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Intelligent control of DC motor driven electromechanical fi n actuator Milan Ristanovic a n Zarko C ojba sic b Dragan Lazic a aUniversity of Belgrade Faculty of Mechanical Engineering Department of Automatic Control Kraljice Marije 16 11120 Belgrade 35 Serbia bUniversity of Ni s Faculty of Mechanical Engineering Department of Mechatronics and Control Aleksandra Medvedeva 14 18000 Ni s Serbia a r t i c l e i n f o Article history Received 18 March 2011 Accepted 25 February 2012 Available online 21 March 2012 Keywords Electromechanical actuator Aerofi n DC motor Current motor driver Genetic algorithms Fuzzy control a b s t r a c t In this paper modeling simulation and control of an electromechanical actuator EMA system for aerofi n control AFC with permanent magnet brush DC motor driven by a constant current driver are investigated Nonlinear model of the EMA AFC system has been developed and experimentally verifi ed in actuator test bench Model has been used as the starting point for PID position controller synthesis To improve performances of the system computational intelligence has been applied Genetic PID optimization genetic algorithm GA optimized fuzzy supervisory PID control and fi nally GA optimized nonlinear PID algorithm modifi cation are proposed Improved transient response and system behavior have also been experimentally validated Schinstock fax 381 11 3370364 E mail address mristanovic mas bg ac rs M Ristanovic Control Engineering Practice 20 2012 610 617 draw inspiration from nature biology and artifi cial intelligence Computational intelligence Engelbrecht 2007 techniques such as fuzzy logic neural networks and genetic algorithms constitute the main areas of the fi eld with applications to nonlinear identifi cation nonlinear control design controller tuning system optimization and encapsulation of human operator expertise In this paper intelligent control is used in conjunction with conventional control in order to encompass vast experience in system development provide for high demands by improving performance and to overcome analytical diffi culties resulting from system nonlinearities and specifi c motor driver that has been developed 2 System description 2 1 Electromechanically actuating aerofi n system Aerofi n control AFC system considered here is the control of the missile using four grid fi ns The grid fi ns confi guration is presented in Fig 1 By defl ecting them moments are generated about the center of mass which in turn rotate the airframe The resulting incidence angles generate aerodynamic forces which accelerate the vehicle in the desired direction Zipfel 2000 The missile autopilot sends roll pitch and yaw commands dx dyanddz to the AFC system Before they can be utilized they have to be separated into individual fi n commands i e anglesai where i 0 1 2 3 Each actuator module can convert the refer ence fi n command into an actual surface defl ection and requires tight independent position control of the surface defl ection usually less then 101 2 2 Hardware and instrumentation The AFC testing system is schematically presented in Fig 2 The actuator assembly consists of the Maxon RE 30 permanent magnet brush DC motor with integrated Maxon planetary gear head GP 32 and a 3 7 1 reduction which drives the screw shaft SRCW 10 3 R with precision SKF roller nut SH 10 3 R The actuator s assembly output shaft is connected to the roller nut via lever mechanism driving the grid fi n Fig 3 On the motor s rear side an incremental encoder is mounted and fi xed to the rotor s shaft Incremental encoder is Maxon Encoder MR Type M with resolution of 256 pulses per revolution Pulses from the encoder are forwarded to the control computer The control computer is an onboard computer OBC consist ing of two digital signal processing DSP modules based on Analog Devices ADSP 21065L processor Namely one DSP module is used for angle measurements while the other realizes control algorithm All electrical connections between the DSP modules in the OBC are via a motherboard The OBC is connected with the industrial PC via a serial communication providing bi directional transfer of set points and acquisition data Main control loop is performed on 2 kHz sampling rate while the serial communica tion with PC operates on 500 Hz The OBC receives autopilot commands converts them into individual fi n angles and calcu lates control based on control algorithm Control signal is pulse width modulated