Torque Control for DC Servo Motor Using Adaptive Load Torque Compensation

SELECTED TOPICS in SYSTEM SCIENCE and SIMULATION in ENGINEERING Torque Control for DC Servo Motor Using Adaptive Load Torque Compensation CHANYUT KHAJORNTRAIDET JIRAPHON SRISERTPOL School of Mechanical Engineering, Institute of Engineering, Suranaree University of Technology Address: Nakhon Ratchasima 30000 THAILAND [email protected] Abstract: - A torque control system is an important process in industries. The value of torque which is generated by DC servomotor depends upon a motor current. Since the torque control system uses the estimated current from an observer, it will receive an effect from torque disturbance (load torque) during an operation. The incorrect estimated current from the observer affects a current feedback signal. This paper presents a technique for torque control of DC servomotor by using adaptive load torque compensation. The load torque can be compensated to the observer, the result show that the estimated current error from the observer is reduced. Therefore, this method can be applied to improve an efficiency of the torque control system and estimate the load torque of DC servomotor. Key-Words: - Adaptive compensation, Observer, and Torque control system 1 Introduction 2 Mathematical Descriptions The DC servomotors are widely used for a variety of The permanent magnet DC motor is used to acquire actuator applications. When a system interacts with the data as a DC servo motor. The torque control system of environment, it will receive disturbance from load DC motor is controlled by the armature current (ia). The torque. The torque control system is an important speed of the system is depended on armature voltage system to control a force when the system interacts with (Va) when the field current is held constant. An the environment during the task [1]. The output torque armature circuit is shown in Figure 1. The differential of the motor is proportional to the input current. The equations of the armature controlled are as follows: torque control method, is used direct current control, is degraded by disturbance torque in the actuator [2]. Iωɺ = − b ω + Tm − T L (1) There are many applications where the load torque di V− V = La + R ⋅ i (2) fluctuates and a fluctuating load torque should be a b a dt a a considered to maintain a constant speed in the drive where VK= ⋅ω and T= K ⋅ i machines [3-4]. For the servo application, significant b b m t a parameter variations are often arising by unknown loads [5]. Generally, the load torque of a DC servomotor is difficult to measure in practice but it can be estimated. The Lyapunov’s direct method is a high performance to estimate the DC motor load torque [6]. The load compensation method which is composed of deadbeat observer is well-known method [7]. Lyapunov theory is a well know method that guarantee the stability of adaptive algorithms for adjusting parameters in adaptive Fig. 1 Armature Circuit systems [8]. This paper describes method to control 2 torque of DC servomotor using adaptive load torque where I is the moment of inertia (kg·m ), Kt is the compensation. The simulation results show that the torque constant (N·m/A), Kb is the electromotive force method can be used to improve the efficiency of DC constant (V·s/rad), TL is the load torque (N·m), b is the servomotor torque control system under loading linear approximation of viscous friction (N·m·s/rad), Ra condition and estimate load torque of the system. is the resistance (Ω ), La is the inductance (H), ia is the ISSN: 1792-507X 454 ISBN: 978-960-474-230-1 SELECTED TOPICS in SYSTEM SCIENCE and SIMULATION in ENGINEERING armature current (A), ω is the angular velocity (rad/s), A PI controller is used in outer loop control. The current Va is the armature voltage (V), Vb is the back EMF (V) of the observer is feedbacked to the torque control In the servo applications, the unknown load is a system before it is conversed to torque of the motor. significant parameter. The propose scheme for DC The equation of PI controller is shown in Eq.5. servomotor torque control is shown in Figure 2. The K GK= + i (5) outer loop controller is designed to achieve a fast and PI p s accurate response under loading operation. 