation is delivered by attaching one end of the tendon-sheath to the trailing edge of the FMW, while the other end is connected to a servomotor secured inside the fuselage that will generate the motion. Tension forces can be transmitted via the tendon-sheath to the FMW when the servomotor is activated. This approach still allows the FMW to fold as the tendon-sheath can be routed along the wing while taking only minimal space. Sufficient warping for roll control can be achieved using the TSM and is shown in experiments [8]. However, it is observed that there are some nonlinear behaviors of the TSM, which will deteriorate the wing-warping accuracy without an appropriate control strategy. Flight control systems are required to provide aerodynamic assistance in any aircraft systems. Most of the commercial autopilots implement the PID control algorithm [9]. There are a few works involving adaptive control techniques, such as fuzzy logic controllers [10], adaptive neural network controllers [11], or robust controllers such as LQG/LTR and H∞ controllers [12] as well. Boundary layer control is another effective method of controlling the mini-UAV, especially during low Reynold's number or high angle of attack [13,14]. This paper presents the characterization of a TSM applied for FMW wing-warping application. Nonlinear dynamic behavior that is apparent in the TSM will be identified and modeled as well, which later on is utilized to implement a model based controller to regulate the wing-warping. Subsequently, the performance of the system is validated experimentally in a wind tunnel under a specific gusty environment scenario simulated by a CFD model. The experiments and results of the nonlinear behavior identification of the TSM wing-warping are shown in Section 3. A nonlinear model based on General Bouc–Wen model for hysteresis is introduced for the TSM wing-warping in Section 4. Section 5 presents the controller design and testing for the wing-warping, and also a CFD simulation to design the testing environment. Finally, the conclusion of this paper is drawn in Section 6.
2. Flexible membrane wing characteristics Being foldable is the main characteristic of the FMW. The FMW is specifically designed to fold around the fuselage of the UAV for storage, as illustrated in Fig. 1a. In order to fold downwards around the fuselage while be able to withstand the aerodynamic loads when unfolded, the airfoil is designed to be very thin and also curved in the chord-wise direction, measuring only 1.2 mm in thickness. The FMW is curved along the chord-wise direction at the leading edge, allowing the wing to only fold downwards spanwise while being rigid against the forces from below the wing. This allows the FMW to bear the aerodynamic loads without buckling easily. Fig. 1 shows the FMW at the folded and unfolded stage. Reinforced ribs which start from the mid to the trailing edge support the nylon fabric, which carries most of the aerodynamic loads. Weighing at only 160 g and spanning 1 m with an area of 0.19 square meters, the FMW is very light for its size. During wind tunnel tests, the FMW can generate up to 20 N of lift force without buckling. In addition to the ability to fold, the FMW also has a passive mechanism known as the adaptive washout, which allows the wing to flex and adapt to the gusty airflow [4]. As the wing is also flexible in the chord-wise direction, the wing will flex according to the direction of the gusts, changing the effective angle-of-attack on the wing in favor of the flight response. For example, if the gust perturbs from below, the wing will then flex upwards in the chord-wise direction, decreasing the effective angle-of-attack and also reducing the aerodynamic loads on the wing. The FMW will also flex with the changes in
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Fig. 1. Flexible membrane wing in both folded and normal state. (a) Flexible membrane wing in the folded state. (b) Flexible membrane wing unfolded.
the headwind velocity, increasing or decreasing the lift forces generated and providing a smoother flight and better stall resistance. The FMW will recover to the original airfoil shape, restoring the lift forces when there are no disturbances. This adaptive washout phenomenon helps to provide a smoother flight and allow an easier flight control. 2.1. wing-warping wing-warping, or morphing in other technical writings, are essentially the intentional change of shape of the wing or the airfoil. wing-warping has been practiced since the invention of the airplane by the Wright brothers [15]. In their case, the wings were twisted via cable and pulleys to achieve roll control. Similarly, the FMW mini-UAV can achieve more roll control authority by wing-warping. Roll control can be achieved via wing-warping as it changes the effective angle-of-attack of the FMW by changing the airfoil shape. A higher angle-of-attack will provide a higher lift at the warped wing. wing-warping has been shown to provide ample rolling moment for a FMW mini-UAV in [5,16], which utilizes torque rods in their design. The main drawback is that the FMW becomes unfoldable. The location for warping is critical as it will affect the roll rate and also the lift over drag of the aircraft. High roll rates can be achieved if the wing is warped near the tip, but if done excessively near the wing tip, the wing will experience tip stall, and therefore inducing an adverse roll moment [17]. The degree of warping should, therefore, be limited, and also not be done at the wing tip. In [17], an optimized location of warping was identified by comparing the roll rate and lift over drag of the aircraft. In this paper, a similar location was chosen for this FMW for optimal performance. There is a conflicting requirement regarding wing-warping with regards to the structural stiffness of the wing. To enable warping, the wing has to be flexible enough to allow large deformations, and still have sufficient stiffness to bear the aerodynamic loads. If a high stiffness is chosen, the wing will excel at carrying the aerodynamic loads, but the energy required to warp will be enormous. On the other hand, highly flexible, low stiffness wings will require much less energy to warp, but may not be able to maintain the shape to bear the aerodynamic loads [18]. In this paper, some iteration has been done to fabricate a FMW which can achieve the balanced stiffness for warping, flying and folding. 2.2. Flexible membrane wing actuation methods wing-warping can be achieved via many different approaches. Contributions from [19,20] are crucial to cambered wingwarping. Piezoceramic actuators were used for UAV flight control, and the actuators were found to be effective in both wind tunnel and flight tests [21]. However, it is not applicable in mini-UAVs as a heavy transformer is required to step up the voltage for the piezo-ceramic actuators. Dielectric materials were also proposed to actuate the FMW by securing a dielectric elastomer actuator (DEA) on the FMW for actuation [8]. But, the area of actuation was fully covered by the DEA and the whole setup was very bulky, which will alter the aerodynamic properties of the FMW. In addition, the DEA is very fragile and will break easily, making it a very difficult object to mount to the wing. Very high voltage, to the range of 5–10 V is required to actuate the DEA, which results in a requirement of a heavy step up transformer to be mounted on the mini-UAV. Another investigated method to actuate a FMW is by using the Nylon string. The trailing edge of the wing is tied to a piece of Nylon string, and the other end of the string is connected directly to the servo that is located inside the fuselage of the mini-UAV. As the servo rotates, the Nylon string will tighten and pull the trailing edge of the wing. Although warping can be achieved, this method is not robust, as the Nylon string tends to get tangled when the wing is folded. Besides, based on our observation during preliminary flight tests that we conducted, robustness is also an issue as the Nylon string tends to break easily.
