- Email: [email protected]
Force control system design for aerodynamic load simulator
Control Engineering Practice 10 (2002) 549–558
Force control system design for aerodynamic load simulator Yoonsu Nama,*, Sung Kyung Hongb a
Department of Mechanical Engineering, Kangwon National University, 192-1 Hyoja 2 Dong, Chunchon City, Kangwon Do 200-701, South Korea b School of Mechanical and Aerospace Engineering, Sejong University, 98 Kunja-Dong, Kwangjin-Ku, Seoul 143-747, South Korea Received 18 July 2000; accepted 2 November 2001
Abstract A dynamic load simulator which can reproduce on-ground the aerodynamic hinge moment of control surface is an essential rig for the performance and stability test of an aircraft actuation system. The hinge moment varies widely over the flight envelope depending on the specific flight condition and maneuvering status. To replicate the wide spectrum of this hinge moment variation within some accuracy bounds, a force controller is designed based on the quantitative feedback theory (QFT). A dynamic model of load actuation system is derived, and verified through the experiment. The efficacy of QFT force controller is verified by a numerical simulation, in which combined aircraft dynamics, flight control law and hydraulic actuation system dynamics of aircraft control surface are considered. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: QFT; Aerodynamic load simulator; Hinge moment; Hydraulic actuator; Force control
1. Introduction A hydraulic actuation system is the common choice for driving aircraft control surfaces because of its high power to weight ratio, and stiffness to the external load. To prove the stability and performance of aircraft actuation system in the first-flight and future airborne operation, a lot of test procedures should be prepared, and successfully passed on-ground (Boeing Commercial Airplane Company, 1985). One of these is the loaded performance test, in which the aerodynamic loads on the control surface are considered. The aerodynamic load, i.e. hinge moment, depends on the aircraft attitude (deflection of control surface, angle of attack, etc.), and flight condition (Mach and altitude), and therefore varies widely over the whole flight envelope. Special equipment called a dynamic load simulator (DLS), which can reproduce on-ground the aerodynamic hinge moment is required for this loaded test. Two independent actuation systems are needed for the DLS. One is the real actuation system driving aircraft control surface, and the other is for aerodynamic load simula*Corresponding author. Tel.: +82-33-250-6376; fax: +82-33-2574190. E-mail addresses: [email protected] (Y. Nam), [email protected] (S.K. Hong).
tion. By setting up the load actuator as counter acting with the control surface driving actuator and designing an appropriate force control system for the load actuator, the DLS can be mechanized. By analyzing hinge moment variations due to deflection angle change of control surface in the whole flight envelope, a design specification for the load replication system can be drawn for any specific application. The dynamic characteristics of the load actuation system using hydraulic power is basically nonlinear. This nonlinearity mainly comes from the fluid flow dynamics through servo valve port (Merritt, 1967). A force control system using quantitative feedback theory (QFT) design for the load replication system is proposed, and its efficacy is verified through the simulation. A mathematical model of the DLS dynamics and design specification for the load replication system are derived in Section 2. The nonlinear dynamics of the load actuation system is represented as a set of linear systems using parametric uncertainty model. Also, the validity of derived model is investigated by the comparison with initial experimental results. Section 3 contains the QFT force controller design procedures and results. The load actuation system dynamics is incorporated in the pitch axis flight control system, in which longitudinally unstable flight dynamics, pitch axis control law, and control surface driving actuator
0967-0661/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 2 ) 0 0 0 0 4 - 7
550
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
dynamics are combined. The performance of the QFT force controller for the aerodynamic load replication is verified by the simulation for the whole integrated system, and its results are provided in Section 4.
2. Mathematical model of dynamic load simulator A schematic diagram of the dynamic load simulator (DLS) with the structure of a pitch axis flight control system is shown in Fig. 1. The DLS described in the upper part of Fig. 1 is composed of a backup stiffness to simulate the attachment effect of a control surfacedriving actuator on the flexible airframe structure, a flywheel to emulate the moment of inertia of control surface, and two actuation systems which represent the control surface driving actuator and the load replicating actuator. The force command for the load actuation system comes from the flight dynamics real time simulation computer (FMSC), which numerically solves the aircraft flight dynamics and the hinge moment for the given flight condition.
ment for the load replication system is a reasonable design specification. 2.2. Modeling of actuation system Due to the apparent advantages in weight, size, and simplified fault-monitoring mechanism compared with the electro hydraulic valve (EHV) actuation, the use of direct drive valve (DDV) as a control surface driving actuator becomes very common in a modern flight control system design (Schaefer, Inderhees, & Moynes, 1991; Vieten, Snyder, & Clark, 1993). The model of the DDV actuator has a complicated internal structure for the performance enhancement and fault monitoring. However, the following simplified linear model is sufficient for this study. The DDV spool dynamics is determined by the following equations. In Eq. (2), the hydraulic Bernoulli flow forces, FB are considered, because they are not negligible amount compared with the case of a flapper nozzle-type servo valve. K m i ¼ Mv
2.1. Design specification for load replication system The taileron hinge moment can be modeled approximately as follows (Roskam, 1979): Mh ðsÞ ¼ qScfC % ha aðsÞ þ Chd dðsÞg aðsÞ þ Chd dðsÞ; ¼ qSc Cha % dðsÞ
ð1Þ
where q% denotes the aerodynamic pressure, S and c are, respectively, the area and mean aerodynamic chord (MAC) of the main wing, and Cha and Chd represent the hinge moment coefficients for the taileron control surface with respect to the angle of attack (a) and the deflection angle (d). The transfer function of the hinge moment variation for the pilot command can be found from the closed-loop structure of Fig. 1 by using Eq. (1). A sample of the hinge moment (HM) frequency response variation for the 1 g normal load factor command is given as solid lines in Fig. 2. This result, which shows the wide variations of the hinge moment dynamics, is calculated from the analysis for the 32 flight conditions. These are selected over the whole flight envelope of the fighter-type relaxed static stability (RSS) aircraft. The magnitude of hinge moment for a 1 g command input varies in the range 100–10,000 lbf in up to 4–5 Hz from DC, and decreases rapidly in the highfrequency region above 5 Hz. If the load replication system is designed about 10 times faster than the hinge moment dynamics, the hinge moment replication can be done without any magnitude and phase distortion. From the above analysis, the 35 Hz bandwidth require-
2 X d2 xv dxv þ K þ B x þ ðFB Þi ; v v v dt2 dt i¼1
V ¼ Ri þ L
di dxv þ KvB ; dt dt
ð2Þ
where xv is the DDV spool displacement, V the voltagedriving DDV motor, i the current flow to DDV coil, Km and Kv are the DDV motor force constant and spring rate of DDV spool, Mv and Bv are the mass and damping coefficient of DDV spool, R and L are the resistance and inductance of DDV coil, KvB is the back EMF constant of DDV motor, and ðFB Þi the flowinduced force for hydraulic system #i: The following equation is obtained by applying the continuity equation of fluid flow in the DDV actuator chambers and combining the load flow equation (2). pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi QL ¼ Kq xv PS signðxv ÞPL EKq xv Kc PL dYP=B Vt dPL þ þ ðCip þ Cep =2ÞPL ; ¼A ð3Þ dt 4b dt where QL is the load flow rate, Kq and Kc are the flow gain and flow-pressure coefficient, A and Vt are the DDV actuator piston area and total chamber volume, b the bulk modulus of operating oil, Cip and Cep are the internal and external leakage coefficients, and PS and PL are the supply pressure and load pressure. YP=B in Eq. (3) is the relative displacement of the piston (YP ) to the actuator body (YB ), and picked up by the LVDT sensor installed on the body. The parameter of KB in Eq. (4) represents the stiffness of the spring to simulate the attachment effect of a control surface driving actuator on a flexible airframe body.
