- Email: [email protected]
Throttle actuator control system for vehicle traction control
Mechatronics 9 (1999) 477±495
Throttle actuator control system for vehicle traction control Jae-Bok Song*, Kyung-Seok Byun Department of Mechanical Engineering, Korea University, 5-Ka Anam-Dong Sungbuk-Ku, Seoul, 136-701, South Korea Received 23 July 1998; accepted 17 December 1998
Abstract Accurate and quick positioning of the throttle valve in a gasoline engine is required to implement various systems such as traction control systems (TCS), cruise control systems and drive-by-wire systems. In this research, the throttle actuator system for TCS application was developed. Unlike other systems, this system consists of only one throttle body to obtain small volume and low manufacturing cost, and uses a DC servo motor for quick and accurate responses. In order to drive the DC motor, a PWM signal generator and PWM ampli®er were built and interfaced to the motor and controller. This paper also presents the position control logic of the throttle actuator with the TDC (time delay control) scheme with a variable reference model. By varying the reference model based on the size of the step changes in the target throttle angle, the TDC scheme yields good transient response characteristics in that both overshoot prevention and a quick response time are achieved. Actual vehicle tests with this developed system incorporated with the TCS system show that it satis®es all the conditions required for the TCS operation. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction The throttle body mounted in a gasoline engine is used to control engine power
* Corresponding author. Tel.: +82-2-3290-3363; fax: +82-2-928-9769. E-mail address: [email protected] (J.B. Song) 0957-4158/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 7 - 4 1 5 8 ( 9 9 ) 0 0 0 1 0 - 0
478
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
by regulating the amount of air in¯ow into the engine. In normal driving situations, the throttle valve of a throttle body connected to the accelerator pedal is controlled by a driver through the mechanical linkage. However, recent advances in control and electronics technology have enabled the throttle valve to be operated by electric actuators and control systems. Some typical applications include traction control systems (TCS), cruise control systems and drive-by-wire (DBW) systems. In all of the systems listed above, the throttle valve needs to be operated by electronic control systems rather than by manual operation of the driver. Although all the above applications require position control of the throttle valve, this research is focused mainly on TCS application. TCS, one of many vehicle active safety systems, improves the vehicle acceleration performance and stability, particularly on low-friction roads. When the vehicle starts o on lowfriction roads such as snowy or icy roads, excessive slip between the driving wheels and the road usually occurs and thus makes the vehicle's forward movement dicult. Since this slip is caused by the excessive opening of the
Fig. 1. Appearance of throttle actuator.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
479
throttle valve by the driver (thus excessive engine power), properly closing o the throttle valve in opposition to the driver's intention greatly helps the vehicle to regain its acceleration capability. In this situation, it is very important to control the throttle actuator quickly and accurately to satisfy the requirement of the throttle movement determined by the TCS controller. Capability of accurate and quick positioning of the throttle valve is also required for cruise control systems and DBW (drive-by-wire) systems in which the traditional mechanical linkage between the accelerator pedal and throttle valve will be replaced by signal wires in the near future. This research is divided into two parts. One is to design the mechanism and structure of the throttle actuator system for the TCS and the other is to develop the control logic capable of accurate and quick positioning of the throttle valve. Some throttle actuator systems use a vacuum actuator to operate the throttle valve [1]. While this has the advantage of using the back pressure which can easily be obtained from the intake manifold, the response is not quick enough to successfully satisfy the TCS controller. Other throttle bodies consist of two throttle valves for the TCS purpose; a main throttle valve linked to the accelerator pedal by a mechanical cable, and a sub-throttle valve driven by separate actuators such as DC or step motors. These systems are simple in structure since an electric throttle actuator system is separated from the main throttle body, but the manufacturing cost and the volume of the system increase due to the twin body structure. The throttle actuator system developed in this research has only one throttle valve, but provides both functions of the twin-throttle body systems mentioned above (see Fig. 1). That is, it is used as a normal throttle valve linked to the accelerator pedal when the TCS system is not activated, but is driven by the DC servo motor when the throttle actuation diers from the driver's intention with the TCS function activated. Advantages of this type are small volume and low manufacturing cost (compared with the throttle bodies with two valves) and quick response characteristics (compared with some types which use vacuum actuators instead of electric motors). With this type of throttle structure, however, precise positioning of the throttle valve for engine management is dicult to achieve for several reasons. One reason is the constantly varying load torque imposed on the throttle valve by the traction spring depending on the throttle valve position. Another reason is the friction of the four-bar linkage and the valve axis, which cannot be reduced by mechanical improvement due to consideration of manufacturing cost. Therefore, this research also aims at developing a simple but accurate position control system for this type of throttle actuator. To this end, some controllers are tested. Although a PID controller showed good performance, it was dicult to tune the gains for a wide operating range. Therefore, the time delay control (TDC) scheme is adopted for the main control scheme. Since the throttle valve movement contains both large and small changes in the set-point, even well-tuned TDC controllers cannot produce the best performance for the entire operating conditions. To cope with this problem, the
480
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
variable reference model approach was suggested in this research. This idea is simple yet yields good control performance for all operating conditions. With this suggested control system, various tests including actual vehicle tests on the proving ground have been conducted. The test results show that the developed throttle actuator system incorporated with the time delay controller with variable reference model yields good performance for practical use. Chapter 2 introduces the structure and functions of the throttle actuator systems developed in this research and PWM servo driver built for this actuator. Chapter 3 explains the time control law and proposes a new idea called the variable reference model to improve transient response characteristics of the position control system. Some simulation and experimental results are presented in Chapter 4. 2. Structure and modeling of throttle actuator system 2.1. Structure of throttle actuator Fig. 1(a) shows the structure of the engine throttle actuator system developed in this research. As mentioned earlier, this system consists of only one throttle body while most throttle bodies for the TCS purpose consist of two throttle valves. During normal operation, the throttle valve rotates according to the driver's intention through a mechanical cable connected to the accelerator pedal. When the TCS function is activated, the throttle valve rotates by means of the throttle actuator system (in this case, DC servo motor) according to the command from the TCS controller, independent of the driver's intention. The simple four-bar
Fig. 2. Operation of throttle actuator system and de®nition of throttle angle.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
481
linkage in Fig. 1(b) is used to transmit the rotation of the motor to that of the throttle valve. Fig. 2 de®nes the throttle angle and represents the operation of the throttle actuator. As shown in Fig. 1, the right side of the throttle valve is directly linked to the accelerator pedal and is allowed to rotate in the range of the fully-closed throttle (y=08) when the accelerator pedal is not pressed down on at all to the wide open throttle (y=908) when it is fully pressed down on. Two mechanical stoppers at y=08 and 908 prevent the rotation beyond this allowable range. Suppose that the driver sets the throttle angle to ydriver by stepping on the accelerator pedal, thus activating the TCS, which indicates that the excessively open throttle valve has to be properly closed to reduce engine power. Then, the throttle valve positions are limited to the throttle angle set by the driver and the fully-closed position, but within these limits the throttle valve can freely rotate by the throttle actuator system to the angle commanded by the TCS controller. When the TCS function is not further needed, the motor is deenergized and the traction spring returns the throttle valve to the throttle angle set by the driver. Note that the traction spring always tends to force the throttle valve to rotate toward the throttle position set by the driver (i.e., in the direction of the increasing throttle angle). Hence, the main purpose of the throttle actuator system is to position the throttle valve to the opening required by the TCS controller. In typical TCS applications, both large but quick rotation and ®ne rotation of the throttle angle are required. When the TCS controller decides the need for the TCS operation, it attempts to quickly move the throttle valve, which is usually almost wide open at this situation, close to the fully-closed position. Once the throttle valve is almost closed, the controller gradually increases the throttle angle, but even in this case ®ne positioning to the commanded angle is important. There are some diculties in position control of the throttle actuator system. One diculty is caused by the load torque imposed by the traction spring. The traction spring assists the motion of the throttle valve in the increasing throttle angle, while it impedes its motion in the decreasing throttle angle. When position control of the throttle valve is performed, therefore, the required size of the motor torque greatly varies depending on the direction of motor rotation even for the same change in the throttle angle. In addition, the size of the torque introduced by the traction spring varies depending on the throttle angle. In summary, the direction and size of the load torque constantly vary during the position control action. Another diculty is associated with the overshoot of the response. Around the extreme positions of the throttle valve (i.e., at the throttle angles of 0 and 908), the overshoot causes the throttle valve to collide with the mechanical stopper, thus resulting in noise and possible damage to the system. Thus, the overshoot should be avoided even when quick response is required for good control performance. A third problem in position control is friction occurring at the valve and motor axes. Use of bearings in the rotating parts can resolve most of the friction problems, but it raises manufacturing cost. Therefore, this problem would be better overcome by use of the proper feedback control technique.