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3. Tendon-sheath mechanism for FMW actuation A schematic drawing of TSM is illustrated in Fig. 2a. A flexible sheath encloses a tendon that will transmit forces from one end to the other. The tendon-sheath actuated wing-warping mechanism is characterized by a relationship between the input and output position. It is known that there are four distinct phases during the transmission, namely releasing to pulling phase (Phase 1), pulling phase (Phase 2), pulling to releasing phase (Phase 3), releasing phase (Phase 4) [7] as illustrated in Fig. 2b. During Phase 1, the servo rotates and pulls the tendon; the input tension increases and therefore increasing the friction force. At this stage, the output position Pout will not change until the friction force has been overcome. In Phase 2, the static friction has been overcome, and Pout changes with the input position Pin. In Phase 3 the servo starts to rotate in the opposite direction, reducing the input tension. However, Pout does not immediately reduce, as the friction force delays the reduction of force from the input to output. The tension of the tendon is reduced, and it will take some time for the FMW to overcome the friction and start springing back into its original position. Phase 4 shows unloading phase where Pout is moving together with Pin. This unique characteristic of the tendon-sheath is attributed to the friction force occurring between the tendon and the sheath that exhibits nonlocal memory behavior [7,22,23]. Similar behavior is also observed in many electromechanical systems, such as in a pneumatic artificial muscle (PAM) [24,25] or piezoelectric driven mechanisms [26]. For the actuation purpose, the tendon has to be pretensioned to maintain consistent characteristics every time the TSM is activated. If it is loose, there will be less or no transmission of force from the input to the output. It is also concluded that the characteristics of the TSM will be identical if the total curvature of the tendon-sheath is kept constant [6]. Therefore, the total curvature of the tendon-sheath has to be kept the same on the ground experiment setup as the mini-UAV. The same amount of force is needed to actuate the TSM for a sharp bend or a gradual bend of the tendon. 3.1. Experiment setup The experiment in this paper is done using the same setup in [8]. In order to obtain the characteristics of the TSM of the mini-UAV, the tendon-sheath is bent and routed along the span of the wing, as illustrated in Figs. 3a and b. The total curvature angle has to be kept at a constant 270°, as this is the design for the UAV. The servomotor will pull the tendon, causing the end to retract and therefore warping the FMW. wing-warping is considered difficult to quantify and measure [5]. Here, an analog 4.5″ flexsensor by Spectra Symbol that is taped securely onto the rib of the FMW at the main warping area with the largest deflection, as illustrated in Fig. 3c. The flexsensor is reasonably flat, which will not perturb the airflow when mounted on top of the wing. Prior to installation, the flexsensor is calibrated for various angles of bending. All the sensors and servo amplifiers are connected to a dSPACE 1104 controller board to allow data collection and control activation. 3.2. Observations from experiments In order to characterize the dynamic property of the system, the wing was actuated for 10 s with various constant frequencies and amplitudes. The resulting output motion is captured through the flexsensor reading. The experiment was carried out with different frequencies and amplitudes, ranging from 0.5 Hz to 3 Hz, and from 5° to 20°, referring to maximum aileron sweep rate specified for many existing aircraft with hinged control surfaces [27]. The general shape of the
Fig. 2. Tendon-sheath and its hysteresis characteristics. (a) Schematic of a tendon-sheath [6]. (b) Relation between position input and position output [8].
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FM W.
Fig. 3. Experimental setup. (a) Total tendon curvature is 270° in the experiment setup. (b) A schematic of the total tendon curvature at the FMW. (c) Flexsensor is mounted on top of the wing.
dynamic behavior of the wing-warping with TSM agrees with the theory shown in Fig. 2b, with the four distinct phases being observed. Fig. 4a shows the relation between wing-warping and tendon-sheath input at a frequency of 3 Hz. It is also found that the change in frequency did not affect the general shape and bias of plots significantly. In addition, a non-local memory hysteresis is observed when multiple loops are prescribed to the system, as shown in Fig. 4b. and c shows a closer look at the loops (more explanation about non-local memory hysteresis is available in [22]). However, when Fig. 4a and the ideal TSM property in Fig. 2b is compared in detail, some slight discrepancy at the transition between Phase 1 and 2 and also the transition between Phase 3 and 4 can be observed, where there is a gradual change in gradient instead of a sharp edge, much like a “hardening” effect. 3.3. “Hardening” phenomenon Initially, it was suspected that the FMW in the chord-wise direction possesses nonlinear properties, as the FMW is made of composite materials, therefore contributing to the “hardening” effect. The geometry of the FMW may also be a cause of the “hardening” effect as well. Therefore, a finite element analysis (FEA) was carried out to investigate the exact cause of the “hardening” effect. The software used for the FEA is ANSYS Workbench. In the analysis, as shown in Figs. 5a to d, the wing trailing edge is pulled at the same direction as the tendon pulling it in the experiment. From the FEA result, as illustrated in Fig. 6, the wing was shown to warp with a slightly decreasing rate as the tendon input is increased (“softening”). Even though it does not agree with the experimental results, it can be shown to be mathematically correct. The minor arc model can be used to explain the results from FEA. Pin (refer to Fig. 2b), which is the displacement of the tendon-sheath, is essentially the change of the distance between the two end points of the arc. Pout, the wing-warping is the central angle of the arc, and will change with Pin if the minor arc length rθ , which is the airfoil camber, is kept constant. Therefore, the relationship between Pin and Pout in Phase 2 and Phase 4 can be modeled by:
l + dl =
sin(θ + dθ ) r, π − (θ + dθ ) sin 2
θ + dθ < π (1)
where l is the arc length (FMW camber, equivalent to the initial tendon length), r is the radius of the arc, and dl is the change of displacement of the tendon-sheath input. The relationship between the warping angle θ and dl is nonlinear, as the rate of θ increases with dl.
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Fig. 4. The hysteresis behaviors of tendon-sheath actuated wing-warping. (a) Hysteresis behaviors with 3 Hz inputs. (b) Hysteresis behaviors with 1 Hz and 2 Hz inputs. (c) A closer zoom at the non-local memory hysteresis loops in Fig. 4b.
As the FEA and minor arc model (Fig. 7) showed that the geometry of the FMW cannot be the cause of the “hardening” phenomenon, another experiment is performed to investigate the cause of the nonlinear curves. A simple direct actuation of the FMW was carried out, which consists of a piece of tendon attached to the trailing edge of the FMW, and the other end secured to the servo motor. This experiment allows a thorough investigation of this phenomenon by eliminating all the hysteresis caused by the friction on TSM and focus only on the wing-warping itself. Fig. 8a shows the setup of the experiment. The wing was given different initial warping angles. For both the low and high initial warping angles cases, consistent results are observed. Fig. 8b shows the wing-warping output vs the direct tendon input (no sheath) for the low pre-tension (with 0° initial warping) and high pre-tension case (20° initial warping). For both cases, the relationship of the output vs input of the wing-warping appears to be quite linear. From the results of this experiment, it can be deduced that the “hardening” nonlinearity is not due to the geometry or material properties of the FMW. Even though the direct tendon actuation (with no sheath) exhibits minimum amount of hysteresis, but this cannot be applied in the FMW as a tendon-only-mechanism does not allow a flexible routing, which means that the tendon has to keep straight in the application. As suggested by [7], the pre-tension of the tendon-sheath will affect the general hysteresis behavior, especially in the transition from Phase 1–2 and Phase 3–4. Subsequently, the TSM is installed back to check for the effects of pre-tension. Two different pre-tension levels are prescribed to actuate the FMW, and the hysteresis behavior was recorded. The hysteresis behavior difference between low pre-tensioned and high pre-tensioned tendon-sheath wing-warping is observable in Fig. 8c. In the low pre-tension tendon-sheath, the hysteresis behavior exhibits the arched (nonlinear) line in Phases 2 and 4. There are no definite, sharp corners during the transition from Phase 1–2 (and from 3 to 4). When the tendon-sheath is given very high amounts of pre-tension, the nonlinear “hardening” effect (arched curve degree) lessens. This indicates that the phenomenon in Phases 2 and 4 is, indeed, caused by insufficient pre-tension. Although a linear relationship in Phase
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Fig. 5. Finite element analysis of the wing-warping. (a) Finite element analysis of the wing, viewed from the side. (b) FMW is simulated with a deflection at the trailing edge. (c) Another angle of the FMW during FEA, viewed from the back. (d) Another angle of the FMW during FEA, with a deflection at the trailing edge.
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2 and Phase 4 is desirable for the ease in the modeling and control tasks, it is not achievable in this FMW warping case. As the pre-tension is increased, the FMW will start to warp, affecting the airfoil shape and aerodynamic properties. Therefore, the pre-tension in the tendon-sheath for FMW warping must be kept low enough such that the FMW does not have any initial warping angles.