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
551
CONTROL SURFACE INERTIA
DYNAMIC LOAD SIMULATOR
FORCE SENSOR _
DD
VA
LVD T CTU ATO R S/ V
V S/ AD OR LO UAT T
AC
FLIGHT DYNAMICS REAL-TIME SIMULATION COMPUTER
ATTACHMENT EFFECT AIRCRAFT DYNAMICS G DL
PILOT STICKDemand INPUT
Generate
_
GI
s
ACTUATOR MODEL PAF
TAILERON
PAF: PHASE ADVANCE FILTER
Hinge Moment Aircraft 6 - DOF Nonlinear Dynamics
q
nz Gq G G ov 1
Fig. 1. Schematics of dynamic load simulator.
Fig. 2. Variation of frequency responses from a 1 g load factor command to hinge moment in flight envelope.
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
552
tainty in the model of the load actuation system comes from the nonlinear fluid-flow characteristics through the servo valve. Based on the manufacturer’s catalog for MOOG D761 series servo valve (MOOG, 1997), this uncertainty can be modeled as follows:
YP=B ¼ YP YB ¼ Yp ð2PL AÞ=KB ¼ Yp þ 2PL A=KB :
ð4Þ
By substituting Eq. (4) into (3), the following equation is obtained: dYP Vt 2A2 dPL þ þ QL EKq xv Kc PL ¼ A dt 4b KB dt þ ðCip þ Cep =2ÞPL :
Kqi QL ðsÞ ¼ ; 2 iðsÞ ðs=on Þ þ 2Bðs=on Þ þ 1
ð5Þ
where QL is the flow rate through the servo valve (in3/s/ mA), Kqi the flow gain of servo valve (in3/s/mA), [1.8308, 2.2376], on the natural frequency of servo valve (Hz) [40, 75], and B is the damping ratio of servo valve [0.5, 1.0]. The accuracy of the modeling is verified through the comparison with experimental results. The load actuation system interconnected with the fully pressurized DDV actuator at 3000 psi is excited by a 1 kHz bandlimited pseudo-random binary sequence (PRBS) of 1:8Vpp ; and the movement of the flywheel, i.e. the displacement of the load actuator, is sensed by the rotary potentiometer installed on the rotational axis. Because the DDV spool is constrained to be stationary for this experiment, the DDV actuator can be modeled as a simple spring having the equivalent stiffness of KEFF as described in Fig. 4(b). 1 1 1 1 KEFF ¼ þ þ : ð8Þ KB KACT1 þ KACT2 KRD
The last equation governing the DDV actuator dynamics is Newton’s equation, in which the inertial effect of control surface and hinge moment is considered. 2APL
dYp Mh d2 YP ; ¼ ML þ BL 2 RH dt dt
ð7Þ
ð6Þ
where ML is the equivalent mass of control surface inertia, BL is the damping coefficient of control surface, and Mh and RH are the hinge moment and actuator horn radius. Combining the DDV dynamics, Eqs. (5) and (6) lead to the block diagram shown in Fig. 3, where for the sake of clarity the DDV spool dynamics of Eq. (2) and servo drive amplifier characteristics are contained inside the box in this figure. The filter dynamics and feedback gains in Fig. 3 are determined to meet the DDV actuator outer loop frequency response requirement (Hsu, Lai, Hsu, & Lee, 1991). The load actuation system can be modeled in the same way as above. The lower part of Fig. 3 describes the dynamics of the load actuation system. Most uncer-
In the above equation, KACT 1 and KACT2 represent the DDV actuator stiffness for the hydraulic systems 1 and
DDV Actuator Dynamics
DDV Act CMD _
Outer Loop Control
Inner Loop Control
GOUT(s)
GIN (s)
_
Servo AMP & DDV Dynamics Back EMF
A xv
DDV Cmd
QL Kq
DDV Disp.
Vt
_
YP
PL
2
4
+ 2A KB
2A
_
_
Flow Forces
Leakage
1 M
YP
BL
C ip + C ep 2
_
KL YB
DDV Disp. Feedback K fv
2A KB
YP/B _ K fa RAM LVDT Feedback
Force Feedback
Load Actuator Dynamics QFT Controller CMD
QFT Pre Filter
Leakage
A pL
C ip + C ep 2
_
QFT Controller
K sv
L
EHSV DYNAMICS
Servo AMP
_
K qi
i (
s n
)
2
+
2
(
s n
4
)
+
1
QL
V
L
Fig. 3. Linear model of hydraulic dynamic load simulator.
A pL t
L
PL
L
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
553
i, Command
Servo Valve DDV Actuator
Load Cell
Load Actuator Hyd. System #1
Hyd. System #2
Fly Wheel
Backup Structure
(A) Schematics of Dynamic Load Simulator Structure YB
YPD
K ACT1
KB
xA
Equivalent Surface Mass
K RD
L
K B : Backup Structure Stiffness
K RL M
K ACT2
K ACT : Actuator Chamber Stiffness
L
K RD : DDV Rod Stiffness K RL : Load Actuator Rod Stiffness
YP
(B) Equivalent Stiffness Command
SV AMP
SPOOL DYNAMICS
xv
K qi
K sv
s
Cd w
2
+2
s
+1
Ps - sign(x v ) P L
QL
1 As
_
xA
M L s 2 + cs + K EFF
Vt C ip + C ep /2
L
_
4
YP
A
PL
LOAD FLOW
1 A
Fext
K RL
(C) Model of Load Actuator Fig. 4. Dynamic load simulator stiffness and model of load actuator.