2.4 Adaptive Load Torque Compensation of Control System An adaptive system can self-modify to compensate the load torque of the observer automatically to accommodate changes. Consider the DC servomotor system with the variable torque. The equation of DC servomotor in second order form is K Rb R b K K t ɺɺa ɺ a b t Va =ω + + ω + + ω Fig. 2 DC servomotor torque control system (6) LILILILIa a a a 1 ɺ Ra +TTL + L 2.1 Full-Order State Observer Design ILIa A cost and a complexity of the control system increase Equation (6) can be rewritten as as the number of required sensor increases. A state b V=ωɺɺ + a ω ɺ + a ω + α Tɺ + α T (7) observer can be designed to estimate the state variables 1 a 2 1 2LL 1 of DC servomotor via angular velocity measurement. Introducing new parameters defined by Fortunately, if the system is completely observable, then it is possible to estimate the states that are not measured. Kt Ra b K b K t Ra b b1 =, a1 = + , a2 = + The equations of full-order observer are LILILILIa a a a R 1 α=a , α = ɺ ˆ 1 2 Iωˆ= − b ω ˆ + Kt i a − T L + L1 e (3) LIIa ɺ L iˆ= V − R ⋅i ˆ − Kωˆ + L e (4) The equation of full-order state observer in second order a a a a a b 2 form is Kt ɺɺ Ra b ɺ Ra b K b K t where L1 and L2 are the observer gains, (^) is the Va =ωˆ + + ωˆ + + ωˆ LILILILI estimated state and an error is e =ω − ωˆ . a a a a 1 ˆɺ Ra ˆ +TTL + L 2.2 Current Control Loop ILIa Since an inner loop controller of the system is operated (8) by a current feedback from the motor system, the output When we known the value of system parameter exactly, torque of the motor is a proportion of the motor current. the equation (8) can be simplified, yielding A block diagram of current controlled loop is shown in ɺ b V=ωɺɺˆ + a ω ˆɺ + a ω ˆ + α Tˆ + α T ˆ (9) Figure 3. In practice, the torque control system will uses 1 a 2 1 2LL 1 the current feedback from the observer in current control loop. The G is the integral in the inner loop control From equation (7) and (9) the error between the plant I and the observer is described by (GI=1/s). ɺ ˆɺ ˆ eɺɺ= − a2 e ɺ − a 1 e −α 2 ()() TLL − T − α1 TLL − T (10) Lyapunov’s direct method: Lyapunov function is selected as ɺ2 ˆ ˆɺ a1 2 e 1 ɺ ˆɺ 2 V(,,,) e eɺ TLL T= e + +()TTLL − 2 2 2γ 2 Fig. 3 Current control loop 1 ˆ 2 +()TTL − L 2γ1 2.3 Outer Loop Controller (11) ISSN: 1792-507X 455 ISBN: 978-960-474-230-1 SELECTED TOPICS in SYSTEM SCIENCE and SIMULATION in ENGINEERING received the disturbance torque because of the incorrect where γ1 and γ 2 are adaptive gains. Then, we get the time derivative of V as estimated current from the observer. Therefore, the adaptive load torque compensator was be used to compensate load torque to the observer. The result of ˆɺ dV 1 ɺ ˆɺ dTL =a1 eeɺ + ee ɺɺɺ +() TLL − T − torque compensation to the torque control system is dt γ dt 2 shown in Figure 5 and 6. ˆ 1 ˆ dTL +()TTLL − − Load Disturbance γ1 dt 0.12 (12) Using equations (10) and (12), we obtain 0.1 0.08 ˆɺ dV 2 ɺ ˆɺ 1 dTL = −a2 eɺ +( TLL − T )( − − eɺα 2 ) dt γ 2 dt 0.06 1 dTˆ ˆ L ɺ +(TT − )( − − eα ) (N.m) Torque Load LL 1 0.04 γ 1 dt (13) 0.02 ˆ ˆɺ When the rates of change of TL and TL are 0 ɺ 0 5 10 15 20 25 dTˆ Time (sec) L ɺ = −γ2e α 2 dt Fig. 4 Disturbance torque ˆ dTL = −γeɺ α 0.25 dt 1 1 (14) Thus 0.2 Desired torque dV 2 (15) = −a2 eɺ Output torque dt 0.15 The time derivative of Lyapunov function (V ) is Torque (N.m) Torque 0.1 negative semi-definite. The stability of the system will be stable. 0.05 3 Simulation Results 0 0 1 2 3 4 5 6 7 8 9 10 This section demonstrated the simulation result of Time (sec) DC servomotor torque control system when the Fig. 5 Dynamic response of torque control in the case of system and controller parameters are as follow: the step function input with load torque compensation −5 2 I=1.4 × 10 kgmradK ⋅ / ,t = 0.052 NmA ⋅ / 0.6 K= 0.057 Vsradb⋅ / , = 1.0 × 10−6 Nmsrad ⋅ ⋅ / b 0.58 −3 RLa =2.5 Ω ,a = 2.5 × 10 H 0.56 3 Kp =80 A / N ⋅ m , Ki = 2.5 × 10 A / N ⋅ m 0.54 The simulation of the torque control system was be 0.52 applied the disturbance torque as the step function, as 0.5 Desired torque Torque (N.m) Torque 0.48 shown in Figure 4. In the simulation, there were three Output torque patterns of desired inputs.

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