482
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
2.2. Structure of throttle actuator control system The schematic diagram for the throttle actuator control system is illustrated in Fig. 3. For vehicle implementation, the system is built using relatively cheap components. In order to drive a DC servo motor, a PWM ampli®er based on Hbridge con®guration was built and interfaced to the motor [2]. The PC-based control system was ®rst developed and then the microprocessor 80196KC was employed for actual implementation. The angular position of the throttle angle is measured using a throttle position sensor (TPS) that is an integral part of most throttle bodies. In this system the TPS is based on the potentiometer. The TCS ECU (Electronic Control Unit), which is a separate microprocessor, collects signals from various sensors (e.g., wheel speed sensors, engine RPM sensor) and determines the throttle angle required for the best traction capability. This reference throttle angle signal is sent to the 80196KC microprocessor, which is utilized for the control of the throttle actuator. 2.3. Modeling of throttle actuator system Modeling of the throttle actuator system is required for the simulation and design of a position control system. Fig. 4 illustrates the throttle actuator system using the SIMULINK package [3]. The model is divided into two parts; DC servo motor part and mechanism part which consists of the traction spring and four-bar
Fig. 3. Schematic diagram of throttle actuator control system.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
483
Fig. 4. Modeling of throttle actuator system based on Simulink package.
linkage. Since modeling of the DC motor is treated in much literature, only modeling of the mechanism will be considered here. The mechanical stoppers indicate that the throttle valve can rotate only between the fully-closed position (y=08) and the position set by the accelerator pedal. The four-bar linkage connecting the motor axis to the throttle valve axis is simply modeled as a proportional constant Kl. y s Kl ym s
1
where ym(s ) denotes the angular position of the motor. The load torque imposed by the traction spring is represented by TL s Ks1 y s Ks2
2
where Ks1 represents the spring constant of the traction spring and Ks2 the spring torque oset which accounts for the spring torque applied to the throttle valve at the throttle angle of 08. From the block diagram of Fig. 4, the motor position ym(s ) is obtained by ym
1 Tm ÿ TL s Js f
3
and the motor torque Tm is given by Tm
Kt Va ÿ Eb Kt Ka U ÿ Kb sym Ra La s Ra
4
where Va and Eb are the armature voltage and back emf, La and Ra the inductance and resistance of the armature, Kt and Kb the torque constant and back emf constant and Ka the ampli®er gain, respectively. Note that U(s ) denotes the control signal computed by the position controller. Since the inductance La is usually small in the DC motor and is negligible, the following is obtained by substituting Eqs. (1), (2) and (4) into Eq. (3).
484
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
J 2 b Kt Kb Kt Ka ys U s ys Ks1 y Ks2 Kl Kl Kl Ra Ra Taking the inverse Laplace transform of Eq. (5) gives y t ÿ 1 b Kt Kb y_ t ÿ Kl Ks1 y t ÿ Kl Ks2 Ka Kt Kl u t Ra J J JRa J
5
6
De®ning the state variables as the throttle angle x1(t )=y(t ) and its derivative x 2 t y_ t, Eq. (6) can be converted into the state space representation 3 2 0 1 7 x1 x_ 1 6 4 Kl Ks1 1 Kt Kb 5 x2 x_ 2 ÿ b ÿ J Ra J 7 9 9 8 8 0 0 = = < < Ka Kt Kl u Kl Ks2 ; ; :ÿ : JRa J
3. Time delay control law with variable reference model As mentioned earlier, some requirements exist for successful control of the throttle actuator system. Though some advanced control methods may satisfy the
Fig. 5. Experimental results showing throttle angle responses with PID controller tuned to angles (a) 78, and (b) 778.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
485
above requirements, simple but robust algorithms are desirable for actual vehicle implementation. First, a PID controller was tested. Fig. 5 illustrates two experimental results with the PID controller whose gains are tuned to 7 and 778, respectively. The well-tuned PID control system for some operating point yields the satisfactory performance around that operating range, but it was found that dierent sets of PID gains should be used for dierent operating ranges to achieve optimal performance. Therefore, there were diculties in ®nding many sets of PID gains to cover the entire operating conditions [4]. Another diculty was that the mechanical characteristics of the throttle actuator units dier from unit to unit since they cannot be built accurately due to cost limitations. For example, the traction spring constants and the amount of friction involved in the four-bar linkage and the valve axis sometimes ¯uctuate signi®cantly even if all of them meet the manufacturing tolerance. Furthermore, with long-term use, the throttle actuator parameters tend to vary, which may necessitate new gain tuning. Thus, a more robust control algorithm is required to cope with these diculties. To this end, the time delay control (TDC) scheme was adopted as a basic control algorithm in this development because this scheme is both simple to implement in the microprocessor and accurate enough to ensure the control performance in the presence of disturbance. In addition, the tuning process is relatively simple and only one set of design parameters is needed in covering the entire operating range. Even with the simple TDC scheme, however, it is not easy to yield good transient responses for both large and small changes in target throttle angles. In this research, therefore, some heuristic way called a variable reference model is suggested. In what follows, the TDC scheme with variable reference model will be brie¯y explained. 3.1. TDC law A TDC (Time Delay Control) scheme was suggested as an eective control technique for nonlinear time-varying systems with uncertain dynamics and/or unpredictable disturbances. Basically, it cancels the undesired dynamics and disturbances and substitutes it with desired dynamics. The detailed derivation of the control law can be found in [5,6], but a brief explanation will be given here. Consider a nonlinear time-varying plant in the state-space model xÇ t f x t,t h x t,t B x t,tu t d t
8
where x(t ) represents the state vector (n1), u(t ) the control vector (r1), d(t ) the unpredicted disturbance vector. Dynamics of the plant is divided into the known dynamics vector f(x, t ) and the unknown dynamics vector h(x, t ). Also, the control matrix B(x, t ) is assumed temporarily to be a known matrix. Consider the reference model represented by the following nonlinear timevarying system: xÇ m t F xm t,r t
9
486
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
where xm(t ) and r(t ) denote the state vector of the reference model and the reference input vector, respectively. This reference model yields the ideal state vector that the plant state vector should follow. De®ning the error vector e t xm t ÿ x t, the error dynamics can be written by eÇ t Ae e t
