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1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME AND TECHNOLOGY (IJMET) ISSN 0976 – 6340 (Print) ISSN 0976 – 6359 (Online) Volume 4, Issue 6, November - December (2013), pp. 08-18 © IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2013): 5.7731 (Calculated by GISI) www.jifactor.com IJMET ©IAEME EXPERIMENTAL VALIDATION OF A NOVEL CONTROLLER TO INCREASE THE FREQUENCY RESPONSE OF AN AEROSPACE ELECTRO MECHANICAL ACTUATOR Praveen S. Jambholkar, Prof C.S.P. Rao Cybermotion Technologies, Hyderabad, Dept. of Mechanical Engineering, National Institute of Technology, Warangal ABSTRACT For aerospace applications, such as an air-to-air missile, the system specifications are very high, since the target is a supersonic aircraft capable of sharp manoeuvring. Fin actuation system of such missiles is known as Electro Mechanical Actuators. Unlike general motion control systems, noise level and speed of response are critical. In Electro Mechanical Actuator there is no trajectory generator. The target position has to be reached at the earliest. There is no luxury of a controlled acceleration and declaration. The common challenge in EMA design of various Aerospace projects is that they generally have poor frequency response, primarily due to phase lag. Phase lag results due to reciprocator nature of these actuators across a NULL position .Control systems such as Proportional Integral Differential (PID), Pole Placement , Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian are not ideal for this class of actuators since on their own, they cannot solve the primary problem of phase lag .The main theme of this paper is to reduce the phase lag of an Electro Mechanical Actuator (EMA) by a novel concept, “Piecewise Predictive Estimator (PPE)”. The PPE technique in conjunction with an existing controller can increase the frequency response by up to 15% without any adverse effects on noise characteristics of the EMA. An experimental result based on EMA of an air-to-air missile has been used and instrumentation based on Lab View is used. There is an increase in performance and it matches with the simulation results we achieved using Simulink. Keywords: PID (Proportional Integral Derivative), LQR (Linear Quadratic Regulator), PPE Piecewise Predictive Estimator), BLDC (Brush Less DC), EMA (Electro Mechanical Actuator), SDRE (State Dependent Ricatti Equation) 8
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME 1. INTRODUCTION In this class of motion control application, noise is a major concern. We have to satisfy two criteria. Step response will show speed of response as well as noise levels. Bodes plot will show the system bandwidth in hertz, primarily limited by the -90 degrees phase lag , as well as giving us phase margin , which should be more than 60 degrees. PID controllers can be either be tuned for high gain, high bandwidth, but will result in high noises. LQR controllers by very definition minimize the cost function consisting of state error and effort required. We require speed of response at any cost. Various sources of process noise are gear or ball screw backlash, BLDC motor [1] cogging, commutation current disturbances, MOSFET switching noise, DC-DC converter noise, Load variations. Sources of measurement noises are position sensor noise (Potentiometer or LVDT), ADC quantization noise, control circuit’s EMI coupling to sensor feedback path. As mentioned earlier, the two primary objectives for EMA design are low noise and high speed of response (bandwidth). This paper proposes a unique combination of signal processing and control technologies to achieve these two objectives of low noise and high bandwidth response. 2. HARDWARE DESCRIPTION 2.1 Rotary EMA Rotary EMA consists of a Brush Less DC (BLDC) motor. The output is a rotary motion from +250 to -250 across a null position. A planetary gear box and a sector gear with a high gear ratio of 207:1. The position feedback is through a potentiometer (pot). Fig. 1 Cross sectional view of Rotary EMA 2.2 Linear EMA Linear EMA consists of BLDC motor connected to a ball screw. Here the linear motion is across a null position. 2.3 BLDC Motor DC motor has an ideal torque vs. speed characteristics. BLDC motors consist of permanent magnet rotor and stator has a set of coils. Many disadvantages of DC motors are overcome, such as torque density, etc. Another advantage of using a BLDC motor is that its behavior in terms of current, torque, voltage and rpm is linear. 9
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME 3. MODELLING OF ELECTRO MECHANICAL ACTUATOR The modelling of the Electro Mechanical Actuator [2] [9] is done in stages. By using the mechanical properties and electrical properties and equating with Newton’s and Kirchhoff’s laws, we get the transfer function. u = Output of the plant model (voltage). Motor Parameters: J = Inertia Constant. Kt = Torque Constant B= Friction Coefficient. . R = Resistance L = Inductance Kp = Gain Parameters (J=0.01, K=0.01N.m/A, L=330 µH , R=0.39 , b=0.1). This can be converted to a continuous state space model using Matlab command ss (tf), or directly by replacing mechanical parameters in the A, B, C and D matrices Ra + La θ = wt BM Gear + Kgear Ea = Kawr Load – TL – Fig. 2 DC Motor di = dt – k R I ia – a ωr + ua La La La (1) Newton 2nd law ΣT = Vα = J dω dt (2) Te = k a ia (3) Tviscous = Bωr (4) dωr I = dt J (5) = (Te − Tviscous − TL ) I (kaia − Bωr − TL ) J di R K I =– ia – ωr + ua dt La La La Va (6) 10