4. Hysteresis modeling Due to the large nonlinearity in the TSM, a nonlinear controller is required to accurately control the FMW warping. As such, a model of the hysteresis behavior will be needed. In order to capture the asymmetric hysteresis on the wing-warping actuation, a generalized Bouc–Wen model by Song et al. [28] is referred. Some modifications are introduced to better capture the nonlinearity of Phases 2 and 4 as presented by Do et al [6,7,29]. The model is expressed as:
θ (x)(t ) = α1x2 + α2x + α3 + αzz z ̇ = ẋ[A − |z|n Ψ (x, ẋ, z )] Ψ (x, ẋ, z ) = βϕT
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Fig. 7. Illustration of the arc model.
where
β and ϕ are matrices given as: β = [β1β2β3β4 β5β6] ϕ = [sgn(xż )sgn(xẋ)sgn(xz )sgn(ẋ)sgn(z )sgn(x)]
A total of 12 parameters were first estimated using the Genetic Algorithm (GA), where the results are subsequently used as initial values to optimize the parameters further by using the Nelder–Mead simplex algorithm (detailed discussion is presented in [8]). With respect to the arched curvy line in Phase 2 and Phase 4, a quadratic function was appended to the model (Fig. 4a) to capture the increasing rate curve (“hardening”). For identification purpose, random tendon-sheath position signals were prescribed to the system on the input side, while the wing-warping position output is recorded. Fig. 9 presents the hysteresis plot as a result of the identification procedure. Fig. 10a illustrates the testing input signals, together with the results of the model illustrated in Fig. 10b with the following parameters:
β = ⎡⎣ 19.8351 − 8.6135 0.8325 − 3.1266 10.6984 − 18.5⎤⎦ A = 3.9953 n = 3.1179 α = ⎡⎣ −0.0205 0.7120 0.7958⎤⎦ αz = 0.5369
(2)
with the RMS error being 0.26°. With a severe nonlinear behavior as shown in the experiments, a controller is required for precise wing-warping position control. Without accurate wing-warping control, the mini-UAV will have unreliable roll control, therefore jeopardizing the safety and flight qualities. By utilizing the parameters identified from the experiments, a modified General Bouc–Wen model has been constructed and used for controller design.
5. Controller design and testing In order to compensate for the nonlinearity on the TSM, the identified model obtained in Section 4 is utilized for control purpose. A combined feed-forward/feedback controller is designed, evaluated and implemented. Subsequently, the controller is then tested on the experiment platform after being validated to be effective. With a severe nonlinear dynamics attributed to the TSM as observed in experiments, a dedicated controller is required for precise wing-warping position regulation. By utilizing the model parameters identified from the experiments, a modified General Bouc–Wen model is utilized for control purpose. Here, a combined feed-forward and PID feedback controller are designed, evaluated and implemented. After it is shown to be effective, the controller is then tested on the experiment platform. 5.1. Controller design and simulation The model is implemented in the feed-forward loop as shown in Fig. 11. The reference warping input is fed to the model to compensate for the nonlinearity of the TSM. In order to demonstrate the effectiveness of the proposed control strategy,
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Fig. 8. Hysteresis behaviors of the flexsensor and wing. (a) Direct actuation of the FMW.(b) Input-output relationship of the wing-warping only with the tendon (no sheath) with different pre-tensions. (c) Hysteresis of the wing-warping with tendon-sheath at different pre-tensions.
the system is simulated with three different control schemes, i.e. open loop, PI feedback only and feed-forward/feedback. The gains for the PI were optimized for the control strategies, with Kp ¼7 and Ki ¼1 via the Ziegler–Nichols method. The simulation results are presented in Fig. 12, where the system was simulated by prescribing filtered random input signals with 1 Hz cutoff frequency to the input side of the TSM. As observed from the figure, the PID feedback controller is not as accurate as the combined feed-forward/feedback controller. When some disturbance is present on the system, the combined feed-forward/feedback controller still outperforms. The last simulation was taken by introducing a white noise signal on the TSM model to imitate disturbance on the system. In particular, Fig. 12a and c illustrate the effectiveness of the model-based controller that manage to linearize the system. 5.2. Controller implementation The controller is subsequently tested in a lab bench, by nesting the model into the dSPACE 1104 controller board. The FMW was actuated by a filtered random signal with 1 Hz cutoff frequency and amplitude of 4° without disturbance. The results are illustrated in Fig. 13. The RMS error for the open loop system, PID only system and the feed-forward/feedback system is 1.727°, 2.04°, and 0.285° respectively. The combined feed-forward/feedback controller exhibits superior performance compared to the PID feedback system, with an absolute difference of 1.755° in RMS error. However, the difference in
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Fig. 10. Solid line represents the experimental data, while the dashed line represents the data from the model. (a) The input for the model (wing-warping). (b) The output of the model (tendon-sheath position).
Fig. 11. Block diagram of the tendon-sheath actuated FMW warping control.
performance between the PID only system and the open loop system is insignificant, with an absolute difference of only 0.313° in the RMS error. In this experiment, similar gains from the simulation were used for the PI controller, i.e. Kp ¼7 and Ki ¼1. Higher gains will cause unstable oscillations in the system.
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Fig. 12. Simulation of the controller of the wing-warping via tendon-sheath actuation with given random inputs. The setpoint is represented by the dash lines, while the output is represented by a solid line.(a) Output comparison with disturbance. (b) Output comparison without disturbance. (c) Hysteresis comparison without disturbance. They are open loop, feedback only, feed-forward/feedback respectively. (d) Hysteresis comparison with disturbance. They are open loop, feedback only, feed-forward/feedback respectively.
5.3. Robustness against gusty environment As the atmospheric conditions in tropical areas tend to be gusty, the controller is required to be robust against gust disturbances. Therefore, the robustness of the system in a gusty environment has to be validated. The FMW mini-UAV is designed to dampen high-frequency gusts and to fly in windy conditions, such as over the tropical oceans for surveillance missions. The winds in a tropical climate can be quite gusty, with gust factors reaching up to 2.27 in non-thunderstorm weather and up to 2.78 in thunderstorms [2]. The turbulence intensities are recorded to be around 34–38% in thunderstorms [30]. However, the turbulence intensities and gust factors measured over a day are not fully representative, as the flight duration of mini-UAVs is quite short. In very strong and sudden winds, the mini-UAVs might even be blown away without a chance of following the desired flight path. Therefore, for realistic situations, the FMW mini-UAV is designed to dampen high-frequency gusts over a short period of flight time. In order to operate in such conditions, the wing-warping of the miniUAV is required to be controllable and the adaptive washout mechanism should still function to dampen high-frequency gusts. In the first place, in order to validate the robustness of the controller, an artificial gusty environment has to be designed, presenting the atmospheric scenario. FLUENT, a computational fluid dynamics (CFD) software was utilized to design the testing environment. Based on the CFD simulation, when a solid cube with dimensions 60 200 100 mm was placed in a test section with dimensions 780 720 2000 mm and the inlet flow velocity was set to be 7 m/s, a velocity profile, as shown in Fig. 14a, will be obtained. It is shown that at 600 mm away from the solid cube and 390 mm from the ground, as indicated by the white colored sphere, is the best location for mounting the FMW, as the wing is within the turbulence area generated by the vortex shedding. Fig. 14b shows the velocity vector and profiles in three dimensions.
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Open loop (output)
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Fig. 13. Experimental results – Controller performances of the wing-warping via tendon-sheath actuation with given random inputs and without disturbance. The setpoint is represented by the dash lines, while the output is represented by a solid line. (a) Output comparison. (b) Tracking error comparison. (c) Input comparison. (d) Hysteresis comparison.
Fig. 14. CFD simulation configuration and results. (a) Two dimensional velocity profile of the solid obstacle. (b) Velocity vectors of the wind around the obstacle.
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Fig. 15. Vortex structure identified using Q-criterion (Q¼ 10,000). The Q-criterion is colored with velocity magnitude. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 16. Flexible membrane wing in wind tunnel for controller robustness testing.