10
where Ae is the error system matrix. When Ae is selected so that all eigenvalues are placed in the left-half s-plane, the error dynamics becomes asymptotically stable. After substitution of the relation xÇ t xÇ m t ÿ Ae e t from Eq. (10) into Eq. (8), the following equation is obtained B x t,tu t ÿf x t,t ÿ h x t,t ÿ d t xÇ m t ÿ Ae e t
11
Since h(x, t )+d(t ) is an unknown function, the control eort u(t ) cannot be à obtained from Eq. (11). Thus, the estimate of this function hà x,t d t must be found. Assuming that time delay L is suciently small and h+d is a continuous function, h(x, t )+d(t ) at time t is close to h x,t ÿ L d t ÿ L at time tÿL. Hence, the estimate of h+d can be described by à hà x t,t d t1h x t ÿ L,t ÿ L d t ÿ L xÇ t ÿ L ÿ f x t ÿ L,t ÿ L ÿ B x t ÿ L,t ÿ Lu t ÿ L
12
If B(x, t ) is unknown or uncertain, then its estimate BÃ(t ) is used. After substituting Eq. (12) into Eq. (11), the following TDC control law is obtained. u t BÃ tfÿf x t,t ÿ xÇ t ÿ L f x t ÿ L,t ÿ L BÃ t ÿ Lu t ÿ L
xÇ m t ÿ Ae e tg
13
where B+ denotes the pseudo-inverse matrix B+=(BTB)ÿ1BT, which happens to be an inverse matrix when the number of control input (r ) is equal to the number of Equations (n ). This control law can be easily implemented in digital control system by taking the time delay L as an integer multiple of the sampling period T s. 3.2. TDC for throttle actuator control system The TDC requires the reference model which is of the second-order dynamics in this case, which is characterized by a natural frequency (on) and a damping ratio (z ). The second-order reference model is given by 0 1 0 x m1 t x_ m1 t r t 14 ÿo 2n ÿ2zo n o 2n x_ m2 t x m2 t
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
487
where r(t ) is the reference input computed from the TCS controller, xm1(t ) and xm2(t ) are the reference throttle angle and its angular velocity, respectively. On the other hand, if the error is de®ned as e t xm t ÿ x t, then the error dynamics is described by eÇ t Ae e t, where Ae
0 ÿo 2ne
1 ÿ2ze o ne
15
Also, the estimate of the control matrix is given by ^T 0 ÃB t f0 bg
Ka KT Kl JRa
T
16
and thus the design parameter bà can be estimated with relative ease. Then, the TDC law (13) can be written by 1 ^ ÿ L x_ m2 t o 2 x m1 t ÿ x 1 t u t fÿx_ 2 t ÿ L bu t ne ^ b 2ze o ne x m2 t ÿ x 2 tg
17
where x1(t ) and x2(t ) are the throttle angle and its angular velocity, respectively. Note that the time L is usually chosen as the sampling period for convenience. 3.3. TDC law with variable reference model Quickness and accuracy in response are required for the position control of the throttle actuator system like other servo systems. Also, as the throttle valve is limited by the mechanical stoppers, overshoot around the limits causes collisions, leading to noise and possible danger; therefore, overshoot prevention is an important criterion for controller design. Because this kind of overshoot usually occurs when the system attempts to quickly track the large commanded change in the reference input, it can be prevented by making the response slow. However, if the control system is made to respond slowly, then another problem arises that the slow response is also obtained even for the small change in the reference input where overshoot is of no concern. Therefore, if the reference model is properly varied depending on the size of the change in the reference input, then it is possible to obtain both overshoot prevention and quick response. Considering the above observations, a simple yet eective way to vary the reference model in the design of a time delay controller is proposed in this research. The reference input r(t ) in Eq. (14) is always given in the form of step functions from the TCS controller every sampling instant. The reference state vector xm(t ) which the actual plant output x(t ) should follow depends on the natural frequency (on) and damping ratio (z ) in the case of the second-order reference model. For overshoot prevention and mathematical convenience, critical damping (i.e., z=1) is assumed here, which is the minimum requirement to
488
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
prevent actual overshoot. Therefore, the reference model is now characterized by only one parameter, the natural frequency. Given the same reference input r(t ), the larger the value of on, the faster the reference model. The fast reference model represents the reference state xm(t ) attempting to quickly track the reference inputs which change in a stepwise fashion, and thus in the extreme end xm(t ) is quite similar to r(t ). To elaborate this point, consider the response characteristics of TDC-based position control system with the fast and slow reference models. Fig. 6 illustrates the throttle angle response to randomly varying targets with on ®xed at 200 rad/s. For small step changes in the target throttle angle, quick responses are observed (see portion B), but for large step changes large overshoots (see portion A) occur. On the other hand, Fig. 7 shows the throttle angle response to the same targets as in Fig. 6 with on ®xed at 100 rad/s. In this case no overshoot is observed even for large step changes, but responses are slow for small step changes in which overshoot is unlikely to occur. Therefore, if the natural frequency can be varied properly depending upon the size of step changes in the reference input, transient response characteristics may improve signi®cantly. The look-up table that contains an experimentally determined set of natural frequencies for various sizes of step changes can be used, but in this case many experiments should be carried out and interpolation based on the look-up table should be performed every time. Therefore, a more systematic way to compute and implement the proper value of the natural frequency is desired. In what follows, this procedure will be explained in detail. Fig. 8 shows the open-loop test results of the throttle actuator system for
Fig. 6. Experimental results of throttle angle responses with natural frequency ®xed at 200 rad/s.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
489
Fig. 7. Experimental results of throttle angle responses with natural frequency ®xed at 100 rad/s.
various duty ratios of the PWM signal input to the DC motor. It takes about 30 ms to move from the wide open to the fully-closed position with the duty ratio of 100% and from this curve the maximum velocity and maximum acceleration turn out to be approximately 0.28/ms and 3.08/ms2, respectively. Since the throttle actuator system cannot operate beyond these limits, they should be taken into account in the determination of the speci®cations for position control systems. One optimum on can be found by employing the velocity pro®les shown in Fig. 9 [8]. The acceleration a and maximum velocity oo are determined from the above
Fig. 8. Responses of throttle actuator system for various duty ratios.