and two control fl ags are forwarded to the motor driver As mentioned before the motor driver has been designed as to be simple and reliable In order to be controlled it needs one fl ag for enabling the current output and the other for changing the current direction The output current is adjustable thus the driver can be used for different motors Once the driver is enabled the x y z x x z z y y 0 1 2 3 O Fig 1 AFC system Fig 2 EMA AFC testing system M Ristanovic et al Control Engineering Practice 20 2012 610 617611 constant current either positive or negative supplies the motor setting the shaft into rotation The motor shaft is kept around zero by duty cycle of around 50 providing the rotor shaft oscillating Having in mind the large gear ratio in the actuator assembly the magnitude of the oscillations is attenuated thus it can be neglected compared to the gear backlash In order to simulate inertial load the grid fi n has been mounted on the actuator assembly A calibrated torsion bar is connected to the opposite end of the output shaft and cantilev ered with the load cell to the test bench stand The torsion bar is designed to produce load torque induced by the aerodynamic force It has been calibrated to give maximum torque for max imum fi n defl ection angle e g 101 Actual fi n angle defl ection is measured by the potentiometer fi xed to the output shaft The industrial PC has been used for acquisition of the load torque and defl ection angle Fig 4 3 System modeling Mathematical model of the permanent magnet DC motor presented here emphasizes mechanical part of the system Thus the motor torque Tm is proportional to the magnetic fl ux which is proportional to the armature current IA Tm KMIA 1 where KMis the motor torque constant KM Due to motor shaft rotation there is induced back electro motor force Emin the rotor coils Back electromotor force is proportional to the rotor angular velocityom Em Keom 2 where Keis the motor electrical constant The torque constant and the motor electrical constant are the same for an ideal motor For real motors they are similar Voltage equation of the rotor circuitry is Um RAIA LA dIA dt Em 3 where RAis the armature resistance while LAis the armature inductance Combining Eqs 1 3 yields LA RA dTm dt Tm KM RA Um Keom 4 Ratio LA RA defi nes motor electrical time constantte The two moments of inertia Jmand JLare equivalent moments of inertia of the rotating motor components and the actuator assembly moment of inertia respectively In almost all cases the motor inertia will be signifi cant because of the large mechanical advantage of the screw drive system Referring the inertia for each of the rotating components in the actuator assembly to the motor shaft results JL Jfin Jlever N2 Z2 g Jscrew Jpg 5 where J fi n is the fi n moment of inertia Jleveris the moment of inertia of the lever in the screw drive mechanism Jscrewis the screw shaft moment of inertia Jpgis the planetary gearhead moment of inertia Zg is the effi ciency of the screw drive system and N is the total transmission ratio Now the following differential equation describes dynamics of the motor J dom dt Tm TL 6 where J Jm JLis the total moment of inertia Letymbe the angle of the motor shaft rotation then dym dt om 7 Fig 3 Actuator assembly Fig 4 Actuator test bench M Ristanovic et al Control Engineering Practice 20 2012 610 617612 Two kinds of load are taken into account a friction torque and an aerodynamic torque The friction torque can be modeled by Tfric C sign ym B ym 8 where C Tf N and sign ym 1for ymZ0 1for ymo0 9 The load torque Tafinduced by the aerodynamic forces is proportional to the fi n defl ection anglea thus Taf Ta N a 10 The factor of proportionality Tadepends on maximum aerody namics torque and maximum fi n defl ection angle Ta Tamax amax Finally for the screw lever mechanism the total gear ratio is N 2p cosa l h 11 where l is the normal distance from the roller nut and the output shaft axes and h is the screw shaft pitch Obviously the gear ratio depends on the fi n defl ection angle but for small angles it can be taken that cosa 1 For large angles this approximation is usually not allowed due to considerable error Eqs 1 11 are used to develop nonlinear simulation model of the EMA AFC system But the motor driver has still not been modeled Such current driver can be modeled with the nonlinear ity type of sign with the gain of maximal current Imax that is time sampled with the frequency of interapting routine of the controller