Table 1 Mean velocity at different locations in the test setup. Velocity (m/s)
y (mm)
300 200 100 0
8.4 0.9 1.3 100
7.1 1.3 1.5 200 x (mm)
8.8 1.5 1.8 300
9.1 2.2 3.7 400
9.0 5.1 4.3 500
7.1 6.6 5.1 600
8.31 1.38 2.08 300 x (mm)
9.0 2.58 3.46 400
7.62 4.85 4.15 500
6.92 6.23 4.85 600
Table 2 Mean velocity at different locations from CFD simulation. Velocity (m/s)
y (mm)
300 200 100 0
8.31 1.04 1.38 100
7.27 1.38 1.63 200
Fig. 15 shows the instantaneous vortex cores generated by the bluff body placed in the vicinity of ground. The second frame shows how the vortex is detached and shed downstream, introducing perturbation at a frequency of approximately 110 Hz to the flow. With the simulation turbulence values being higher than the values found in a standard atmospheric condition, the artificial gusty environment is comparable, or even more severe than the real environment. The blue sphere in the figure indicates the desired location for the FMW during the wind tunnel tests. Upon the completion of the design, in order to test the robustness of the system against gusty conditions, the whole experimental setup was placed inside a designed closed loop wind tunnel. The wind tunnel test section has 780 mm in width, 720 mm in height and 2000 mm in length (due to the space constraint and the symmetrical structure of the mini-UAV, only half of the structure was tested in the wind tunnel, where the flex sensor and tendon-sheath is installed at the tested wing only). Fig. 16 shows the FMW setup secured inside the closed loop wind tunnel test section. Both the gusty and steady flow experiments based on the simulation results were performed for comparison. Prior to the experiment, the velocity profile of the gusty environment inside the wind tunnel was investigated to ensure its agreement to the CFD simulation result. The profile was recorded by taking the average of velocity components measured using Sentry ST732 hot wire anemometer
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Fig. 17. Controller performances of the wing-warping with tendon-sheath actuation under gusty environments, with wind speed of 7 m/s. The setpoint is represented by the dash lines, while the output is represented by a solid line for Fig. 17a. (a) Output comparison. (b) Tracking error. (c) Input comparison. (d) Hysteresis comparison.
(capable of 0–40 m/s velocity measurement range with 0.01 m/s resolution) at 18 different points indicated by black dots in (Fig. 14). The averaged measured velocity profile and the mean velocity from CFD simulation at the respective 18 points are listed in Table 1 and Table 2 for comparison. From the tables, we can see that the generated gusty profile at the wind tunnel exhibits good agreement with that obtained from simulation. The gusts generated were quite severe and, as a result from FMW testing, the whole FMW was oscillating vigorously. To satisfy our curiosity, besides the 7 m/s flow velocity, a 12 m/s flow velocity was also prescribed. Since both demonstrate similar results, only the results for 7 m/s are shown in this paper. Fig. 17 shows the results of the robustness testing. Even under severe gusty airflow conditions, the FMW warping is still robust and controllable. Due to the very high degree of perturbations, the tracking error is slightly higher when compared to the lab bench test. The open loop system under the disturbance is greatly affected and shows little to non-existent accuracy in the wing-warping control. When the feed-forward/feedback control is activated, the performance of the wing-warping is improved significantly, due to the ability of the TSM model that captures its nonlinear dynamic behavior. In general, the results suggest similar conclusion compared to the results from the lab bench test when no gusty disturbance is involved.
6. Conclusion The main objective of utilizing a FMW is to fold the wing around the fuselage for storage and quick deployment, and also
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to benefit from the adaptability of the FMW on gusty disturbance. This paper has demonstrated that the TSM is suitable for wing-warping to achieve roll control, while still allowing the FMW to fold towards the fuselage for storage. The TSM has numerous advantages over other means of actuation, in particular, it does not take up much space and is relatively robust. Nonlinear hysteresis and backlash behaviors of the wing-warping with TSM have been identified, and a robust feed-forward plus feedback control has been designed to control the wing-warping position of the FMW. However, there were a number of difficulties in this experiment. It has been observed that initializing the pre-tension of the tendon-sheath is challenging as it is difficult to obtain the same pretension at every experiment. If the pre-tension is not constant, the model will change and thus rendering the feed-forward control not as effective. The wing-warping control has been shown to work in gusty environments, further proving the robustness. The TSM also enables the adaptive washout to still be effective. The proposed model based controller is offered as a platform to develop the flight control structure for the FMW mini-UAV based on TSM actuation. The future work will be to solve the pre-tension initialization or to apply adaptive control techniques to handle the inconsistent model, and also finally to control the roll rate of the mini-UAV with wing-warping via TSM.
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Contents lists available at ScienceDirect
Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Investigation of a robust tendon-sheath mechanism for flexible membrane wing application in mini-UAV Shian Lee a, Tegoeh Tjahjowidodo a,n, Hsuchew Lee b, Benedict Lai a a School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, North Spine (N3), Singapore 639798, Singapore b Dept. of Mechanical and Manufacturing Engineering, University of Calgary, 2500 University Drive N.W., Calgary, Canada T2N 1N4
a r t i c l e in f o
abstract
Article history: Received 15 March 2016 Received in revised form 8 August 2016 Accepted 11 August 2016
Two inherent issues manifest themselves in flying mini-unmanned aerial vehicles (miniUAV) in the dense area at tropical climate regions, namely disturbances from gusty winds and limited space for deployment tasks. Flexible membrane wing (FMW) UAVs are seen to be potentials to mitigate these problems. FMWs are adaptable to gusty airflow as the wings are able to flex according to the gust load to reduce the effective angle-of-attack, thus, reducing the aerodynamic loads on the wing. On the other hand, the flexible structure is allowing the UAV to fold in a compact package, and later on, the mini-UAV can be deployed instantly from the storage tube, e.g. through a catapult mechanism. This paper discusses the development of an FMW UAV actuated by a tendon-sheath mechanism (TSM). This approach allows the wing to morph to generate a rolling moment, while still allowing the wing to fold. Dynamic characteristics of the mechanism that exhibits the strong nonlinear phenomenon of friction on TSM are modeled and compensated for. A feed-forward controller was implemented based on the identified nonlinear behavior to control the warping position of the wing. The proposed strategy is validated experimentally in a wind tunnel facility by creating a gusty environment that is imitating a realistic gusty condition based upon the results of computational fluid dynamics (CFD) simulation. The results demonstrate a stable and robust wing-warping actuation, even in gusty conditions. Accurate wing-warping can be achieved via the TSM, while also allowing the wings to fold. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Drone UAV CFD Gust Flexible membrane wing Control and identification Tendon-sheath Wing-warping Bouc–Wen
1. Introduction Mini-unmanned aerial vehicles (UAV), also known as drones, can be deployed for various purposes, for example, surveillance missions or payload delivery, therefore sparking an increasing amount of research interest. The mini-UAVs can be separated into two main categories, which are the fixed wings and the rotary wings. The difference in performance between these two is significant [1]. Fixed wings are more suitable for example for border patrol missions as the aircraft will be able to handle longer flight time and carry more payload. The mini-UAV discussed in this paper will solely be a fixed wing. Mini-UAVs are extremely stealthy, and are usually defined as a UAV light and small enough to be carried and operated by a single human operator. However, due to the small weight and moment of inertia, they are also very susceptible to gusts n
Corresponding author. E-mail address: [email protected] (T. Tjahjowidodo).
http://dx.doi.org/10.1016/j.ymssp.2016.08.014 0888-3270/& 2016 Elsevier Ltd. All rights reserved.