490
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
open-loop test. Suppose that the size of the step change in the throttle angle required is Dy, which can be negative. Then the time required for acceleration and deceleration is 2ta=2oo/a, and the change in the throttle angle for this region is ya o 2o =a
18
since the angular position happens to be the area under the velocity curve. If j Dy j> ya , then a constant velocity region exists and the trapezoidal velocity pro®le is used; otherwise, the triangular pro®le is used. The reach time to for the trapezoidal velocity pro®le is obtained by to 2ta tc
2o o j Dy j ÿya o o j Dy j a oo a oo
In the case of the triangular velocity pro®le, the reach time becomes p to 2 j Dy j =a
19
20
The 2% settling time for the second-order system [7] ts j2% 4=zo n
21
is often used to represent the time required for the response to reach the steadystate region. The basic idea in computing the natural frequency for the variable reference model is replacing the settling time with the reach time de®ned in either Eq. (19) or Eq. (20). Then, the natural frequency on can be estimated as follows: o n 4=to
22
At every sampling instant of the TCS controller, a new target throttle angle is commanded to the position controller. Note that the sampling instant of the TCS controller is about 100 ms, while that of the position controller is about 1 ms. As
Fig. 9. Velocity pro®les: (a) trapezoidal, (b) triangular.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
491
soon as the new target is given, the position controller computes the reach time according to either Eq. (19) or Eq. (20) and the optimal natural frequency by Eq. (22). Then, the variable reference model with this natural frequency yields the reference trajectory xm(t ), which the plant attempts to track until a new target throttle angle is commanded the next sampling instant from the TCS controller. By varying the natural frequency of the reference model in the above suggested manner, the overshoot can be prevented by the slow reference model with a small value of the natural frequency, while the quick response can be obtained by the quick reference model with a large value of the natural frequency. 4. Simulations and experiments Fig. 10 shows the block diagram of the position control system of the throttle actuator system with the TDC scheme with the variable reference model. In Fig. 10, the DC motor drive and the throttle actuator system are explained in detail in Figs. 3 and 4, respectively. The TDC controller computes the control signal u(t ) from the reference input signal from the TCS controller and the output is measured by the TPS. Figs. 11 and 12 illustrate the simulation and experimental results showing the position control of the throttle actuator system with the TDC scheme with the variable reference model, respectively. Both responses show very similar tendency. As shown in the ®gures, the low natural frequency (on) is selected for a large change in the reference input, while a high natural frequency is selected for a small change. As a result, no overshoot is observed even for large changes in the reference input and also very quick responses are obtained for small changes in the reference input thanks to the variable reference model scheme. Particularly, for a very small change in the reference, the natural frequency is set to almost 600 rad/s without any overshoot. The control signals in the experiment show somewhat oscillatory behavior. This is because the throttle angle is measured by a
Fig. 10. Block diagram of position control system with TDC with variable reference model.
492
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
Fig. 11. Simulation results of throttle angle responses with variable natural frequencies.
potentiometer type sensor, which inevitably introduces some noise, but such noises do not have a great in¯uence on the control performance. Fig. 13 shows the resolution of the position control system. Since the engine torque can be aected greatly even by a small change in the throttle angle in the region of small throttle angles, the resolution of the position systems is also of practical importance. Fig. 13(a) and (b) shows the responses when the target throttle angles change by 1.0 and 0.48, respectively. Although the responses are contaminated with some noise from the sensor, the average responses clearly indicate that the resulting responses are well behaved. Note that the noises shown in Fig. 13 are of approximately the same level as those in Fig. 12, although they appear to be large due to the scaling involved in Fig. 13. It is shown that the resolution of the angular position is ®ner than that of stepping motor which is usually adopted for commercial vehicles.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
493
Fig. 12. Experimental results of throttle angle responses with variable natural frequency.
This developed throttle actuator system with the TDC scheme has been tested in corporation with the TCS system on the proving ground. The test results indicate that the developed system successfully satis®es all the conditions that the TCS system requires. 5. Conclusions In this research, the structure and mechanism of the throttle system for the TCS application was developed. In addition, the position control system was also developed based on the TDC scheme with variable reference model. Considering the requirements for actual vehicle implementation, we attempted to build simple
494
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
Fig. 13. Resolutions of position control systems (changes in target throttle angle: (a) 1.08 and (b) 0.48).
and cost eective hardware and achieve accuracy and quickness of the position responses. From this study, the following conclusions are obtained: 1. The throttle actuator system developed in this research has some advantages over other similar systems in that only a single throttle body is used to perform various functions. 2. The TDC scheme with variable reference model which depends upon the size of step changes in the target throttle angle can produce better transient responses than that with the ®xed reference model in that both overshoot prevention and quick response can be achieved. 3. In the developed position control systems, it takes about 35 msec for the throttle angle to vary from 0 to 908, and 5±6 ms for a change of 58. Also, the resolution of angular position is about 0.3±0.48, which is better than that of stepping motors also used as throttle actuators in some products.
References [1] Ribbens WB. Understanding automotive electronics, 4th ed. Sams, 1992. [2] Kuo BC, Tal J. DC motors and control systems. SRL Publishing Co, 1978. [3] Ong C-M. Dynamic simulation of electric machinery: using Matlab and Simulink. Prentice-Hall, 1998. [4] Song JB, Kim HJ, Byeon KS. Position control system for engine throttle actuator. Proceedings of the 2nd Asian Control Conference, Vol.3. 1997, p. 383±386.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
495
[5] Youcef-Toumi K, Ito O. A time delay controller for systems with unknown dynamics. ASME Journal of Dynamic Systems, Measurement, and Control 1990;112(1):133±42. [6] Youcef-Toumi K, Reddy S. Dynamic analysis and control of high speed and high precision active magnatic bearings. ASME Journal of Dynamic Systems, Measurement, and Control 1992;114:623± 33. [7] Ogata K. Discrete-time control system. Prentice-Hall, 1987. [8] Craig JJ. Introduction to robotics: Mechanics and control, 2nd ed. Addison-Wesley, 1995. p. 238± 46.