2, which are caused by trapped oil inside the two oil chambers. Fig. 5 shows the experimental frequency response with the analytic ones, which are plotted as dashed lines. Two analytic frequency responses in this figure are obtained based on Eq. (7). The upper one is calculated for the operating condition of the maximum flow gain, maximum natural frequency, and minimum damping, and the lower one for the opposite condition to the above, which are the two extreme case dynamics in Eq. (7). The deviation of experimental results from the analytical ones for the high-frequency region above 100 Hz is due to the effect of the noise corruption, and that for the low-frequency region below 1 Hz is from the weakened performance of the frequency response analyzer at this frequency. Therefore, the load actuator modeling based on Eq. (7) is considered to be acceptable.
the following specification of the load replication system.
3. QFT force controller design
These boundaries are determined from the requirements of 35 Hz bandwidth, peak overshoot o1.5%, and steady state error o1% for the closed-loop load actuation system. Besides these requirements, the stability margins of 5 dB gain and 451 phase are assumed, which are automatically satisfied when all the perturbed loop gain Bode plots due to uncertainties exist outside of 2 dB Mcircle shown in Fig. 6.
QFT is one method of designing a robust control system (Reynolds, Pachter, & Houpis, 1996; Snell & Stout, 1996; D’Azzo & Houpis, 1988). For the uncertain servo valve dynamics described in Eq. (7), twodegrees-of-freedom (DOF) force controllers which have the structure shown in Fig. 3 are designed to meet
3.1. Design specification on QFT force controller The QFT force control loop of the load actuation system is to be designed to meet the following upper and lower tracking boundary specifications: TL ðsÞ ¼
0:99 ; ðs=220 þ 1Þ ðs=280 þ 1Þ ðs=2200 þ 1Þ
TU ðsÞ ¼ 1:01ðs=242 þ 1Þ ðs=528 þ 1Þ : ðs2 =2202 þ 2 0:8s=220 þ 1Þ ðs=990 þ 1Þ ðs=2200 þ 1Þ ð9Þ
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
554 20
0
Load Actuator Disp/ V (in/V) in dB
_ 20
_
40
_ 60
_ 80
_100
_120
_140 _1 10
0
10
1
10 Frequency (Hz)
2
10
3
10
Fig. 5. Comparison of analytic and experimental bode plot of load actuator model.
3.2. QFT force controller design The templates at the frequency of oT (rad/s)A[10, 17.5, 30.8, 54.1, 95.1, 293.2, 514.8, 904, 1198, 1587.4, 2103.5, 2787.5, 3693.8, 4894.7] are shown in Fig. 6 as the dotted boundaries, which are caused by the nonlinear characteristic of the servo valve flow dynamics of Eq. (7). The relatively larger templates are observed at the servo valve natural frequency range (290–514.8 rad/ s), and templates for low- and high-frequencies are determined from the magnitude variation of the servo valve flow gain. The points designated by ‘*’ at each frequency of oT in this figure means the Nichols plot of the nominal plant, which is defined for the condition of minimum flow gain, natural frequency, and damping in Eq. (7). The QFT force controller which guarantees that the closed-loop load actuation system will meet the performance and stability requirements for the given plant uncertainties of Eq. (7) can be found by making the Nichols plot of the nominal plant loop gain function to be placed over the tracking bounds for each specific frequency. The 7 dashed lines in Fig. 6 represent the tracking bounds for the frequency of oB (rad/s)A[10, 17.5, 30.8, 54.1, 95.1, 293.2, 514.8], respectively. As shown in this figure, the Nichols plot of the nominal
plant for the frequencies of oB is located above the matching tracking bounds by selecting the QFT controller as GðsÞ ¼
0:001795ðs=154 þ 1Þ ðs=330 þ 1Þ : ðs=1700 þ 1Þ ðs2 =22002 þ 2 0:55s=2200 þ 1Þ ð10Þ
The DC gain of GðsÞ is determined such that the nominal loop gain plot at 10 rad/s is located over the corresponding tracking bound. Two zeros of GðsÞ are inserted to meet the tracking bound requirements and to give enough phase margin at the crossover frequency. Three poles of GðsÞ are required for the controller to be realizable. The pole having a frequency of 1700 rad/s in GðsÞ is required for the perturbed loop gain Nichols plot to have the gain margin of 5 dB. And the frequencies of the two complex poles are determined so high as to minimize the phase delay effect, but not so high for the GðsÞ not to be a high bandwidth controller. A slight penetration of the template at a frequency of oB ¼ 904 rad/s into the 2 dB M-circle can be seen in Fig. 6, which means an imperfect fulfillment of the stability margin requirement. However, this can be accepted as a satisfactory design,
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
555
40
30
20
QFT Loop Gain (dB)
10
0 _10 _20 _ 30 _ 40 _ 50 _ 60
_350
_ 300
_ 250
_ 200
_150 Phase (Degree)
_100
_ 50
0
Fig. 6. Nichols plot for QFT design.
considering that no significant impact on phase, or gain margin results. Loop shaping by GðsÞ of Eq. (10) guarantees only that the magnitude variations in the closedloop Bode plot due to plant uncertainties are within the range of jdðjoÞj ¼ jTU ðjoÞ TL ðjoÞj at each frequency. Therefore, a pre-filter like the one in Eq. (11) is required for the closed-loop TðjoÞ to be within the frequency domain performance specifications of Eq. (9). F ðsÞ ¼
ðs=150 þ 1Þ : ðs2 =1802 þ 2 0:7s=180 þ 1Þ
ð11Þ
The frequency response of the QFT closed-loop load actuation system is compared with the upper ðTU ðjoÞÞ and lower ðTL ðjoÞÞ performance bounds in Fig. 7. The Bode plots shown as the dashed lines in this figure are for eight extreme case dynamics from the uncertain servo valve characteristics, which are obtained from the mini–max value combination of Kqi ; on ; and B in Eq. (7). All the extreme case dynamics are almost within the desired performance bounds up to the 200 Hz. The deviation from these bounds at the high-frequency region above 200 Hz is a rather favorable characteristic
in the points of the unmodeled high-frequency dynamic and sensor noise effects.
4. Evaluation of force controller design 4.1. QFT force force loop design As shown in Fig. 7, there are slight deviations of the perturbed closed-loop frequency responses from the desired performance bounds in the frequency region around 10 Hz and the high-frequency region above 200 Hz. The effect of this poor achievements on the performance bound requirements at the mid-frequency range is well noticed in Fig. 8, which shows the step response comparison between the QFT and the following phase lead controller design of Eq. (12). Only the load actuator dynamics which is described on the lower part in Fig. 3 is considered in this simulation. KðsÞ ¼
0:000846ðs=66:4 þ 1Þ : ðs=664:1 þ 1Þ
ð12Þ
The identical design requirements are applied for the phase lead controller design, in which the nominal plant dynamics having the mid values of Kqi ; on ; and B in
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
556
Magnitude of Closed Loop Force Control System (dB)
20
0
_ 20
_ 40
_ 60
_ 80
_100
0
10
1
2
10
3
10
10
Frequency (Hz) Fig. 7. Closed-loop frequency response of force control system.