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and thus becomes a challenging vehicle to pilot. Gusty environments, especially in tropical climates with frequent thunderstorms [2] pose a huge challenge to these aircraft. Huge control surfaces and fins and an onboard autopilot are the conventional methods to help increase the control authority and stability of the mini-UAVS. Quick deployment and easy storage of the mini-UAV are also critical for a surveillance mission. Usual fixed wing mini-UAVs may take up a lot of space as the wingspan can reach up to more than 1 m. In typical operations, the operator will have to disassemble the mini-UAV for transportation and then assemble it again for deployment. This will expose the operator to dangerous elements, as well as cause a delay which might allow the surveillance target to exit the surveillance area before the mini-UAV is ready. For the purpose of quick deployment and easier storage, the foldable wing is one of the solutions. Research on flexible wings for fighter aircraft already exists [3], but recently there is an increasing number of works being done specifically for mini-UAVs. FMW by [4] has paved a way for the work in this paper. Being able to deploy immediately without any installation or assembly is one of the advantages of the FMW mini-UAV. By folding the wings around the fuselage for storage and transportation, the mini-UAV can also be launched directly from the storage tube, which has been shown by Prioria Robotics Maveric UAV from Florida. Adaptive washout, a phenomenon which occurs in the FMW, allows the FMW mini-UAV to handle higher angle of attack, delay stall response and dampen gust disturbances as well [4]. The ease of repair of the FMW is also a very valuable feature. A damaged wing can be repaired fairly quickly and easily by applying some adhesive on the damaged area. Developed by the University of Florida, the FMW is fabricated by curing layers of prepreg carbon fiber [4]. It is impossible to install a servo and actuate a conventional aileron on the wing as the wing is very thin and flexible, thereby rendering the very little amount of roll control. This is a major drawback of the FMW. In [5], the FMW is warped to increase the roll control authority. Various wing-warping methods have been tried, but most are not suitable as the wing is constrained span-wise and becomes unfoldable. In this research, the application of a tendon-sheath mechanism (TSM)to actuate the FMW is investigated. The inspiration for this research originated from the mechanism of a flexible endoscopic system that uses tendon-sheath as the mechanism for actuation [6,7]. The actuation is delivered by attaching one end of the tendon-sheath to the trailing edge of the FMW, while the other end is connected to a servomotor secured inside the fuselage that will generate the motion. Tension forces can be transmitted via the tendon-sheath to the FMW when the servomotor is activated. This approach still allows the FMW to fold as the tendon-sheath can be routed along the wing while taking only minimal space. Sufficient warping for roll control can be achieved using the TSM and is shown in experiments [8]. However, it is observed that there are some nonlinear behaviors of the TSM, which will deteriorate the wing-warping accuracy without an appropriate control strategy. Flight control systems are required to provide aerodynamic assistance in any aircraft systems. Most of the commercial autopilots implement the PID control algorithm [9]. There are a few works involving adaptive control techniques, such as fuzzy logic controllers [10], adaptive neural network controllers [11], or robust controllers such as LQG/LTR and H∞ controllers [12] as well. Boundary layer control is another effective method of controlling the mini-UAV, especially during low Reynold's number or high angle of attack [13,14]. This paper presents the characterization of a TSM applied for FMW wing-warping application. Nonlinear dynamic behavior that is apparent in the TSM will be identified and modeled as well, which later on is utilized to implement a model based controller to regulate the wing-warping. Subsequently, the performance of the system is validated experimentally in a wind tunnel under a specific gusty environment scenario simulated by a CFD model. The experiments and results of the nonlinear behavior identification of the TSM wing-warping are shown in Section 3. A nonlinear model based on General Bouc–Wen model for hysteresis is introduced for the TSM wing-warping in Section 4. Section 5 presents the controller design and testing for the wing-warping, and also a CFD simulation to design the testing environment. Finally, the conclusion of this paper is drawn in Section 6.
2. Flexible membrane wing characteristics Being foldable is the main characteristic of the FMW. The FMW is specifically designed to fold around the fuselage of the UAV for storage, as illustrated in Fig. 1a. In order to fold downwards around the fuselage while be able to withstand the aerodynamic loads when unfolded, the airfoil is designed to be very thin and also curved in the chord-wise direction, measuring only 1.2 mm in thickness. The FMW is curved along the chord-wise direction at the leading edge, allowing the wing to only fold downwards spanwise while being rigid against the forces from below the wing. This allows the FMW to bear the aerodynamic loads without buckling easily. Fig. 1 shows the FMW at the folded and unfolded stage. Reinforced ribs which start from the mid to the trailing edge support the nylon fabric, which carries most of the aerodynamic loads. Weighing at only 160 g and spanning 1 m with an area of 0.19 square meters, the FMW is very light for its size. During wind tunnel tests, the FMW can generate up to 20 N of lift force without buckling. In addition to the ability to fold, the FMW also has a passive mechanism known as the adaptive washout, which allows the wing to flex and adapt to the gusty airflow [4]. As the wing is also flexible in the chord-wise direction, the wing will flex according to the direction of the gusts, changing the effective angle-of-attack on the wing in favor of the flight response. For example, if the gust perturbs from below, the wing will then flex upwards in the chord-wise direction, decreasing the effective angle-of-attack and also reducing the aerodynamic loads on the wing. The FMW will also flex with the changes in
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Fig. 1. Flexible membrane wing in both folded and normal state. (a) Flexible membrane wing in the folded state. (b) Flexible membrane wing unfolded.
the headwind velocity, increasing or decreasing the lift forces generated and providing a smoother flight and better stall resistance. The FMW will recover to the original airfoil shape, restoring the lift forces when there are no disturbances. This adaptive washout phenomenon helps to provide a smoother flight and allow an easier flight control. 2.1. wing-warping wing-warping, or morphing in other technical writings, are essentially the intentional change of shape of the wing or the airfoil. wing-warping has been practiced since the invention of the airplane by the Wright brothers [15]. In their case, the wings were twisted via cable and pulleys to achieve roll control. Similarly, the FMW mini-UAV can achieve more roll control authority by wing-warping. Roll control can be achieved via wing-warping as it changes the effective angle-of-attack of the FMW by changing the airfoil shape. A higher angle-of-attack will provide a higher lift at the warped wing. wing-warping has been shown to provide ample rolling moment for a FMW mini-UAV in [5,16], which utilizes torque rods in their design. The main drawback is that the FMW becomes unfoldable. The location for warping is critical as it will affect the roll rate and also the lift over drag of the aircraft. High roll rates can be achieved if the wing is warped near the tip, but if done excessively near the wing tip, the wing will experience tip stall, and therefore inducing an adverse roll moment [17]. The degree of warping should, therefore, be limited, and also not be done at the wing tip. In [17], an optimized location of warping was identified by comparing the roll rate and lift over drag of the aircraft. In this paper, a similar location was chosen for this FMW for optimal performance. There is a conflicting requirement regarding wing-warping with regards to the structural stiffness of the wing. To enable warping, the wing has to be flexible enough to allow large deformations, and still have sufficient stiffness to bear the aerodynamic loads. If a high stiffness is chosen, the wing will excel at carrying the aerodynamic loads, but the energy required to warp will be enormous. On the other hand, highly flexible, low stiffness wings will require much less energy to warp, but may not be able to maintain the shape to bear the aerodynamic loads [18]. In this paper, some iteration has been done to fabricate a FMW which can achieve the balanced stiffness for warping, flying and folding. 2.2. Flexible membrane wing actuation methods wing-warping can be achieved via many different approaches. Contributions from [19,20] are crucial to cambered wingwarping. Piezoceramic actuators were used for UAV flight control, and the actuators were found to be effective in both wind tunnel and flight tests [21]. However, it is not applicable in mini-UAVs as a heavy transformer is required to step up the voltage for the piezo-ceramic actuators. Dielectric materials were also proposed to actuate the FMW by securing a dielectric elastomer actuator (DEA) on the FMW for actuation [8]. But, the area of actuation was fully covered by the DEA and the whole setup was very bulky, which will alter the aerodynamic properties of the FMW. In addition, the DEA is very fragile and will break easily, making it a very difficult object to mount to the wing. Very high voltage, to the range of 5–10 V is required to actuate the DEA, which results in a requirement of a heavy step up transformer to be mounted on the mini-UAV. Another investigated method to actuate a FMW is by using the Nylon string. The trailing edge of the wing is tied to a piece of Nylon string, and the other end of the string is connected directly to the servo that is located inside the fuselage of the mini-UAV. As the servo rotates, the Nylon string will tighten and pull the trailing edge of the wing. Although warping can be achieved, this method is not robust, as the Nylon string tends to get tangled when the wing is folded. Besides, based on our observation during preliminary flight tests that we conducted, robustness is also an issue as the Nylon string tends to break easily.