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME dω r I = (k a ia − Bmωr − TL ) J dt (7) d dt S .θ r ( s ) = ωr (s ) S= K I R ω ( s ) + Va ( s ) S + ia (s ) = − L La La (8) B I I S + ω r (s ) = k a ia ( s ) − TL ( s ) J J J (9) The dynamic equation in state space form d dt ra − i La = θ k a J ka La Bm − J − i I θ + L V 0 (10) Fig.3 Simulink Block Diagram of Servo Actuated by DC Motor 4. CONTROLLER DESIGN 4.1. PID Controller Design A Proportional integral derivative controller is a generic control loop feedback mechanism (controller) and commonly used as feedback controller. In PID controller, the ‘e’ denotes to be tracking error which is been sent to the controller. The control signal u from the controller to the plant to the derivative of the error. ∫ u = k p e + k1 edt + k D de dt (11) 11
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME Parameter of PID controller were choose to accomplish design objectives in terms of fast, non-overshooting transient response and accurate steady state operating small differential gain is required because it stabilizes the system, while integral gain influences fast transient responses. The designer should know the process characteristics, and accordingly must decide on the combination and values of P, I, D parameters to keep [4]. PID controller may not be optimal in many cases since increasing gain will also increase process noise leading to instability. Designers have attempted to modify PID equations to improve its performance [5] [6]. 4.2 LQR Design LQR family of controllers are very effective for linear systems. LQR controllers are designed to minimize the cost function comprising of state error and input effort [7]. ∞ J= ∫ (x T ) Qx + Ru 2 dt (12) 0 ∞ ∫ J = [(trackingerror ) 2 Q + (input ) 2 R]dt (13) 0 J is cost function to be minimized; R and Q are two matrices of the order of state and input. Q and R matrices are selected by designers by trial and error. If Q is large, to keep J small, input u has to be big. If R is large, to keep J small, input u must be small. And control input u is u = − R −1 B T Px (t ) (14) Where P is calculated by solving the Ricatti equation [9] u = Px + AT P − Q + PBR −1 B T P (15) Below figure shows the designed LQR state feedback configuration. Figure 4: Linear Quadratic Regulator Structure 12
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME LQR control can be used for non-linear, time-varying plant by using SDRC (State Dependent Ricatti Equation) [8], where the plant model is based on Euler-Lagrange equations [10]. . X = A( x )x + B ( x )u (16) 4.3 Piecewise Predictive Estimator (PPE) Predicting / estimating the target for an air-to-air missile is critical. One approach is to model the target acceleration as first order Gauss- Markov process [11]. Here an attempt has been made to develop a predictor to enhance the hit capability of an airto-air missile EMA. We name this Piecewise Predictive Estimator (PPE) since we can have finite piecewise estimation of the target position. The origins of PPE are in numerical calculus. Z transform is the foundation of most signal processing. Zx n = xn+1 (17) Delta operator is defined as ∆xn = xn +1 − xn (18) Del operator is defined as ∇xn = xn − x n−1 ∇= (19) ∆ 1+ ∆ xn +1 = (20) 1 (21) (1 − ∇ )xn Using equation (17), we can predict the next sampled value. And also, xn+ 2 = ∇ 2 xn = ∇(∇xn ) (22) If a missile has to track a moving target, it is desirable to be able to make a judicious prediction of future location of the target. Since the target does not follow any continuous function, we can only approximate the target trajectory piecewise, where each piece is continuous within this region. Since Taylor’s series representation is valid for a continuous function, we have, f (x ) = f (0 ) + f ' (0) + x 2 '' x 3 '' ' f (0) + f (0) + .. (23) 2! 3! Expanding equation (2) as Taylor’s series, we have ( ) xn+1 = 1 + ∇ + ∇ 2 + ∇ 3 + ...... xn (24) 13
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME Using equation we can have a finite prediction horizon. Although finite, this prediction can improve the target tracking capability considerably by reducing the phase lag without undue increase in gain. This will serve the dual purpose to reduce the phase lag and to reduce the system noise, since we are not resorting to gain increase. The algorithm of PPE is as follows. This algorithm remains the same in Simulink’s embedded Matlab function block C code , as well as in C code of Code Composer Studio which is used to compile firmware for Texas Instruments 32 bit DSP[3] TMS320F2812. Block diagram of this controller shown below figure 7; Fig. 5 Block Diagram of DSP TMS320F2812 based Controller Fig. 6 Simulink Block Diagram of Plant Model with PPE 14