Eq. (7) are assumed. The dotted lines in these figures mean the step responses obtained from the two performance bounds of Eq. (9), and solid lines are from the eight extreme cases with the QFT and lead controller, respectively. From these time domain responses, the superiority of QFT over the conventional lead design is well understood. In case of the phase lead control, much larger overshoots and settling times are noticed for the load actuator dynamics variation specified by Eq. (7), even though the lead force control system design is satisfactorily made for the abovementioned nominal plant condition. However, the step responses for the QFT design also show some poor performances in the transient response region, which result from the imperfect achievement in the closedloop frequency boundary requirement of Fig. 6 in a mid-frequency range of 10 Hz and in high-frequency region. 4.2. Numerical simulation with the aircraft dynamics For the integrated system of an aircraft dynamics, a pitch axis flight control law, and a hydraulic actuator dynamics, the performance of the force control system proposed in Section 3 is investigated by the numerical simulation. This simulation is made for the control-loop
structure of Fig. 1, in which the taileron actuator model is replaced with the DLS model of Fig. 3. The pitch axis flight dynamics of Eq. (13) is obtained by trimming and linearizing the 6 DOF aircraft dynamics for the Mach 0.9 and sea-level flight condition. The aircraft considered in this study is a statically unstable fighter. ( ) " #( ) " # Zw a’ a Zd =Vt 1 ¼ þ d q’ q Ma M q Md "
2:9367 1 ¼ 27:7276 0:5582 " # 0:0087 þ d; 1:5682
#( ) a q ð13Þ
where a and q is the angle of attack (rad) and pitch rate (r/s), d is the taileron deflection angle (deg), Vt the Aircraft speed (ft/s), and Zw ; Ma ; Mq ; Zd ; and Md are the longitudinal force/moment stability & control derivative. Fig. 9 shows the simulation results for a 1 g normal load factor command. The nonminimum phase effect on the normal load factor due to the taileron deflection can be noticed in the first plot. The second plot represents the DDV taileron deflection angle (solid line) and load
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
557
(a) QFT Design Case
f
Load Force (lb )
15000
10000
5000
0
0
0.01
0.02
0.03
0.04
0.05 Time (sec)
0.06
0.07
0.08
0.09
0.1
0.07
0.08
0.09
0.1
(b) Lead Filter Design Case
f
Load Force (lb )
15000
10000
5000
0
0
0.01
0.02
0.03
0.04
0.05 Time (sec)
0.06
Fig. 8. Time domain step response (QFT and Lead) design.
actuator rotation angle (dashed line). Considering the sign convention, defined in Fig. 4B, the DDV (Yp ) and load actuator displacement (ðxA ÞL ) move almost the same distance amount, as they should. The third plot in Fig. 9 is the developed hinge moment (HM) for the 1 g maneuvering flight (dotted line) and the output of load actuator force control system for all the eight extreme case dynamics, which are obtained from the uncertain servo valve characteristics of Eq. (7). The mismatch of replicated hinge moments to the desired one in this plot is due to imperfect following of the load actuator travel to that of the DDV actuator. The larger discrepancy in the hinge moment replication is expected for the more stiff connection between the DDV and the load actuator, compared with the current design value of KRL ¼ 100; 000 lbf =in: Due to the QFT force controlloop design, a relatively small amount of the replicated hinge moment variation results even for the extreme change of the servo valve dynamics. The problems of the slight penetration of 2 dB Mcircle in Fig. 6 and breakaway from the tracking boundary requirement in Fig. 7 can be resolved by using the more complicated and high-bandwidth QFT compensator. However, this design demands the expense of computational delay and high-sampling rate in
the controller implementation. Therefore, the experimental verification is to be made with the current design, and a study for the enhanced force control algorithm to resolve the mismatching problem in the hinge moment replication is also to be continued.
5. Conclusion An aircraft actuation system test rig, a dynamic load simulator, which can reproduce on-ground the aerodynamic hinge moment of control surface is introduced. From the analysis on the hinge moment variations in the whole flight envelope due to the aircraft longitudinal maneuvering, a design specification for the dynamic load replication system is determined. A mathematical model for the dynamic load simulator is developed. Especially, the nonlinear dynamic characteristics of an electro-hydraulic servo valve of the load replication system is represented with a set of linear systems using the parametric uncertainties in the valve flow gain, natural frequency, and damping. A QFT force control system is designed for the dynamic load simulator to uniformly replicate on-ground aerodynamic hinge moment even for the uncertain dynamic characteristics of
558
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
Fig. 9. Time domain response of 1 g normal load factor input.
the load actuation system servo valve. The efficacy of the QFT force control system is verified by the numerical simulation, in which combined aircraft dynamics, pitch axis flight control law and hydraulic actuation system are considered.
References Boeing Commercial Airplane Company. (1985). Test act system validation final report. NASA CR-172525. D’Azzo, J., & Houpis, C. H. (1988). Linear control system analysis and design conventional and modern. Englewood Cliffs, NJ: McGraw-Hill. Hsu, Y. N., Lai, C. Y., Hsu, M. H., & Lee, Y. K. (1991). Development of the direct drive valve (DDV) actuation system on the IDF aircraft. International pacific air and space technology conference and 29th aircraft symposium. Japan. (pp. 2312–2322).
Merritt, H. (1967). Hydraulic control systems. New York: Wiley (pp. 79–98). MOOG. (1997). Servo and proportional system catalog (pp. 95–98). Reynolds, O. R., Pachter, M., & Houpis, C. H. (1996). Full envelope flight control system design using quantitative feedback theory. Journal of Guidance, Control, and Dynamics, 19(1), 23–29. Roskam, J. (1979). Airplane flight dynamics and automatic flight controls. Roskam aviation and engineering corporation. Schaefer, W. S., Inderhees, L. J., & Moynes, J. F. (1991). Flight control actuation system for B-2 advanced technology bomber. Technical Bulletin, 153(MOOG), 1–8. Snell, S. A., & Stout, P. W. (1996). Quantitative feedback theory with a scheduled gain for full envelope longitudinal control. Journal of Guidance, Control and Dynamics, 19(5), 1095–1101. Vieten, K. W., Snyder, J. D., & Clark, R. P. (1993). Redundancy management concepts for advanced actuation systems. AIAA/ AHS/ASEE aerospace design conference (pp. 1–9).