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3. Tendon-sheath mechanism for FMW actuation A schematic drawing of TSM is illustrated in Fig. 2a. A flexible sheath encloses a tendon that will transmit forces from one end to the other. The tendon-sheath actuated wing-warping mechanism is characterized by a relationship between the input and output position. It is known that there are four distinct phases during the transmission, namely releasing to pulling phase (Phase 1), pulling phase (Phase 2), pulling to releasing phase (Phase 3), releasing phase (Phase 4) [7] as illustrated in Fig. 2b. During Phase 1, the servo rotates and pulls the tendon; the input tension increases and therefore increasing the friction force. At this stage, the output position Pout will not change until the friction force has been overcome. In Phase 2, the static friction has been overcome, and Pout changes with the input position Pin. In Phase 3 the servo starts to rotate in the opposite direction, reducing the input tension. However, Pout does not immediately reduce, as the friction force delays the reduction of force from the input to output. The tension of the tendon is reduced, and it will take some time for the FMW to overcome the friction and start springing back into its original position. Phase 4 shows unloading phase where Pout is moving together with Pin. This unique characteristic of the tendon-sheath is attributed to the friction force occurring between the tendon and the sheath that exhibits nonlocal memory behavior [7,22,23]. Similar behavior is also observed in many electromechanical systems, such as in a pneumatic artificial muscle (PAM) [24,25] or piezoelectric driven mechanisms [26]. For the actuation purpose, the tendon has to be pretensioned to maintain consistent characteristics every time the TSM is activated. If it is loose, there will be less or no transmission of force from the input to the output. It is also concluded that the characteristics of the TSM will be identical if the total curvature of the tendon-sheath is kept constant [6]. Therefore, the total curvature of the tendon-sheath has to be kept the same on the ground experiment setup as the mini-UAV. The same amount of force is needed to actuate the TSM for a sharp bend or a gradual bend of the tendon. 3.1. Experiment setup The experiment in this paper is done using the same setup in [8]. In order to obtain the characteristics of the TSM of the mini-UAV, the tendon-sheath is bent and routed along the span of the wing, as illustrated in Figs. 3a and b. The total curvature angle has to be kept at a constant 270°, as this is the design for the UAV. The servomotor will pull the tendon, causing the end to retract and therefore warping the FMW. wing-warping is considered difficult to quantify and measure [5]. Here, an analog 4.5″ flexsensor by Spectra Symbol that is taped securely onto the rib of the FMW at the main warping area with the largest deflection, as illustrated in Fig. 3c. The flexsensor is reasonably flat, which will not perturb the airflow when mounted on top of the wing. Prior to installation, the flexsensor is calibrated for various angles of bending. All the sensors and servo amplifiers are connected to a dSPACE 1104 controller board to allow data collection and control activation. 3.2. Observations from experiments In order to characterize the dynamic property of the system, the wing was actuated for 10 s with various constant frequencies and amplitudes. The resulting output motion is captured through the flexsensor reading. The experiment was carried out with different frequencies and amplitudes, ranging from 0.5 Hz to 3 Hz, and from 5° to 20°, referring to maximum aileron sweep rate specified for many existing aircraft with hinged control surfaces [27]. The general shape of the
Fig. 2. Tendon-sheath and its hysteresis characteristics. (a) Schematic of a tendon-sheath [6]. (b) Relation between position input and position output [8].
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FM W.
Fig. 3. Experimental setup. (a) Total tendon curvature is 270° in the experiment setup. (b) A schematic of the total tendon curvature at the FMW. (c) Flexsensor is mounted on top of the wing.
dynamic behavior of the wing-warping with TSM agrees with the theory shown in Fig. 2b, with the four distinct phases being observed. Fig. 4a shows the relation between wing-warping and tendon-sheath input at a frequency of 3 Hz. It is also found that the change in frequency did not affect the general shape and bias of plots significantly. In addition, a non-local memory hysteresis is observed when multiple loops are prescribed to the system, as shown in Fig. 4b. and c shows a closer look at the loops (more explanation about non-local memory hysteresis is available in [22]). However, when Fig. 4a and the ideal TSM property in Fig. 2b is compared in detail, some slight discrepancy at the transition between Phase 1 and 2 and also the transition between Phase 3 and 4 can be observed, where there is a gradual change in gradient instead of a sharp edge, much like a “hardening” effect. 3.3. “Hardening” phenomenon Initially, it was suspected that the FMW in the chord-wise direction possesses nonlinear properties, as the FMW is made of composite materials, therefore contributing to the “hardening” effect. The geometry of the FMW may also be a cause of the “hardening” effect as well. Therefore, a finite element analysis (FEA) was carried out to investigate the exact cause of the “hardening” effect. The software used for the FEA is ANSYS Workbench. In the analysis, as shown in Figs. 5a to d, the wing trailing edge is pulled at the same direction as the tendon pulling it in the experiment. From the FEA result, as illustrated in Fig. 6, the wing was shown to warp with a slightly decreasing rate as the tendon input is increased (“softening”). Even though it does not agree with the experimental results, it can be shown to be mathematically correct. The minor arc model can be used to explain the results from FEA. Pin (refer to Fig. 2b), which is the displacement of the tendon-sheath, is essentially the change of the distance between the two end points of the arc. Pout, the wing-warping is the central angle of the arc, and will change with Pin if the minor arc length rθ , which is the airfoil camber, is kept constant. Therefore, the relationship between Pin and Pout in Phase 2 and Phase 4 can be modeled by:
l + dl =
sin(θ + dθ ) r, π − (θ + dθ ) sin 2
θ + dθ < π (1)
where l is the arc length (FMW camber, equivalent to the initial tendon length), r is the radius of the arc, and dl is the change of displacement of the tendon-sheath input. The relationship between the warping angle θ and dl is nonlinear, as the rate of θ increases with dl.
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15 degrees deflection
18 16
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14 12 10 8 6 4 2 0 0
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Input frequency 1 Hz & 2 Hz
Input frequency 1 Hz & 2 Hz
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Warping output (deg)
14
10 8 6 4 2
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3
2 0 0
0. 2
0. 4
0. 6
0. 8
Tendon input (mm)
1
1.2
0. 5
0.5 5
0. 6
0.6 5
0.7
Tendon input (mm)
Fig. 4. The hysteresis behaviors of tendon-sheath actuated wing-warping. (a) Hysteresis behaviors with 3 Hz inputs. (b) Hysteresis behaviors with 1 Hz and 2 Hz inputs. (c) A closer zoom at the non-local memory hysteresis loops in Fig. 4b.
As the FEA and minor arc model (Fig. 7) showed that the geometry of the FMW cannot be the cause of the “hardening” phenomenon, another experiment is performed to investigate the cause of the nonlinear curves. A simple direct actuation of the FMW was carried out, which consists of a piece of tendon attached to the trailing edge of the FMW, and the other end secured to the servo motor. This experiment allows a thorough investigation of this phenomenon by eliminating all the hysteresis caused by the friction on TSM and focus only on the wing-warping itself. Fig. 8a shows the setup of the experiment. The wing was given different initial warping angles. For both the low and high initial warping angles cases, consistent results are observed. Fig. 8b shows the wing-warping output vs the direct tendon input (no sheath) for the low pre-tension (with 0° initial warping) and high pre-tension case (20° initial warping). For both cases, the relationship of the output vs input of the wing-warping appears to be quite linear. From the results of this experiment, it can be deduced that the “hardening” nonlinearity is not due to the geometry or material properties of the FMW. Even though the direct tendon actuation (with no sheath) exhibits minimum amount of hysteresis, but this cannot be applied in the FMW as a tendon-only-mechanism does not allow a flexible routing, which means that the tendon has to keep straight in the application. As suggested by [7], the pre-tension of the tendon-sheath will affect the general hysteresis behavior, especially in the transition from Phase 1–2 and Phase 3–4. Subsequently, the TSM is installed back to check for the effects of pre-tension. Two different pre-tension levels are prescribed to actuate the FMW, and the hysteresis behavior was recorded. The hysteresis behavior difference between low pre-tensioned and high pre-tensioned tendon-sheath wing-warping is observable in Fig. 8c. In the low pre-tension tendon-sheath, the hysteresis behavior exhibits the arched (nonlinear) line in Phases 2 and 4. There are no definite, sharp corners during the transition from Phase 1–2 (and from 3 to 4). When the tendon-sheath is given very high amounts of pre-tension, the nonlinear “hardening” effect (arched curve degree) lessens. This indicates that the phenomenon in Phases 2 and 4 is, indeed, caused by insufficient pre-tension. Although a linear relationship in Phase
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Fig. 5. Finite element analysis of the wing-warping. (a) Finite element analysis of the wing, viewed from the side. (b) FMW is simulated with a deflection at the trailing edge. (c) Another angle of the FMW during FEA, viewed from the back. (d) Another angle of the FMW during FEA, with a deflection at the trailing edge.