Throttle actuator control system for vehicle traction control Jae-Bok Song*, Kyung-Seok Byun Department of Mechanical Engineering, Korea University, 5-Ka Anam-Dong Sungbuk-Ku, Seoul, 136-701, South Korea Received 23 July 1998; accepted 17 December 1998
Abstract Accurate and quick positioning of the throttle valve in a gasoline engine is required to implement various systems such as traction control systems (TCS), cruise control systems and drive-by-wire systems. In this research, the throttle actuator system for TCS application was developed. Unlike other systems, this system consists of only one throttle body to obtain small volume and low manufacturing cost, and uses a DC servo motor for quick and accurate responses. In order to drive the DC motor, a PWM signal generator and PWM ampli®er were built and interfaced to the motor and controller. This paper also presents the position control logic of the throttle actuator with the TDC (time delay control) scheme with a variable reference model. By varying the reference model based on the size of the step changes in the target throttle angle, the TDC scheme yields good transient response characteristics in that both overshoot prevention and a quick response time are achieved. Actual vehicle tests with this developed system incorporated with the TCS system show that it satis®es all the conditions required for the TCS operation. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction The throttle body mounted in a gasoline engine is used to control engine power
* Corresponding author. Tel.: +82-2-3290-3363; fax: +82-2-928-9769. E-mail address: [email protected] (J.B. Song) 0957-4158/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 9 5 7 - 4 1 5 8 ( 9 9 ) 0 0 0 1 0 - 0
478
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
by regulating the amount of air in¯ow into the engine. In normal driving situations, the throttle valve of a throttle body connected to the accelerator pedal is controlled by a driver through the mechanical linkage. However, recent advances in control and electronics technology have enabled the throttle valve to be operated by electric actuators and control systems. Some typical applications include traction control systems (TCS), cruise control systems and drive-by-wire (DBW) systems. In all of the systems listed above, the throttle valve needs to be operated by electronic control systems rather than by manual operation of the driver. Although all the above applications require position control of the throttle valve, this research is focused mainly on TCS application. TCS, one of many vehicle active safety systems, improves the vehicle acceleration performance and stability, particularly on low-friction roads. When the vehicle starts o on lowfriction roads such as snowy or icy roads, excessive slip between the driving wheels and the road usually occurs and thus makes the vehicle's forward movement dicult. Since this slip is caused by the excessive opening of the
Fig. 1. Appearance of throttle actuator.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
479
throttle valve by the driver (thus excessive engine power), properly closing o the throttle valve in opposition to the driver's intention greatly helps the vehicle to regain its acceleration capability. In this situation, it is very important to control the throttle actuator quickly and accurately to satisfy the requirement of the throttle movement determined by the TCS controller. Capability of accurate and quick positioning of the throttle valve is also required for cruise control systems and DBW (drive-by-wire) systems in which the traditional mechanical linkage between the accelerator pedal and throttle valve will be replaced by signal wires in the near future. This research is divided into two parts. One is to design the mechanism and structure of the throttle actuator system for the TCS and the other is to develop the control logic capable of accurate and quick positioning of the throttle valve. Some throttle actuator systems use a vacuum actuator to operate the throttle valve [1]. While this has the advantage of using the back pressure which can easily be obtained from the intake manifold, the response is not quick enough to successfully satisfy the TCS controller. Other throttle bodies consist of two throttle valves for the TCS purpose; a main throttle valve linked to the accelerator pedal by a mechanical cable, and a sub-throttle valve driven by separate actuators such as DC or step motors. These systems are simple in structure since an electric throttle actuator system is separated from the main throttle body, but the manufacturing cost and the volume of the system increase due to the twin body structure. The throttle actuator system developed in this research has only one throttle valve, but provides both functions of the twin-throttle body systems mentioned above (see Fig. 1). That is, it is used as a normal throttle valve linked to the accelerator pedal when the TCS system is not activated, but is driven by the DC servo motor when the throttle actuation diers from the driver's intention with the TCS function activated. Advantages of this type are small volume and low manufacturing cost (compared with the throttle bodies with two valves) and quick response characteristics (compared with some types which use vacuum actuators instead of electric motors). With this type of throttle structure, however, precise positioning of the throttle valve for engine management is dicult to achieve for several reasons. One reason is the constantly varying load torque imposed on the throttle valve by the traction spring depending on the throttle valve position. Another reason is the friction of the four-bar linkage and the valve axis, which cannot be reduced by mechanical improvement due to consideration of manufacturing cost. Therefore, this research also aims at developing a simple but accurate position control system for this type of throttle actuator. To this end, some controllers are tested. Although a PID controller showed good performance, it was dicult to tune the gains for a wide operating range. Therefore, the time delay control (TDC) scheme is adopted for the main control scheme. Since the throttle valve movement contains both large and small changes in the set-point, even well-tuned TDC controllers cannot produce the best performance for the entire operating conditions. To cope with this problem, the
480
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
variable reference model approach was suggested in this research. This idea is simple yet yields good control performance for all operating conditions. With this suggested control system, various tests including actual vehicle tests on the proving ground have been conducted. The test results show that the developed throttle actuator system incorporated with the time delay controller with variable reference model yields good performance for practical use. Chapter 2 introduces the structure and functions of the throttle actuator systems developed in this research and PWM servo driver built for this actuator. Chapter 3 explains the time control law and proposes a new idea called the variable reference model to improve transient response characteristics of the position control system. Some simulation and experimental results are presented in Chapter 4. 2. Structure and modeling of throttle actuator system 2.1. Structure of throttle actuator Fig. 1(a) shows the structure of the engine throttle actuator system developed in this research. As mentioned earlier, this system consists of only one throttle body while most throttle bodies for the TCS purpose consist of two throttle valves. During normal operation, the throttle valve rotates according to the driver's intention through a mechanical cable connected to the accelerator pedal. When the TCS function is activated, the throttle valve rotates by means of the throttle actuator system (in this case, DC servo motor) according to the command from the TCS controller, independent of the driver's intention. The simple four-bar
Fig. 2. Operation of throttle actuator system and de®nition of throttle angle.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
481
linkage in Fig. 1(b) is used to transmit the rotation of the motor to that of the throttle valve. Fig. 2 de®nes the throttle angle and represents the operation of the throttle actuator. As shown in Fig. 1, the right side of the throttle valve is directly linked to the accelerator pedal and is allowed to rotate in the range of the fully-closed throttle (y=08) when the accelerator pedal is not pressed down on at all to the wide open throttle (y=908) when it is fully pressed down on. Two mechanical stoppers at y=08 and 908 prevent the rotation beyond this allowable range. Suppose that the driver sets the throttle angle to ydriver by stepping on the accelerator pedal, thus activating the TCS, which indicates that the excessively open throttle valve has to be properly closed to reduce engine power. Then, the throttle valve positions are limited to the throttle angle set by the driver and the fully-closed position, but within these limits the throttle valve can freely rotate by the throttle actuator system to the angle commanded by the TCS controller. When the TCS function is not further needed, the motor is deenergized and the traction spring returns the throttle valve to the throttle angle set by the driver. Note that the traction spring always tends to force the throttle valve to rotate toward the throttle position set by the driver (i.e., in the direction of the increasing throttle angle). Hence, the main purpose of the throttle actuator system is to position the throttle valve to the opening required by the TCS controller. In typical TCS applications, both large but quick rotation and ®ne rotation of the throttle angle are required. When the TCS controller decides the need for the TCS operation, it attempts to quickly move the throttle valve, which is usually almost wide open at this situation, close to the fully-closed position. Once the throttle valve is almost closed, the controller gradually increases the throttle angle, but even in this case ®ne positioning to the commanded angle is important. There are some diculties in position control of the throttle actuator system. One diculty is caused by the load torque imposed by the traction spring. The traction spring assists the motion of the throttle valve in the increasing throttle angle, while it impedes its motion in the decreasing throttle angle. When position control of the throttle valve is performed, therefore, the required size of the motor torque greatly varies depending on the direction of motor rotation even for the same change in the throttle angle. In addition, the size of the torque introduced by the traction spring varies depending on the throttle angle. In summary, the direction and size of the load torque constantly vary during the position control action. Another diculty is associated with the overshoot of the response. Around the extreme positions of the throttle valve (i.e., at the throttle angles of 0 and 908), the overshoot causes the throttle valve to collide with the mechanical stopper, thus resulting in noise and possible damage to the system. Thus, the overshoot should be avoided even when quick response is required for good control performance. A third problem in position control is friction occurring at the valve and motor axes. Use of bearings in the rotating parts can resolve most of the friction problems, but it raises manufacturing cost. Therefore, this problem would be better overcome by use of the proper feedback control technique.