Force control system design for aerodynamic load simulator Yoonsu Nama,*, Sung Kyung Hongb a
Department of Mechanical Engineering, Kangwon National University, 192-1 Hyoja 2 Dong, Chunchon City, Kangwon Do 200-701, South Korea b School of Mechanical and Aerospace Engineering, Sejong University, 98 Kunja-Dong, Kwangjin-Ku, Seoul 143-747, South Korea Received 18 July 2000; accepted 2 November 2001
Abstract A dynamic load simulator which can reproduce on-ground the aerodynamic hinge moment of control surface is an essential rig for the performance and stability test of an aircraft actuation system. The hinge moment varies widely over the flight envelope depending on the specific flight condition and maneuvering status. To replicate the wide spectrum of this hinge moment variation within some accuracy bounds, a force controller is designed based on the quantitative feedback theory (QFT). A dynamic model of load actuation system is derived, and verified through the experiment. The efficacy of QFT force controller is verified by a numerical simulation, in which combined aircraft dynamics, flight control law and hydraulic actuation system dynamics of aircraft control surface are considered. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: QFT; Aerodynamic load simulator; Hinge moment; Hydraulic actuator; Force control
1. Introduction A hydraulic actuation system is the common choice for driving aircraft control surfaces because of its high power to weight ratio, and stiffness to the external load. To prove the stability and performance of aircraft actuation system in the first-flight and future airborne operation, a lot of test procedures should be prepared, and successfully passed on-ground (Boeing Commercial Airplane Company, 1985). One of these is the loaded performance test, in which the aerodynamic loads on the control surface are considered. The aerodynamic load, i.e. hinge moment, depends on the aircraft attitude (deflection of control surface, angle of attack, etc.), and flight condition (Mach and altitude), and therefore varies widely over the whole flight envelope. Special equipment called a dynamic load simulator (DLS), which can reproduce on-ground the aerodynamic hinge moment is required for this loaded test. Two independent actuation systems are needed for the DLS. One is the real actuation system driving aircraft control surface, and the other is for aerodynamic load simula*Corresponding author. Tel.: +82-33-250-6376; fax: +82-33-2574190. E-mail addresses: [email protected] (Y. Nam), [email protected] (S.K. Hong).
tion. By setting up the load actuator as counter acting with the control surface driving actuator and designing an appropriate force control system for the load actuator, the DLS can be mechanized. By analyzing hinge moment variations due to deflection angle change of control surface in the whole flight envelope, a design specification for the load replication system can be drawn for any specific application. The dynamic characteristics of the load actuation system using hydraulic power is basically nonlinear. This nonlinearity mainly comes from the fluid flow dynamics through servo valve port (Merritt, 1967). A force control system using quantitative feedback theory (QFT) design for the load replication system is proposed, and its efficacy is verified through the simulation. A mathematical model of the DLS dynamics and design specification for the load replication system are derived in Section 2. The nonlinear dynamics of the load actuation system is represented as a set of linear systems using parametric uncertainty model. Also, the validity of derived model is investigated by the comparison with initial experimental results. Section 3 contains the QFT force controller design procedures and results. The load actuation system dynamics is incorporated in the pitch axis flight control system, in which longitudinally unstable flight dynamics, pitch axis control law, and control surface driving actuator
0967-0661/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 2 ) 0 0 0 0 4 - 7
550
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
dynamics are combined. The performance of the QFT force controller for the aerodynamic load replication is verified by the simulation for the whole integrated system, and its results are provided in Section 4.
2. Mathematical model of dynamic load simulator A schematic diagram of the dynamic load simulator (DLS) with the structure of a pitch axis flight control system is shown in Fig. 1. The DLS described in the upper part of Fig. 1 is composed of a backup stiffness to simulate the attachment effect of a control surfacedriving actuator on the flexible airframe structure, a flywheel to emulate the moment of inertia of control surface, and two actuation systems which represent the control surface driving actuator and the load replicating actuator. The force command for the load actuation system comes from the flight dynamics real time simulation computer (FMSC), which numerically solves the aircraft flight dynamics and the hinge moment for the given flight condition.
ment for the load replication system is a reasonable design specification. 2.2. Modeling of actuation system Due to the apparent advantages in weight, size, and simplified fault-monitoring mechanism compared with the electro hydraulic valve (EHV) actuation, the use of direct drive valve (DDV) as a control surface driving actuator becomes very common in a modern flight control system design (Schaefer, Inderhees, & Moynes, 1991; Vieten, Snyder, & Clark, 1993). The model of the DDV actuator has a complicated internal structure for the performance enhancement and fault monitoring. However, the following simplified linear model is sufficient for this study. The DDV spool dynamics is determined by the following equations. In Eq. (2), the hydraulic Bernoulli flow forces, FB are considered, because they are not negligible amount compared with the case of a flapper nozzle-type servo valve. K m i ¼ Mv
2.1. Design specification for load replication system The taileron hinge moment can be modeled approximately as follows (Roskam, 1979): Mh ðsÞ ¼ qScfC % ha aðsÞ þ Chd dðsÞg aðsÞ þ Chd dðsÞ; ¼ qSc Cha % dðsÞ
ð1Þ
where q% denotes the aerodynamic pressure, S and c are, respectively, the area and mean aerodynamic chord (MAC) of the main wing, and Cha and Chd represent the hinge moment coefficients for the taileron control surface with respect to the angle of attack (a) and the deflection angle (d). The transfer function of the hinge moment variation for the pilot command can be found from the closed-loop structure of Fig. 1 by using Eq. (1). A sample of the hinge moment (HM) frequency response variation for the 1 g normal load factor command is given as solid lines in Fig. 2. This result, which shows the wide variations of the hinge moment dynamics, is calculated from the analysis for the 32 flight conditions. These are selected over the whole flight envelope of the fighter-type relaxed static stability (RSS) aircraft. The magnitude of hinge moment for a 1 g command input varies in the range 100–10,000 lbf in up to 4–5 Hz from DC, and decreases rapidly in the highfrequency region above 5 Hz. If the load replication system is designed about 10 times faster than the hinge moment dynamics, the hinge moment replication can be done without any magnitude and phase distortion. From the above analysis, the 35 Hz bandwidth require-
2 X d2 xv dxv þ K þ B x þ ðFB Þi ; v v v dt2 dt i¼1
V ¼ Ri þ L
di dxv þ KvB ; dt dt
ð2Þ
where xv is the DDV spool displacement, V the voltagedriving DDV motor, i the current flow to DDV coil, Km and Kv are the DDV motor force constant and spring rate of DDV spool, Mv and Bv are the mass and damping coefficient of DDV spool, R and L are the resistance and inductance of DDV coil, KvB is the back EMF constant of DDV motor, and ðFB Þi the flowinduced force for hydraulic system #i: The following equation is obtained by applying the continuity equation of fluid flow in the DDV actuator chambers and combining the load flow equation (2). pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi QL ¼ Kq xv PS signðxv ÞPL EKq xv Kc PL dYP=B Vt dPL þ þ ðCip þ Cep =2ÞPL ; ¼A ð3Þ dt 4b dt where QL is the load flow rate, Kq and Kc are the flow gain and flow-pressure coefficient, A and Vt are the DDV actuator piston area and total chamber volume, b the bulk modulus of operating oil, Cip and Cep are the internal and external leakage coefficients, and PS and PL are the supply pressure and load pressure. YP=B in Eq. (3) is the relative displacement of the piston (YP ) to the actuator body (YB ), and picked up by the LVDT sensor installed on the body. The parameter of KB in Eq. (4) represents the stiffness of the spring to simulate the attachment effect of a control surface driving actuator on a flexible airframe body.