Instantaneous value of the current between the sub sequent time samples is held and hence modeled by the zero order hold Thus the continuous control signal from the OBC is sampled fi rst at 2 kHz and then clipped to the maximum current The clipped current signal is held and forwarded to the motor The simulation environment is presented in Fig 5 while representa tion of the motor driver is shown in Fig 6 The following model coeffi cients defi ned by mechanical design parameters and motor specifi cations provided by vendor have been used Jfin 1 5 10 2kg m2 Jlever 5 10 3kg m2 Jpg 0 15 10 6kg m2 Jscrew 2 10 6kg m2 Jm 3 33 10 6kg m2 N 395 Ta 108 86 N m rad Tf 10 N m KM 0 026 N m A RA 0 611O LA 1 2 10 4H Imax 6 5 A omax 9500 min 1 mechanical time constant of the motor is 3 ms and the gear backlash is 0 11 4 Controller design 4 1 PID and GA optimized PID control First approximation of the considered controller was simple yet reliable PID position controller Synthesis of the PID position controller u t Kpe t Ki Z t 0 e t dt Kd de dt 12 where e t aref t a t is the error arefis the reference andais the measured fi n angle has been done using simulation model since it was not possible to linearize the current motor driver due to two level current output Hence the extensive simulation of the nonlinear model was very helpful for controller parameters selection Finally parameters of the PID controller were chosen on the basis of numerous experiments with the system as to accomplish design objectives in terms of fast non overshooting transient response and accurate steady state operating Small differential gain in 12 is required because it stabilizes the system while integral gain is responsible for steady state error Proportional gain infl uences fast transient responses and it has been increased until the control reached its limitations Following previous guidelines parameters of the PID control ler were selected using nonlinear simulation model to obtain maximal performances and were adopted as Kp 1 5 V rad Ki 0 1 V s rad and Kd 0 1 V s rad Just as it was in this case tuning of PID controllers is frequently diffi cult and time consuming while widely accepted automated Ziegler Nichols method does not yield optimal closed loop performance and its application range is rather limited Astr om and ii linear systems where nonlinear PID control is used to achieve performance not achievable by linear compensation Armstrong et al 2001 Here the interest is obviously taken in nonlinear PID control applied to nonlinear system with the objective of improved performance Actually the EMA AFC system performed well with GA optimized PID when the error signal is large i e the transient response is fast but when the error approaches zero system becomes slow This is quite reasonable because for large values of the reference input anglesaref the load torque from aerodynamic force is maximal In addition there are considerable effects of friction and gear backlash Since the fast response and large bandwidth is critical for the application of the EMA AFC system the following nonlinear modifi cation of the error signal is proposed ec t sign e t ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi 9e t 9 q 15 The error function 15 has a large gradient around zero i e it behaves as scheduled parameters of the PID Now modifi ed PID controller becomes u t Kpec t Ki Z t 0 ec t dt Kd dec dt 16 The reason that nonlinear PID controller performs better is that it provides higher gain when error is small and lower gain 051015 0 0 5 1 absolute error deg SMALLMEDIUMLARGE degree of memebership Fig 9 Primary fuzzy sets for decisive input variable 01020304050 2 4 2 6 2 8 3 3 2 3 4 3 6 x 105 Best fitness Mean fitness Fitness value Generation Fig 10 GA optimization of parameters of two PIDs 00 511 52 15 10 5 0 5 10 15 Time s deg ref deg u V ref deg u V control reference deg fin angle Fig 11 Response of the optimally tuned fuzzy supervisory system M Ristanovic et al Control Engineering Practice 20 2012 610 617615 when error is large It completely agrees with the intuition obtained from working with practical problems As a matter of fact many fuzzy logic controllers and gain scheduling controllers exhibit this kind of characteristics on its error surface but demanding somewhat more complex implementation Gao Hu Gao Huang Han 2001 In order to obtain optimal performance from the NPID control system the same offl ine GA optimization as with conventional PID controller has been conducted using