Wing warping simulation in FEA
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Wing warping angle (deg)
17
16
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12 0
0.5
1
1.5
2
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3
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Trailing edge deflection (mm) Fig. 6. Warping angles vs trailing edge deflection in the FEA.
2 and Phase 4 is desirable for the ease in the modeling and control tasks, it is not achievable in this FMW warping case. As the pre-tension is increased, the FMW will start to warp, affecting the airfoil shape and aerodynamic properties. Therefore, the pre-tension in the tendon-sheath for FMW warping must be kept low enough such that the FMW does not have any initial warping angles.
4. Hysteresis modeling Due to the large nonlinearity in the TSM, a nonlinear controller is required to accurately control the FMW warping. As such, a model of the hysteresis behavior will be needed. In order to capture the asymmetric hysteresis on the wing-warping actuation, a generalized Bouc–Wen model by Song et al. [28] is referred. Some modifications are introduced to better capture the nonlinearity of Phases 2 and 4 as presented by Do et al [6,7,29]. The model is expressed as:
θ (x)(t ) = α1x2 + α2x + α3 + αzz z ̇ = ẋ[A − |z|n Ψ (x, ẋ, z )] Ψ (x, ẋ, z ) = βϕT
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Fig. 7. Illustration of the arc model.
where
β and ϕ are matrices given as: β = [β1β2β3β4 β5β6] ϕ = [sgn(xż )sgn(xẋ)sgn(xz )sgn(ẋ)sgn(z )sgn(x)]
A total of 12 parameters were first estimated using the Genetic Algorithm (GA), where the results are subsequently used as initial values to optimize the parameters further by using the Nelder–Mead simplex algorithm (detailed discussion is presented in [8]). With respect to the arched curvy line in Phase 2 and Phase 4, a quadratic function was appended to the model (Fig. 4a) to capture the increasing rate curve (“hardening”). For identification purpose, random tendon-sheath position signals were prescribed to the system on the input side, while the wing-warping position output is recorded. Fig. 9 presents the hysteresis plot as a result of the identification procedure. Fig. 10a illustrates the testing input signals, together with the results of the model illustrated in Fig. 10b with the following parameters:
β = ⎡⎣ 19.8351 − 8.6135 0.8325 − 3.1266 10.6984 − 18.5⎤⎦ A = 3.9953 n = 3.1179 α = ⎡⎣ −0.0205 0.7120 0.7958⎤⎦ αz = 0.5369
(2)
with the RMS error being 0.26°. With a severe nonlinear behavior as shown in the experiments, a controller is required for precise wing-warping position control. Without accurate wing-warping control, the mini-UAV will have unreliable roll control, therefore jeopardizing the safety and flight qualities. By utilizing the parameters identified from the experiments, a modified General Bouc–Wen model has been constructed and used for controller design.
5. Controller design and testing In order to compensate for the nonlinearity on the TSM, the identified model obtained in Section 4 is utilized for control purpose. A combined feed-forward/feedback controller is designed, evaluated and implemented. Subsequently, the controller is then tested on the experiment platform after being validated to be effective. With a severe nonlinear dynamics attributed to the TSM as observed in experiments, a dedicated controller is required for precise wing-warping position regulation. By utilizing the model parameters identified from the experiments, a modified General Bouc–Wen model is utilized for control purpose. Here, a combined feed-forward and PID feedback controller are designed, evaluated and implemented. After it is shown to be effective, the controller is then tested on the experiment platform. 5.1. Controller design and simulation The model is implemented in the feed-forward loop as shown in Fig. 11. The reference warping input is fed to the model to compensate for the nonlinearity of the TSM. In order to demonstrate the effectiveness of the proposed control strategy,
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Fig. 8. Hysteresis behaviors of the flexsensor and wing. (a) Direct actuation of the FMW.(b) Input-output relationship of the wing-warping only with the tendon (no sheath) with different pre-tensions. (c) Hysteresis of the wing-warping with tendon-sheath at different pre-tensions.
the system is simulated with three different control schemes, i.e. open loop, PI feedback only and feed-forward/feedback. The gains for the PI were optimized for the control strategies, with Kp ¼7 and Ki ¼1 via the Ziegler–Nichols method. The simulation results are presented in Fig. 12, where the system was simulated by prescribing filtered random input signals with 1 Hz cutoff frequency to the input side of the TSM. As observed from the figure, the PID feedback controller is not as accurate as the combined feed-forward/feedback controller. When some disturbance is present on the system, the combined feed-forward/feedback controller still outperforms. The last simulation was taken by introducing a white noise signal on the TSM model to imitate disturbance on the system. In particular, Fig. 12a and c illustrate the effectiveness of the model-based controller that manage to linearize the system. 5.2. Controller implementation The controller is subsequently tested in a lab bench, by nesting the model into the dSPACE 1104 controller board. The FMW was actuated by a filtered random signal with 1 Hz cutoff frequency and amplitude of 4° without disturbance. The results are illustrated in Fig. 13. The RMS error for the open loop system, PID only system and the feed-forward/feedback system is 1.727°, 2.04°, and 0.285° respectively. The combined feed-forward/feedback controller exhibits superior performance compared to the PID feedback system, with an absolute difference of 1.755° in RMS error. However, the difference in
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Modeling of wing warping vs tendon-sheath (random input)
12 11
Warping output (deg)
10 9 8 7 6 5 Model Experiment
4 3 2
3
4
5
6
7
8
Tendon input (mm) Fig. 9. Modeling of wing-warping with tendon-sheath using random inputs, with parameters (2). This diagram is plotted as wing-warping position vs. tendon sheath position.
Experimental data Output vs time
8
Input vs time
12
7
Tendon (mm)
Warping (deg)
10 8 6
6
5
4
4
3 Model Experiment
2 0
5
10
Time (s)
15
20
2 0
5
10
15
20
Time (s)
Fig. 10. Solid line represents the experimental data, while the dashed line represents the data from the model. (a) The input for the model (wing-warping). (b) The output of the model (tendon-sheath position).
Fig. 11. Block diagram of the tendon-sheath actuated FMW warping control.
performance between the PID only system and the open loop system is insignificant, with an absolute difference of only 0.313° in the RMS error. In this experiment, similar gains from the simulation were used for the PI controller, i.e. Kp ¼7 and Ki ¼1. Higher gains will cause unstable oscillations in the system.
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15 10 5 0
15 10 5 0
Open loop (Output)
12 12
0
2
4
6
8
10
PID Feedback only
0
2
4
6
8
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Warping output (deg)
Warping (deg)
15 10 5 0
12
11 10
10
10
9 8
8 8 7
6
6
6
Feed-forward + feedback
4
4 5
2
0
2
4
6
8
4 0
10
10
20
2 0
10
20
0
10
20
0
10
20
Warping input (deg)
Time (s)
15 10 5 0 15 10 5 0
Open loop (Output)
0
2
4
6
8
10
PID Feedback only
0
2
4
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8
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Feed-forward + feedback
0
2
4
6
Time (s)
8
10
Warping output (deg)
Warping (deg)
15 10 5 0
12
12
12
10
10
10
8
8
8
6
6
6
4
4
4
2
2 0
10
20
2 0
10
20
Warping input (deg)
Fig. 12. Simulation of the controller of the wing-warping via tendon-sheath actuation with given random inputs. The setpoint is represented by the dash lines, while the output is represented by a solid line.(a) Output comparison with disturbance. (b) Output comparison without disturbance. (c) Hysteresis comparison without disturbance. They are open loop, feedback only, feed-forward/feedback respectively. (d) Hysteresis comparison with disturbance. They are open loop, feedback only, feed-forward/feedback respectively.