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
551
CONTROL SURFACE INERTIA
DYNAMIC LOAD SIMULATOR
FORCE SENSOR _
DD
VA
LVD T CTU ATO R S/ V
V S/ AD OR LO UAT T
AC
FLIGHT DYNAMICS REAL-TIME SIMULATION COMPUTER
ATTACHMENT EFFECT AIRCRAFT DYNAMICS G DL
PILOT STICKDemand INPUT
Generate
_
GI
s
ACTUATOR MODEL PAF
TAILERON
PAF: PHASE ADVANCE FILTER
Hinge Moment Aircraft 6 - DOF Nonlinear Dynamics
q
nz Gq G G ov 1
Fig. 1. Schematics of dynamic load simulator.
Fig. 2. Variation of frequency responses from a 1 g load factor command to hinge moment in flight envelope.
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
552
tainty in the model of the load actuation system comes from the nonlinear fluid-flow characteristics through the servo valve. Based on the manufacturer’s catalog for MOOG D761 series servo valve (MOOG, 1997), this uncertainty can be modeled as follows:
YP=B ¼ YP YB ¼ Yp ð2PL AÞ=KB ¼ Yp þ 2PL A=KB :
ð4Þ
By substituting Eq. (4) into (3), the following equation is obtained: dYP Vt 2A2 dPL þ þ QL EKq xv Kc PL ¼ A dt 4b KB dt þ ðCip þ Cep =2ÞPL :
Kqi QL ðsÞ ¼ ; 2 iðsÞ ðs=on Þ þ 2Bðs=on Þ þ 1
ð5Þ
where QL is the flow rate through the servo valve (in3/s/ mA), Kqi the flow gain of servo valve (in3/s/mA), [1.8308, 2.2376], on the natural frequency of servo valve (Hz) [40, 75], and B is the damping ratio of servo valve [0.5, 1.0]. The accuracy of the modeling is verified through the comparison with experimental results. The load actuation system interconnected with the fully pressurized DDV actuator at 3000 psi is excited by a 1 kHz bandlimited pseudo-random binary sequence (PRBS) of 1:8Vpp ; and the movement of the flywheel, i.e. the displacement of the load actuator, is sensed by the rotary potentiometer installed on the rotational axis. Because the DDV spool is constrained to be stationary for this experiment, the DDV actuator can be modeled as a simple spring having the equivalent stiffness of KEFF as described in Fig. 4(b). 1 1 1 1 KEFF ¼ þ þ : ð8Þ KB KACT1 þ KACT2 KRD
The last equation governing the DDV actuator dynamics is Newton’s equation, in which the inertial effect of control surface and hinge moment is considered. 2APL
dYp Mh d2 YP ; ¼ ML þ BL 2 RH dt dt
ð7Þ
ð6Þ
where ML is the equivalent mass of control surface inertia, BL is the damping coefficient of control surface, and Mh and RH are the hinge moment and actuator horn radius. Combining the DDV dynamics, Eqs. (5) and (6) lead to the block diagram shown in Fig. 3, where for the sake of clarity the DDV spool dynamics of Eq. (2) and servo drive amplifier characteristics are contained inside the box in this figure. The filter dynamics and feedback gains in Fig. 3 are determined to meet the DDV actuator outer loop frequency response requirement (Hsu, Lai, Hsu, & Lee, 1991). The load actuation system can be modeled in the same way as above. The lower part of Fig. 3 describes the dynamics of the load actuation system. Most uncer-
In the above equation, KACT 1 and KACT2 represent the DDV actuator stiffness for the hydraulic systems 1 and
DDV Actuator Dynamics
DDV Act CMD _
Outer Loop Control
Inner Loop Control
GOUT(s)
GIN (s)
_
Servo AMP & DDV Dynamics Back EMF
A xv
DDV Cmd
QL Kq
DDV Disp.
Vt
_
YP
PL
2
4
+ 2A KB
2A
_
_
Flow Forces
Leakage
1 M
YP
BL
C ip + C ep 2
_
KL YB
DDV Disp. Feedback K fv
2A KB
YP/B _ K fa RAM LVDT Feedback
Force Feedback
Load Actuator Dynamics QFT Controller CMD
QFT Pre Filter
Leakage
A pL
C ip + C ep 2
_
QFT Controller
K sv
L
EHSV DYNAMICS
Servo AMP
_
K qi
i (
s n
)
2
+
2
(
s n
4
)
+
1
QL
V
L
Fig. 3. Linear model of hydraulic dynamic load simulator.
A pL t
L
PL
L
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
553
i, Command
Servo Valve DDV Actuator
Load Cell
Load Actuator Hyd. System #1
Hyd. System #2
Fly Wheel
Backup Structure
(A) Schematics of Dynamic Load Simulator Structure YB
YPD
K ACT1
KB
xA
Equivalent Surface Mass
K RD
L
K B : Backup Structure Stiffness
K RL M
K ACT2
K ACT : Actuator Chamber Stiffness
L
K RD : DDV Rod Stiffness K RL : Load Actuator Rod Stiffness
YP
(B) Equivalent Stiffness Command
SV AMP
SPOOL DYNAMICS
xv
K qi
K sv
s
Cd w
2
+2
s
+1
Ps - sign(x v ) P L
QL
1 As
_
xA
M L s 2 + cs + K EFF
Vt C ip + C ep /2
L
_
4
YP
A
PL
LOAD FLOW
1 A
Fext
K RL
(C) Model of Load Actuator Fig. 4. Dynamic load simulator stiffness and model of load actuator.