the same fi tness func tion and optimization parameters and with similar convergence as presented in Fig 10 In this case optimal parameters for the NPID have been obtained as Kp 1 548 V rad Ki 0 355 V s rad and Kd 0 128 V s rad the best obtained fi tness was J 249 102 while the performance of obtained GA optimized NPID controller is discussed in Section 5 5 Results 5 1 Comparison of the proposed controllers Performances of proposed controllers have been summarized in Table 1 which overviews the integral of the absolute error IAE criterion Astr om H agglund 1995 values for all controllers for square reference of magnitude 101 lasting 4 s with frequency of 1 Hz Smaller IAE value indicates better performance i e smaller overall output error 5 2 Experimental results Experimental validations of the proposed PID GA optimized PID GA optimized fuzzy and GA optimized modifi ed PID con trollers in the EMA AFC testing system have been conducted As during the genetic optimization square wave reference input with the maximum allowed magnitude 9armax9 101 was used for testing Fig 12 presents step responses of the proposed controllers on the rising and falling edge of the reference signal It can be seen that when the error is large all controllers have almost the same behavior what was actually expected However GA optimized PID and NPID controllers show improvement compared to the experi mentally tuned PID and NPID controllers Namely the rise time with GA optimized PID is considerably smaller and transient response is very close to the NPID controller On the other hand GA optimized NPID provided even better behavior than experimentally tuned NPID Both rise time and settling time were improved and all proposed controllers provide non overshooting transient response It can be noticed that the chartering in control signal only occurs in NPID algorithm since even for the small error the gradient of the error function 15 is large around the zero making the control sensitive to backlash but it does not negatively infl uence the performance On the other hand chattering in both PID and GA optimized PID control signals are practically negligible Another design objective was the improvement of the closed loopsystemfrequencyresponse InFig 13onecansee experimentally determined closed loop magnitude and phase response for the PID controller Frequency response has been determined for sine wave input signal of 101 magnitude and frequency range from 0 1 to 3 Hz with increments of 0 1 Hz Same procedure has been conducted for modifi ed PID controllers NPID GA optimized PID and GA optimized NPID System with GA optimized NPID controller has the best frequency response slightly better than with NPID and GA optimized PID controllers but considerably broader bandwidth than the closed loop system with PID controller It should be noticed that the magnitude and phase are attenuated considerably after 2 7 Hz because the sine Table 1 Comparison of controller performances ControllerIAE PID experimentally suboptimally tuned548 36 NPID experimentally suboptimally tuned517 46 PID GA optimally tuned503 15 NPID GA optimally tuned498 20 Fuzzy supervisor with GA tuned PIDs496 16 00 20 40 60 81 10 8 6 4 2 0 2 4 6 8 10 Time s deg ref deg u V PID PID GA NPID NPID GA NPID GA u PID u PID GA u NPID u ref reference Fig 12 Comparison of the square wave responses for different controllers 0 11234 5 3 2 5 2 1 5 1 0 5 0 Frequency Hz Magnitude dB L LPID 0 11234 5 45 40 35 30 25 20 15 10 5 0 Frequency Hz Phase deg NPID GA PID NPID GA Fig 13 Experimental magnitude and phase shift system response M Ristanovic et al Control Engineering Practice 20 2012 610 617616 wave response is saturated by the slew rate i e the maximum angular velocity of the rotor shaft is reached 6 Conclusion A nonlinear model of the electromechanical actuator system for aerofi n control has been presented and used as a basis for design and testing of several control systems Based on the experiments performed on the specially designed EMA AFC testing system simulating real operating conditions genetic optimization of both PID controller and nonlinear mod ifi cation of the PID controller has been proposed Also a form of fuzzy gain scheduling of PID controller has been introduced and likewise combined with off line genetic optimization strategy Especially proposed control solutions have been designed in order to match practical requirements taking into account con structive characteristic of the AFC assembly and the aerodynami