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – (IJMET), 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME Fig. 7 Flow Chart for PPE Embedded Function 15
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME 4. EXPERIMENTAL VALIDATION 4.1 Experimental setup The experimental setup consists of an Electro Mechanical Actuator from an Aerospace project, 28V, 30A power supply. Frequency Response Analyzer, DSP processor, Digital drive and Function generator. A sweeping sine wave from 40Hz to 0Hz at ±1V peak to peak is applied as command input. Input and output full scale are ±10V corresponding to a rotary motion of ±25°. Input and output signals are given to the Frequency Response Analyzer to generator Bede’s plot of phase lag, gain vs. frequency. The bandwidth of a system is both measure of tracking speed of the system. We also get stability information through gain margin and phase margin. Electro Mechanical Actuator PC Analyzer Fin control Command Command DAQ Feedback Feedback Power Supply Fig. 8 Block Diagram of Experimental Setup of EMA System Fig. 9 Experimental Setup of EMA System 4.2 Experimental Result We have prepared an experimental setup consisting of Electro Mechanical Actuator, Frequency Response analyser, Power supply and sinusoidal signal generator to find out the effect of stochastic filter along with a PD controller. For the same noise levels of 100mV for a +-10V feedback signal, the bandwidth jumped from 22 Hz to 25 Hz. This is a significant increase in applications where low noise and high speed response are critical. 16
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME Fig. 10 Bandwidth Response (22 Hz) with PID Controller Fig 11: Bandwidth Response (25 Hz) with PID and PPE CONCLUSION We have experimentally verified that there is a significant improvement in frequency response due to reduction in phase lag at higher frequencies, from 22Hz without PPE, to 25Hz with PPE, thus meeting our goal. 17
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 6, November - December (2013) © IAEME REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] Armando Bellini, Stefano Bifaretti , Stefano Costantini , “A Digital Speed Filter for Motion Control Drives with a Low Resolution Position Encoder” , AUTOMATICA 44 (2003) 1-2, 67-74. Wai Phyo Aung, “Analysis on Modelling and Simulink of DC motor and its Driving System Used for Wheeled Mobile Robot”, World Academy of Science, Engineering and Technology, 32 2007. Padmakumar S. , Vivek Agarwal, Kallol Roy,”A Tutorial on Dynamic Simulation of DC Motor on Floating Point DSP “, World Academy of Science, Engineering and Technology , 53 2009. Astrom K.J. and Hagglund T., “PID Controllers: Theory, Design and Tuning”. Instrument Society of America, 1995, 343p. Milan R. Ristanovic, Dragan V. Lazic, Ivica Indin, “Non Linear PID Controller Modification of the Electromechanical actuator system For Aerofin Control With a PWM Controlled DC Motor “,Facta Universities, series : automatic control and Robotics, Vol. 7 No. 1, pp131-139, 2008. Milan Risanovic, Dragan Lazic, Ivica Indin, “Experimental Validation of Improved Performance of Electro Mechanical Aerofin Control System with a PWM Controlled DC Motor, FME Transactions (2006) 34, 15-20. Brain D.O. Anderson, John B. Moore, “Optimal Control: Linear Quadric Methods”. Prentice Hall information and System Sciences Series, 1989, pp25-35. Bogdanov, M. Carlsson, G. Harvey, J. Hunt , R. Kieburtz , R. van der Merve , and E. Wan, “ State Dependent Ricatti Equation control of a small unmanned helicopter”, Proceedings of the AIAA Guidance Navigation and Control Conference , Austin , TX, August 11–14 , 2003 Ruba M.K. Al-Mulla Hummadi ,”Simulation of Optimal Speed Control for a DC Motor using Linear Quadratic Regulator (LQR)”, Journal of Engineering ,Number 3, Vol. 18 March 2012. N.M. Singh , Jayant Dubey , and Ghanshyam Laddha , “Control of Pendulum on a Cart with State Dependent Ricatti Equations, International Journal of Computer and Information Engineering, 3:2 2009. Peter S. May beck , James E. Negro, Salvatore J. Cusumano, and Manuel De Ponte, Jr. , “A New Tracker for Air-to-Air Missile Targets , IEEE Transactions On Automatic Control, Vol. AC-24, No. 6 , December 1979. Amged S. El-Wakeel, F.Hassan, A.Kamel and A.Abdel-Hamed, “Optimum Tuning of PID Controller for a Permanent Magnet Brushless DC Motor”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 2, 2013, pp. 53 - 64, ISSN Print: 0976-6545, ISSN Online: 0976-6553. Vilas S Bugade and Dr. Y. P. Nerkar, “Comparison of Brushless D. C. (BLDC) and Printed Circuit D. C. Motors for the Electric Bicycle Application”, International Journal of Electrical Engineering & Technology (IJEET), Volume 1, Issue 1, 2010, pp. 144 - 156, ISSN Print : 0976-6545, ISSN Online: 0976-6553. Praveen S. Jambholkar and C.S.P Rao, “Design of a Novel Controller to Increase the Frequency Response of an Aerospace Electro Mechanical Actuator”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 4, Issue 1, 2013, pp. 92 - 100, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359. 18
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