2, which are caused by trapped oil inside the two oil chambers. Fig. 5 shows the experimental frequency response with the analytic ones, which are plotted as dashed lines. Two analytic frequency responses in this figure are obtained based on Eq. (7). The upper one is calculated for the operating condition of the maximum flow gain, maximum natural frequency, and minimum damping, and the lower one for the opposite condition to the above, which are the two extreme case dynamics in Eq. (7). The deviation of experimental results from the analytical ones for the high-frequency region above 100 Hz is due to the effect of the noise corruption, and that for the low-frequency region below 1 Hz is from the weakened performance of the frequency response analyzer at this frequency. Therefore, the load actuator modeling based on Eq. (7) is considered to be acceptable.
the following specification of the load replication system.
3. QFT force controller design
These boundaries are determined from the requirements of 35 Hz bandwidth, peak overshoot o1.5%, and steady state error o1% for the closed-loop load actuation system. Besides these requirements, the stability margins of 5 dB gain and 451 phase are assumed, which are automatically satisfied when all the perturbed loop gain Bode plots due to uncertainties exist outside of 2 dB Mcircle shown in Fig. 6.
QFT is one method of designing a robust control system (Reynolds, Pachter, & Houpis, 1996; Snell & Stout, 1996; D’Azzo & Houpis, 1988). For the uncertain servo valve dynamics described in Eq. (7), twodegrees-of-freedom (DOF) force controllers which have the structure shown in Fig. 3 are designed to meet
3.1. Design specification on QFT force controller The QFT force control loop of the load actuation system is to be designed to meet the following upper and lower tracking boundary specifications: TL ðsÞ ¼
0:99 ; ðs=220 þ 1Þ ðs=280 þ 1Þ ðs=2200 þ 1Þ
TU ðsÞ ¼ 1:01ðs=242 þ 1Þ ðs=528 þ 1Þ : ðs2 =2202 þ 2 0:8s=220 þ 1Þ ðs=990 þ 1Þ ðs=2200 þ 1Þ ð9Þ
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
554 20
0
Load Actuator Disp/ V (in/V) in dB
_ 20
_
40
_ 60
_ 80
_100
_120
_140 _1 10
0
10
1
10 Frequency (Hz)
2
10
3
10
Fig. 5. Comparison of analytic and experimental bode plot of load actuator model.
3.2. QFT force controller design The templates at the frequency of oT (rad/s)A[10, 17.5, 30.8, 54.1, 95.1, 293.2, 514.8, 904, 1198, 1587.4, 2103.5, 2787.5, 3693.8, 4894.7] are shown in Fig. 6 as the dotted boundaries, which are caused by the nonlinear characteristic of the servo valve flow dynamics of Eq. (7). The relatively larger templates are observed at the servo valve natural frequency range (290–514.8 rad/ s), and templates for low- and high-frequencies are determined from the magnitude variation of the servo valve flow gain. The points designated by ‘*’ at each frequency of oT in this figure means the Nichols plot of the nominal plant, which is defined for the condition of minimum flow gain, natural frequency, and damping in Eq. (7). The QFT force controller which guarantees that the closed-loop load actuation system will meet the performance and stability requirements for the given plant uncertainties of Eq. (7) can be found by making the Nichols plot of the nominal plant loop gain function to be placed over the tracking bounds for each specific frequency. The 7 dashed lines in Fig. 6 represent the tracking bounds for the frequency of oB (rad/s)A[10, 17.5, 30.8, 54.1, 95.1, 293.2, 514.8], respectively. As shown in this figure, the Nichols plot of the nominal
plant for the frequencies of oB is located above the matching tracking bounds by selecting the QFT controller as GðsÞ ¼
0:001795ðs=154 þ 1Þ ðs=330 þ 1Þ : ðs=1700 þ 1Þ ðs2 =22002 þ 2 0:55s=2200 þ 1Þ ð10Þ
The DC gain of GðsÞ is determined such that the nominal loop gain plot at 10 rad/s is located over the corresponding tracking bound. Two zeros of GðsÞ are inserted to meet the tracking bound requirements and to give enough phase margin at the crossover frequency. Three poles of GðsÞ are required for the controller to be realizable. The pole having a frequency of 1700 rad/s in GðsÞ is required for the perturbed loop gain Nichols plot to have the gain margin of 5 dB. And the frequencies of the two complex poles are determined so high as to minimize the phase delay effect, but not so high for the GðsÞ not to be a high bandwidth controller. A slight penetration of the template at a frequency of oB ¼ 904 rad/s into the 2 dB M-circle can be seen in Fig. 6, which means an imperfect fulfillment of the stability margin requirement. However, this can be accepted as a satisfactory design,
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
555
40
30
20
QFT Loop Gain (dB)
10
0 _10 _20 _ 30 _ 40 _ 50 _ 60
_350
_ 300
_ 250
_ 200
_150 Phase (Degree)
_100
_ 50
0
Fig. 6. Nichols plot for QFT design.
considering that no significant impact on phase, or gain margin results. Loop shaping by GðsÞ of Eq. (10) guarantees only that the magnitude variations in the closedloop Bode plot due to plant uncertainties are within the range of jdðjoÞj ¼ jTU ðjoÞ TL ðjoÞj at each frequency. Therefore, a pre-filter like the one in Eq. (11) is required for the closed-loop TðjoÞ to be within the frequency domain performance specifications of Eq. (9). F ðsÞ ¼
ðs=150 þ 1Þ : ðs2 =1802 þ 2 0:7s=180 þ 1Þ
ð11Þ
The frequency response of the QFT closed-loop load actuation system is compared with the upper ðTU ðjoÞÞ and lower ðTL ðjoÞÞ performance bounds in Fig. 7. The Bode plots shown as the dashed lines in this figure are for eight extreme case dynamics from the uncertain servo valve characteristics, which are obtained from the mini–max value combination of Kqi ; on ; and B in Eq. (7). All the extreme case dynamics are almost within the desired performance bounds up to the 200 Hz. The deviation from these bounds at the high-frequency region above 200 Hz is a rather favorable characteristic
in the points of the unmodeled high-frequency dynamic and sensor noise effects.
4. Evaluation of force controller design 4.1. QFT force force loop design As shown in Fig. 7, there are slight deviations of the perturbed closed-loop frequency responses from the desired performance bounds in the frequency region around 10 Hz and the high-frequency region above 200 Hz. The effect of this poor achievements on the performance bound requirements at the mid-frequency range is well noticed in Fig. 8, which shows the step response comparison between the QFT and the following phase lead controller design of Eq. (12). Only the load actuator dynamics which is described on the lower part in Fig. 3 is considered in this simulation. KðsÞ ¼
0:000846ðs=66:4 þ 1Þ : ðs=664:1 þ 1Þ
ð12Þ
The identical design requirements are applied for the phase lead controller design, in which the nominal plant dynamics having the mid values of Kqi ; on ; and B in
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
556
Magnitude of Closed Loop Force Control System (dB)
20
0
_ 20
_ 40
_ 60
_ 80
_100
0
10
1
2
10
3
10
10
Frequency (Hz) Fig. 7. Closed-loop frequency response of force control system.