482
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
2.2. Structure of throttle actuator control system The schematic diagram for the throttle actuator control system is illustrated in Fig. 3. For vehicle implementation, the system is built using relatively cheap components. In order to drive a DC servo motor, a PWM ampli®er based on Hbridge con®guration was built and interfaced to the motor [2]. The PC-based control system was ®rst developed and then the microprocessor 80196KC was employed for actual implementation. The angular position of the throttle angle is measured using a throttle position sensor (TPS) that is an integral part of most throttle bodies. In this system the TPS is based on the potentiometer. The TCS ECU (Electronic Control Unit), which is a separate microprocessor, collects signals from various sensors (e.g., wheel speed sensors, engine RPM sensor) and determines the throttle angle required for the best traction capability. This reference throttle angle signal is sent to the 80196KC microprocessor, which is utilized for the control of the throttle actuator. 2.3. Modeling of throttle actuator system Modeling of the throttle actuator system is required for the simulation and design of a position control system. Fig. 4 illustrates the throttle actuator system using the SIMULINK package [3]. The model is divided into two parts; DC servo motor part and mechanism part which consists of the traction spring and four-bar
Fig. 3. Schematic diagram of throttle actuator control system.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
483
Fig. 4. Modeling of throttle actuator system based on Simulink package.
linkage. Since modeling of the DC motor is treated in much literature, only modeling of the mechanism will be considered here. The mechanical stoppers indicate that the throttle valve can rotate only between the fully-closed position (y=08) and the position set by the accelerator pedal. The four-bar linkage connecting the motor axis to the throttle valve axis is simply modeled as a proportional constant Kl. y s Kl ym s
1
where ym(s ) denotes the angular position of the motor. The load torque imposed by the traction spring is represented by TL s Ks1 y s Ks2
2
where Ks1 represents the spring constant of the traction spring and Ks2 the spring torque oset which accounts for the spring torque applied to the throttle valve at the throttle angle of 08. From the block diagram of Fig. 4, the motor position ym(s ) is obtained by ym
1 Tm ÿ TL s Js f
3
and the motor torque Tm is given by Tm
Kt Va ÿ Eb Kt Ka U ÿ Kb sym Ra La s Ra
4
where Va and Eb are the armature voltage and back emf, La and Ra the inductance and resistance of the armature, Kt and Kb the torque constant and back emf constant and Ka the ampli®er gain, respectively. Note that U(s ) denotes the control signal computed by the position controller. Since the inductance La is usually small in the DC motor and is negligible, the following is obtained by substituting Eqs. (1), (2) and (4) into Eq. (3).
484
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
J 2 b Kt Kb Kt Ka ys U s ys Ks1 y Ks2 Kl Kl Kl Ra Ra Taking the inverse Laplace transform of Eq. (5) gives y t ÿ 1 b Kt Kb y_ t ÿ Kl Ks1 y t ÿ Kl Ks2 Ka Kt Kl u t Ra J J JRa J
5
6
De®ning the state variables as the throttle angle x1(t )=y(t ) and its derivative x 2 t y_ t, Eq. (6) can be converted into the state space representation 3 2 0 1 7 x1 x_ 1 6 4 Kl Ks1 1 Kt Kb 5 x2 x_ 2 ÿ b ÿ J Ra J 7 9 9 8 8 0 0 = = < < Ka Kt Kl u Kl Ks2 ; ; :ÿ : JRa J
3. Time delay control law with variable reference model As mentioned earlier, some requirements exist for successful control of the throttle actuator system. Though some advanced control methods may satisfy the
Fig. 5. Experimental results showing throttle angle responses with PID controller tuned to angles (a) 78, and (b) 778.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
485
above requirements, simple but robust algorithms are desirable for actual vehicle implementation. First, a PID controller was tested. Fig. 5 illustrates two experimental results with the PID controller whose gains are tuned to 7 and 778, respectively. The well-tuned PID control system for some operating point yields the satisfactory performance around that operating range, but it was found that dierent sets of PID gains should be used for dierent operating ranges to achieve optimal performance. Therefore, there were diculties in ®nding many sets of PID gains to cover the entire operating conditions [4]. Another diculty was that the mechanical characteristics of the throttle actuator units dier from unit to unit since they cannot be built accurately due to cost limitations. For example, the traction spring constants and the amount of friction involved in the four-bar linkage and the valve axis sometimes ¯uctuate signi®cantly even if all of them meet the manufacturing tolerance. Furthermore, with long-term use, the throttle actuator parameters tend to vary, which may necessitate new gain tuning. Thus, a more robust control algorithm is required to cope with these diculties. To this end, the time delay control (TDC) scheme was adopted as a basic control algorithm in this development because this scheme is both simple to implement in the microprocessor and accurate enough to ensure the control performance in the presence of disturbance. In addition, the tuning process is relatively simple and only one set of design parameters is needed in covering the entire operating range. Even with the simple TDC scheme, however, it is not easy to yield good transient responses for both large and small changes in target throttle angles. In this research, therefore, some heuristic way called a variable reference model is suggested. In what follows, the TDC scheme with variable reference model will be brie¯y explained. 3.1. TDC law A TDC (Time Delay Control) scheme was suggested as an eective control technique for nonlinear time-varying systems with uncertain dynamics and/or unpredictable disturbances. Basically, it cancels the undesired dynamics and disturbances and substitutes it with desired dynamics. The detailed derivation of the control law can be found in [5,6], but a brief explanation will be given here. Consider a nonlinear time-varying plant in the state-space model xÇ t f x t,t h x t,t B x t,tu t d t
8
where x(t ) represents the state vector (n1), u(t ) the control vector (r1), d(t ) the unpredicted disturbance vector. Dynamics of the plant is divided into the known dynamics vector f(x, t ) and the unknown dynamics vector h(x, t ). Also, the control matrix B(x, t ) is assumed temporarily to be a known matrix. Consider the reference model represented by the following nonlinear timevarying system: xÇ m t F xm t,r t
9
486
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
where xm(t ) and r(t ) denote the state vector of the reference model and the reference input vector, respectively. This reference model yields the ideal state vector that the plant state vector should follow. De®ning the error vector e t xm t ÿ x t, the error dynamics can be written by eÇ t Ae e t