5.3. Robustness against gusty environment As the atmospheric conditions in tropical areas tend to be gusty, the controller is required to be robust against gust disturbances. Therefore, the robustness of the system in a gusty environment has to be validated. The FMW mini-UAV is designed to dampen high-frequency gusts and to fly in windy conditions, such as over the tropical oceans for surveillance missions. The winds in a tropical climate can be quite gusty, with gust factors reaching up to 2.27 in non-thunderstorm weather and up to 2.78 in thunderstorms [2]. The turbulence intensities are recorded to be around 34–38% in thunderstorms [30]. However, the turbulence intensities and gust factors measured over a day are not fully representative, as the flight duration of mini-UAVs is quite short. In very strong and sudden winds, the mini-UAVs might even be blown away without a chance of following the desired flight path. Therefore, for realistic situations, the FMW mini-UAV is designed to dampen high-frequency gusts over a short period of flight time. In order to operate in such conditions, the wing-warping of the miniUAV is required to be controllable and the adaptive washout mechanism should still function to dampen high-frequency gusts. In the first place, in order to validate the robustness of the controller, an artificial gusty environment has to be designed, presenting the atmospheric scenario. FLUENT, a computational fluid dynamics (CFD) software was utilized to design the testing environment. Based on the CFD simulation, when a solid cube with dimensions 60 200 100 mm was placed in a test section with dimensions 780 720 2000 mm and the inlet flow velocity was set to be 7 m/s, a velocity profile, as shown in Fig. 14a, will be obtained. It is shown that at 600 mm away from the solid cube and 390 mm from the ground, as indicated by the white colored sphere, is the best location for mounting the FMW, as the wing is within the turbulence area generated by the vortex shedding. Fig. 14b shows the velocity vector and profiles in three dimensions.
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Open loop (output)
Warping output
Open loop (Tracking error)
5
15 10 5
0 -5 0
2
4
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10
0
PID Feedback only
2
4
6
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PID Feedback only
5 0
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Feed-forward + feedback
5
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2
4
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0
2
4
Time (s)
6
8
Time (s)
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Open loop
14
Feed-forward/feedback
14
Closed loop
Warping output (deg)
feed-forward/feedback
6
4
2 Open loop
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Warping output (deg)
8
Control input (mm)
263
10 8 6 4
12 10 8 6 4
feedback
Feedback
0
2 0
2
4
6
Time (s)
8
10
2 4
8
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Warping input (deg)
4
8
12
Warping input (deg)
Fig. 13. Experimental results – Controller performances of the wing-warping via tendon-sheath actuation with given random inputs and without disturbance. The setpoint is represented by the dash lines, while the output is represented by a solid line. (a) Output comparison. (b) Tracking error comparison. (c) Input comparison. (d) Hysteresis comparison.
Fig. 14. CFD simulation configuration and results. (a) Two dimensional velocity profile of the solid obstacle. (b) Velocity vectors of the wind around the obstacle.
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Fig. 15. Vortex structure identified using Q-criterion (Q¼ 10,000). The Q-criterion is colored with velocity magnitude. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 16. Flexible membrane wing in wind tunnel for controller robustness testing.
Table 1 Mean velocity at different locations in the test setup. Velocity (m/s)
y (mm)
300 200 100 0
8.4 0.9 1.3 100
7.1 1.3 1.5 200 x (mm)
8.8 1.5 1.8 300
9.1 2.2 3.7 400
9.0 5.1 4.3 500
7.1 6.6 5.1 600
8.31 1.38 2.08 300 x (mm)
9.0 2.58 3.46 400
7.62 4.85 4.15 500
6.92 6.23 4.85 600
Table 2 Mean velocity at different locations from CFD simulation. Velocity (m/s)
y (mm)
300 200 100 0
8.31 1.04 1.38 100
7.27 1.38 1.63 200
Fig. 15 shows the instantaneous vortex cores generated by the bluff body placed in the vicinity of ground. The second frame shows how the vortex is detached and shed downstream, introducing perturbation at a frequency of approximately 110 Hz to the flow. With the simulation turbulence values being higher than the values found in a standard atmospheric condition, the artificial gusty environment is comparable, or even more severe than the real environment. The blue sphere in the figure indicates the desired location for the FMW during the wind tunnel tests. Upon the completion of the design, in order to test the robustness of the system against gusty conditions, the whole experimental setup was placed inside a designed closed loop wind tunnel. The wind tunnel test section has 780 mm in width, 720 mm in height and 2000 mm in length (due to the space constraint and the symmetrical structure of the mini-UAV, only half of the structure was tested in the wind tunnel, where the flex sensor and tendon-sheath is installed at the tested wing only). Fig. 16 shows the FMW setup secured inside the closed loop wind tunnel test section. Both the gusty and steady flow experiments based on the simulation results were performed for comparison. Prior to the experiment, the velocity profile of the gusty environment inside the wind tunnel was investigated to ensure its agreement to the CFD simulation result. The profile was recorded by taking the average of velocity components measured using Sentry ST732 hot wire anemometer
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Error (deg)
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Warping output (deg)
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Warping input (deg)
Fig. 17. Controller performances of the wing-warping with tendon-sheath actuation under gusty environments, with wind speed of 7 m/s. The setpoint is represented by the dash lines, while the output is represented by a solid line for Fig. 17a. (a) Output comparison. (b) Tracking error. (c) Input comparison. (d) Hysteresis comparison.
(capable of 0–40 m/s velocity measurement range with 0.01 m/s resolution) at 18 different points indicated by black dots in (Fig. 14). The averaged measured velocity profile and the mean velocity from CFD simulation at the respective 18 points are listed in Table 1 and Table 2 for comparison. From the tables, we can see that the generated gusty profile at the wind tunnel exhibits good agreement with that obtained from simulation. The gusts generated were quite severe and, as a result from FMW testing, the whole FMW was oscillating vigorously. To satisfy our curiosity, besides the 7 m/s flow velocity, a 12 m/s flow velocity was also prescribed. Since both demonstrate similar results, only the results for 7 m/s are shown in this paper. Fig. 17 shows the results of the robustness testing. Even under severe gusty airflow conditions, the FMW warping is still robust and controllable. Due to the very high degree of perturbations, the tracking error is slightly higher when compared to the lab bench test. The open loop system under the disturbance is greatly affected and shows little to non-existent accuracy in the wing-warping control. When the feed-forward/feedback control is activated, the performance of the wing-warping is improved significantly, due to the ability of the TSM model that captures its nonlinear dynamic behavior. In general, the results suggest similar conclusion compared to the results from the lab bench test when no gusty disturbance is involved.
6. Conclusion The main objective of utilizing a FMW is to fold the wing around the fuselage for storage and quick deployment, and also
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to benefit from the adaptability of the FMW on gusty disturbance. This paper has demonstrated that the TSM is suitable for wing-warping to achieve roll control, while still allowing the FMW to fold towards the fuselage for storage. The TSM has numerous advantages over other means of actuation, in particular, it does not take up much space and is relatively robust. Nonlinear hysteresis and backlash behaviors of the wing-warping with TSM have been identified, and a robust feed-forward plus feedback control has been designed to control the wing-warping position of the FMW. However, there were a number of difficulties in this experiment. It has been observed that initializing the pre-tension of the tendon-sheath is challenging as it is difficult to obtain the same pretension at every experiment. If the pre-tension is not constant, the model will change and thus rendering the feed-forward control not as effective. The wing-warping control has been shown to work in gusty environments, further proving the robustness. The TSM also enables the adaptive washout to still be effective. The proposed model based controller is offered as a platform to develop the flight control structure for the FMW mini-UAV based on TSM actuation. The future work will be to solve the pre-tension initialization or to apply adaptive control techniques to handle the inconsistent model, and also finally to control the roll rate of the mini-UAV with wing-warping via TSM.
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