Eq. (7) are assumed. The dotted lines in these figures mean the step responses obtained from the two performance bounds of Eq. (9), and solid lines are from the eight extreme cases with the QFT and lead controller, respectively. From these time domain responses, the superiority of QFT over the conventional lead design is well understood. In case of the phase lead control, much larger overshoots and settling times are noticed for the load actuator dynamics variation specified by Eq. (7), even though the lead force control system design is satisfactorily made for the abovementioned nominal plant condition. However, the step responses for the QFT design also show some poor performances in the transient response region, which result from the imperfect achievement in the closedloop frequency boundary requirement of Fig. 6 in a mid-frequency range of 10 Hz and in high-frequency region. 4.2. Numerical simulation with the aircraft dynamics For the integrated system of an aircraft dynamics, a pitch axis flight control law, and a hydraulic actuator dynamics, the performance of the force control system proposed in Section 3 is investigated by the numerical simulation. This simulation is made for the control-loop
structure of Fig. 1, in which the taileron actuator model is replaced with the DLS model of Fig. 3. The pitch axis flight dynamics of Eq. (13) is obtained by trimming and linearizing the 6 DOF aircraft dynamics for the Mach 0.9 and sea-level flight condition. The aircraft considered in this study is a statically unstable fighter. ( ) " #( ) " # Zw a’ a Zd =Vt 1 ¼ þ d q’ q Ma M q Md "
2:9367 1 ¼ 27:7276 0:5582 " # 0:0087 þ d; 1:5682
#( ) a q ð13Þ
where a and q is the angle of attack (rad) and pitch rate (r/s), d is the taileron deflection angle (deg), Vt the Aircraft speed (ft/s), and Zw ; Ma ; Mq ; Zd ; and Md are the longitudinal force/moment stability & control derivative. Fig. 9 shows the simulation results for a 1 g normal load factor command. The nonminimum phase effect on the normal load factor due to the taileron deflection can be noticed in the first plot. The second plot represents the DDV taileron deflection angle (solid line) and load
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
557
(a) QFT Design Case
f
Load Force (lb )
15000
10000
5000
0
0
0.01
0.02
0.03
0.04
0.05 Time (sec)
0.06
0.07
0.08
0.09
0.1
0.07
0.08
0.09
0.1
(b) Lead Filter Design Case
f
Load Force (lb )
15000
10000
5000
0
0
0.01
0.02
0.03
0.04
0.05 Time (sec)
0.06
Fig. 8. Time domain step response (QFT and Lead) design.
actuator rotation angle (dashed line). Considering the sign convention, defined in Fig. 4B, the DDV (Yp ) and load actuator displacement (ðxA ÞL ) move almost the same distance amount, as they should. The third plot in Fig. 9 is the developed hinge moment (HM) for the 1 g maneuvering flight (dotted line) and the output of load actuator force control system for all the eight extreme case dynamics, which are obtained from the uncertain servo valve characteristics of Eq. (7). The mismatch of replicated hinge moments to the desired one in this plot is due to imperfect following of the load actuator travel to that of the DDV actuator. The larger discrepancy in the hinge moment replication is expected for the more stiff connection between the DDV and the load actuator, compared with the current design value of KRL ¼ 100; 000 lbf =in: Due to the QFT force controlloop design, a relatively small amount of the replicated hinge moment variation results even for the extreme change of the servo valve dynamics. The problems of the slight penetration of 2 dB Mcircle in Fig. 6 and breakaway from the tracking boundary requirement in Fig. 7 can be resolved by using the more complicated and high-bandwidth QFT compensator. However, this design demands the expense of computational delay and high-sampling rate in
the controller implementation. Therefore, the experimental verification is to be made with the current design, and a study for the enhanced force control algorithm to resolve the mismatching problem in the hinge moment replication is also to be continued.
5. Conclusion An aircraft actuation system test rig, a dynamic load simulator, which can reproduce on-ground the aerodynamic hinge moment of control surface is introduced. From the analysis on the hinge moment variations in the whole flight envelope due to the aircraft longitudinal maneuvering, a design specification for the dynamic load replication system is determined. A mathematical model for the dynamic load simulator is developed. Especially, the nonlinear dynamic characteristics of an electro-hydraulic servo valve of the load replication system is represented with a set of linear systems using the parametric uncertainties in the valve flow gain, natural frequency, and damping. A QFT force control system is designed for the dynamic load simulator to uniformly replicate on-ground aerodynamic hinge moment even for the uncertain dynamic characteristics of
558
Y. Nam, S.K. Hong / Control Engineering Practice 10 (2002) 549–558
Fig. 9. Time domain response of 1 g normal load factor input.
the load actuation system servo valve. The efficacy of the QFT force control system is verified by the numerical simulation, in which combined aircraft dynamics, pitch axis flight control law and hydraulic actuation system are considered.
References Boeing Commercial Airplane Company. (1985). Test act system validation final report. NASA CR-172525. D’Azzo, J., & Houpis, C. H. (1988). Linear control system analysis and design conventional and modern. Englewood Cliffs, NJ: McGraw-Hill. Hsu, Y. N., Lai, C. Y., Hsu, M. H., & Lee, Y. K. (1991). Development of the direct drive valve (DDV) actuation system on the IDF aircraft. International pacific air and space technology conference and 29th aircraft symposium. Japan. (pp. 2312–2322).
Merritt, H. (1967). Hydraulic control systems. New York: Wiley (pp. 79–98). MOOG. (1997). Servo and proportional system catalog (pp. 95–98). Reynolds, O. R., Pachter, M., & Houpis, C. H. (1996). Full envelope flight control system design using quantitative feedback theory. Journal of Guidance, Control, and Dynamics, 19(1), 23–29. Roskam, J. (1979). Airplane flight dynamics and automatic flight controls. Roskam aviation and engineering corporation. Schaefer, W. S., Inderhees, L. J., & Moynes, J. F. (1991). Flight control actuation system for B-2 advanced technology bomber. Technical Bulletin, 153(MOOG), 1–8. Snell, S. A., & Stout, P. W. (1996). Quantitative feedback theory with a scheduled gain for full envelope longitudinal control. Journal of Guidance, Control and Dynamics, 19(5), 1095–1101. Vieten, K. W., Snyder, J. D., & Clark, R. P. (1993). Redundancy management concepts for advanced actuation systems. AIAA/ AHS/ASEE aerospace design conference (pp. 1–9).