10
where Ae is the error system matrix. When Ae is selected so that all eigenvalues are placed in the left-half s-plane, the error dynamics becomes asymptotically stable. After substitution of the relation xÇ t xÇ m t ÿ Ae e t from Eq. (10) into Eq. (8), the following equation is obtained B x t,tu t ÿf x t,t ÿ h x t,t ÿ d t xÇ m t ÿ Ae e t
11
Since h(x, t )+d(t ) is an unknown function, the control eort u(t ) cannot be à obtained from Eq. (11). Thus, the estimate of this function hà x,t d t must be found. Assuming that time delay L is suciently small and h+d is a continuous function, h(x, t )+d(t ) at time t is close to h x,t ÿ L d t ÿ L at time tÿL. Hence, the estimate of h+d can be described by à hà x t,t d t1h x t ÿ L,t ÿ L d t ÿ L xÇ t ÿ L ÿ f x t ÿ L,t ÿ L ÿ B x t ÿ L,t ÿ Lu t ÿ L
12
If B(x, t ) is unknown or uncertain, then its estimate BÃ(t ) is used. After substituting Eq. (12) into Eq. (11), the following TDC control law is obtained. u t BÃ tfÿf x t,t ÿ xÇ t ÿ L f x t ÿ L,t ÿ L BÃ t ÿ Lu t ÿ L
xÇ m t ÿ Ae e tg
13
where B+ denotes the pseudo-inverse matrix B+=(BTB)ÿ1BT, which happens to be an inverse matrix when the number of control input (r ) is equal to the number of Equations (n ). This control law can be easily implemented in digital control system by taking the time delay L as an integer multiple of the sampling period T s. 3.2. TDC for throttle actuator control system The TDC requires the reference model which is of the second-order dynamics in this case, which is characterized by a natural frequency (on) and a damping ratio (z ). The second-order reference model is given by 0 1 0 x m1 t x_ m1 t r t 14 ÿo 2n ÿ2zo n o 2n x_ m2 t x m2 t
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
487
where r(t ) is the reference input computed from the TCS controller, xm1(t ) and xm2(t ) are the reference throttle angle and its angular velocity, respectively. On the other hand, if the error is de®ned as e t xm t ÿ x t, then the error dynamics is described by eÇ t Ae e t, where Ae
0 ÿo 2ne
1 ÿ2ze o ne
15
Also, the estimate of the control matrix is given by ^T 0 ÃB t f0 bg
Ka KT Kl JRa
T
16
and thus the design parameter bà can be estimated with relative ease. Then, the TDC law (13) can be written by 1 ^ ÿ L x_ m2 t o 2 x m1 t ÿ x 1 t u t fÿx_ 2 t ÿ L bu t ne ^ b 2ze o ne x m2 t ÿ x 2 tg
17
where x1(t ) and x2(t ) are the throttle angle and its angular velocity, respectively. Note that the time L is usually chosen as the sampling period for convenience. 3.3. TDC law with variable reference model Quickness and accuracy in response are required for the position control of the throttle actuator system like other servo systems. Also, as the throttle valve is limited by the mechanical stoppers, overshoot around the limits causes collisions, leading to noise and possible danger; therefore, overshoot prevention is an important criterion for controller design. Because this kind of overshoot usually occurs when the system attempts to quickly track the large commanded change in the reference input, it can be prevented by making the response slow. However, if the control system is made to respond slowly, then another problem arises that the slow response is also obtained even for the small change in the reference input where overshoot is of no concern. Therefore, if the reference model is properly varied depending on the size of the change in the reference input, then it is possible to obtain both overshoot prevention and quick response. Considering the above observations, a simple yet eective way to vary the reference model in the design of a time delay controller is proposed in this research. The reference input r(t ) in Eq. (14) is always given in the form of step functions from the TCS controller every sampling instant. The reference state vector xm(t ) which the actual plant output x(t ) should follow depends on the natural frequency (on) and damping ratio (z ) in the case of the second-order reference model. For overshoot prevention and mathematical convenience, critical damping (i.e., z=1) is assumed here, which is the minimum requirement to
488
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
prevent actual overshoot. Therefore, the reference model is now characterized by only one parameter, the natural frequency. Given the same reference input r(t ), the larger the value of on, the faster the reference model. The fast reference model represents the reference state xm(t ) attempting to quickly track the reference inputs which change in a stepwise fashion, and thus in the extreme end xm(t ) is quite similar to r(t ). To elaborate this point, consider the response characteristics of TDC-based position control system with the fast and slow reference models. Fig. 6 illustrates the throttle angle response to randomly varying targets with on ®xed at 200 rad/s. For small step changes in the target throttle angle, quick responses are observed (see portion B), but for large step changes large overshoots (see portion A) occur. On the other hand, Fig. 7 shows the throttle angle response to the same targets as in Fig. 6 with on ®xed at 100 rad/s. In this case no overshoot is observed even for large step changes, but responses are slow for small step changes in which overshoot is unlikely to occur. Therefore, if the natural frequency can be varied properly depending upon the size of step changes in the reference input, transient response characteristics may improve signi®cantly. The look-up table that contains an experimentally determined set of natural frequencies for various sizes of step changes can be used, but in this case many experiments should be carried out and interpolation based on the look-up table should be performed every time. Therefore, a more systematic way to compute and implement the proper value of the natural frequency is desired. In what follows, this procedure will be explained in detail. Fig. 8 shows the open-loop test results of the throttle actuator system for
Fig. 6. Experimental results of throttle angle responses with natural frequency ®xed at 200 rad/s.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
489
Fig. 7. Experimental results of throttle angle responses with natural frequency ®xed at 100 rad/s.
various duty ratios of the PWM signal input to the DC motor. It takes about 30 ms to move from the wide open to the fully-closed position with the duty ratio of 100% and from this curve the maximum velocity and maximum acceleration turn out to be approximately 0.28/ms and 3.08/ms2, respectively. Since the throttle actuator system cannot operate beyond these limits, they should be taken into account in the determination of the speci®cations for position control systems. One optimum on can be found by employing the velocity pro®les shown in Fig. 9 [8]. The acceleration a and maximum velocity oo are determined from the above
Fig. 8. Responses of throttle actuator system for various duty ratios.
490
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
open-loop test. Suppose that the size of the step change in the throttle angle required is Dy, which can be negative. Then the time required for acceleration and deceleration is 2ta=2oo/a, and the change in the throttle angle for this region is ya o 2o =a
18
since the angular position happens to be the area under the velocity curve. If j Dy j> ya , then a constant velocity region exists and the trapezoidal velocity pro®le is used; otherwise, the triangular pro®le is used. The reach time to for the trapezoidal velocity pro®le is obtained by to 2ta tc
2o o j Dy j ÿya o o j Dy j a oo a oo
In the case of the triangular velocity pro®le, the reach time becomes p to 2 j Dy j =a
19
20
The 2% settling time for the second-order system [7] ts j2% 4=zo n
21
is often used to represent the time required for the response to reach the steadystate region. The basic idea in computing the natural frequency for the variable reference model is replacing the settling time with the reach time de®ned in either Eq. (19) or Eq. (20). Then, the natural frequency on can be estimated as follows: o n 4=to
22
At every sampling instant of the TCS controller, a new target throttle angle is commanded to the position controller. Note that the sampling instant of the TCS controller is about 100 ms, while that of the position controller is about 1 ms. As
Fig. 9. Velocity pro®les: (a) trapezoidal, (b) triangular.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
491
soon as the new target is given, the position controller computes the reach time according to either Eq. (19) or Eq. (20) and the optimal natural frequency by Eq. (22). Then, the variable reference model with this natural frequency yields the reference trajectory xm(t ), which the plant attempts to track until a new target throttle angle is commanded the next sampling instant from the TCS controller. By varying the natural frequency of the reference model in the above suggested manner, the overshoot can be prevented by the slow reference model with a small value of the natural frequency, while the quick response can be obtained by the quick reference model with a large value of the natural frequency. 4. Simulations and experiments Fig. 10 shows the block diagram of the position control system of the throttle actuator system with the TDC scheme with the variable reference model. In Fig. 10, the DC motor drive and the throttle actuator system are explained in detail in Figs. 3 and 4, respectively. The TDC controller computes the control signal u(t ) from the reference input signal from the TCS controller and the output is measured by the TPS. Figs. 11 and 12 illustrate the simulation and experimental results showing the position control of the throttle actuator system with the TDC scheme with the variable reference model, respectively. Both responses show very similar tendency. As shown in the ®gures, the low natural frequency (on) is selected for a large change in the reference input, while a high natural frequency is selected for a small change. As a result, no overshoot is observed even for large changes in the reference input and also very quick responses are obtained for small changes in the reference input thanks to the variable reference model scheme. Particularly, for a very small change in the reference, the natural frequency is set to almost 600 rad/s without any overshoot. The control signals in the experiment show somewhat oscillatory behavior. This is because the throttle angle is measured by a
Fig. 10. Block diagram of position control system with TDC with variable reference model.
492
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
Fig. 11. Simulation results of throttle angle responses with variable natural frequencies.
potentiometer type sensor, which inevitably introduces some noise, but such noises do not have a great in¯uence on the control performance. Fig. 13 shows the resolution of the position control system. Since the engine torque can be aected greatly even by a small change in the throttle angle in the region of small throttle angles, the resolution of the position systems is also of practical importance. Fig. 13(a) and (b) shows the responses when the target throttle angles change by 1.0 and 0.48, respectively. Although the responses are contaminated with some noise from the sensor, the average responses clearly indicate that the resulting responses are well behaved. Note that the noises shown in Fig. 13 are of approximately the same level as those in Fig. 12, although they appear to be large due to the scaling involved in Fig. 13. It is shown that the resolution of the angular position is ®ner than that of stepping motor which is usually adopted for commercial vehicles.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
493
Fig. 12. Experimental results of throttle angle responses with variable natural frequency.
This developed throttle actuator system with the TDC scheme has been tested in corporation with the TCS system on the proving ground. The test results indicate that the developed system successfully satis®es all the conditions that the TCS system requires. 5. Conclusions In this research, the structure and mechanism of the throttle system for the TCS application was developed. In addition, the position control system was also developed based on the TDC scheme with variable reference model. Considering the requirements for actual vehicle implementation, we attempted to build simple
494
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
Fig. 13. Resolutions of position control systems (changes in target throttle angle: (a) 1.08 and (b) 0.48).
and cost eective hardware and achieve accuracy and quickness of the position responses. From this study, the following conclusions are obtained: 1. The throttle actuator system developed in this research has some advantages over other similar systems in that only a single throttle body is used to perform various functions. 2. The TDC scheme with variable reference model which depends upon the size of step changes in the target throttle angle can produce better transient responses than that with the ®xed reference model in that both overshoot prevention and quick response can be achieved. 3. In the developed position control systems, it takes about 35 msec for the throttle angle to vary from 0 to 908, and 5±6 ms for a change of 58. Also, the resolution of angular position is about 0.3±0.48, which is better than that of stepping motors also used as throttle actuators in some products.
References [1] Ribbens WB. Understanding automotive electronics, 4th ed. Sams, 1992. [2] Kuo BC, Tal J. DC motors and control systems. SRL Publishing Co, 1978. [3] Ong C-M. Dynamic simulation of electric machinery: using Matlab and Simulink. Prentice-Hall, 1998. [4] Song JB, Kim HJ, Byeon KS. Position control system for engine throttle actuator. Proceedings of the 2nd Asian Control Conference, Vol.3. 1997, p. 383±386.
J. Song, K. Byun / Mechatronics 9 (1999) 477±495
495
[5] Youcef-Toumi K, Ito O. A time delay controller for systems with unknown dynamics. ASME Journal of Dynamic Systems, Measurement, and Control 1990;112(1):133±42. [6] Youcef-Toumi K, Reddy S. Dynamic analysis and control of high speed and high precision active magnatic bearings. ASME Journal of Dynamic Systems, Measurement, and Control 1992;114:623± 33. [7] Ogata K. Discrete-time control system. Prentice-Hall, 1987. [8] Craig JJ. Introduction to robotics: Mechanics and control, 2nd ed. Addison-Wesley, 1995. p. 238± 46.