Anti-windup Robust Controller Considering Saturation of Current and Speed for Speed Servo System

Anti-windup Robust Controller Considering Saturation of Current and Speed for Speed Servo System

D. Balachandra K. Mani

PG Student, Dept. of EEE Asst Professor, Dept. of EEE Siddharth Institute Of Engg. And Technology, Puttur Siddharth Institute Of Engg. And Technology, Puttur

Chittoor (Dt), Andhra Pradesh, India. Chittoor (Dt), Andhra Pradesh, India.

B. Ramesh

Asstprofessor, Dept. of EEE

Siddharth Institute Of Engg. And Technology, Puttur Chittoor (Dt), Andhra Pradesh, India.

Abstract In general, a speed servo system has a controller with an integrator, such as a PI controller. A robustly stable PI-controller is designed and implemented in order to control the AC motor speed. Wind-up affect due to actuator saturation is removed by implementing anti-windup compensator. When PI controller output variable is saturated by a current and/or voltage limiter, a wind-up phenomenon and an unstable response often occur. We have already proposed an anti-windup algorithm considering voltage saturation for speed servo system that regulates the current response smoothly and stably. Moreover, we considered the saturation of current and speed for position servo system, and the anti-windup algorithm regulated the speed response stably. However, the speed response has the overshoot, which is caused by current saturation and the speed controller not keeping the response performance. This paper proposes an anti-windup algorithm considering the motor dynamics and current saturation for speed servo system of SPM synchronous motor. The experimental and numerical simulation results confirm that the speed servo system having the proposed algorithm regulates the motor speed smoothly and stably.

Keywords: Anti-windup controller, robust control, Servo Permanent Synchronous Motor, PI controller.

1. INTRODUCTION

   A robust servo system is important for improving the performance of motion control systems in several industry applications. A PI controller has been widely used for the speed control of variable-speed motor drives [1]. In this motor drives, a large step change in the speed command will cause the generated current

   command from the speed controller to exceed the prescribed maximum value and the current command will cause the generated voltage command from the current controller to exceed the prescribed maximum value, which determines the allowable current of the motor and the maximum output voltage of the inverter respectively. Consequently, the PI controller output variable will be saturated by the current and voltage limiters.

   This problem may occur because the integral state accumulates control errors even while the output variable saturates, often leading to a wind-up phenomenon. This phenomenon is called integrator windup and can lead to a large overshoot, long settling times and an unstable response. Therefore, a design method for a limitation compensator considering output variable saturation is required. For this several anti-windup control methods have been researched. For example, while the plant input variable is different from the PI controller output variable, a realizable command, instead of the command, is applied to the controller in order to restore the consistency of the integral state [2]. Furthermore, the general framework for the anti-windup design having a co-prime factorization for a feedback controller has been presented [3]. The design criteria are as follows: 1) The nonlinear closed-loop system must be stable; 2) When there is no saturation, the closed- loop performance should meet the specifications for the linear design; and 3) When the saturation occurs, the closed-loop performance should degrade gracefully from the linear performance.

   For ideal anti-windup PI control, it is desirable that the control performance satisfies the specifications determined by the PI gains in the linear region. The anti- windup control method considering the vector control condition has been applied to a current controller in order

   to restore the consistency of the integral state. Furthermore, we have already proposed an anti-windup algorithm considering the saturation of current and speed for

   position servo system [9]. In addition, we have already proposed a high performance inverter control method considering the motor driving conditions from the shaft acceleration torque command and the omitted voltage caused by voltage saturation [10]. The proposed method combines the advantages of two different over modulation techniques, and obtains both a quick speed response in the transient state and a small value of total harmonic distortion (THD) in the steady state. However, if the inner- loop of the current controller operates at a high performance, the speed response will overshoot owing to current saturation in the outer-loop of the speed controller, and the speed controller will not keeping proper response performance. In order to overcome this problem, this paper proposes a limitation compensator design in order to keep the response performance for speed servo system. This anti-windup algorithm considering motor dynamics and current saturation is applied to the speed controller in order to restore the consistency of the integral state. The simulation results confirm that the speed servo system having the proposed algorithm regulates the motor speed smoothly and stably.

2. SPEED CONTROLLER BASED ON PI CONTROLLER

   The block diagram for a speed control system based on a PI controller is shown in Fig.1. The open loop transfer function Gos() in this speed control system is defined as

   Fig 1: Block diagram of speed control system

   The block diagram of a speed servo system based on anti- windup PI controllers are shown below.

   Fig 2: Speed servo system based on anti-windup PI controllers.

   Gos s = sKps +Kis Kt

   (1)

   s sJ

   where ps is the proportional gain of the speed controller,and is is the integral gain of the speed controller.

   When the angular frequency of the PI corner pi is sufficiently smaller than the bandwidth of the speed controller sc, the open-loop transfer function Gos() in this speed control system is approximated as

   Gos s Kps Kt

   sJ

   (2)

   ps is calculated such that the open-loop transfer function amplitude becomes one (i.e., /Gos() /= 1). Therefore,

   ps and is are designed as

   Fig 3: Simulink model of speed servo system based on anti windup PI controllers.

   LIST OF MOTOR PARAMETERS AND SPECIFICATIONS OF TESTED SERVO SYSTEM

   Kps =

   (3)

   1. Rated output 200[W]

      Kis = . (4)

      where subscript denotes a nominal parameter. The speed control gain is decided as stated above and can be designed for a speed servo system having arbitrary bandwidth.

   2. Rated speed 3000[min1]

   3. Rated torque 0.64[Nm]

   4. Number of pole pairs 4

   5. Inertia 2×105[kgm2]

   6. Stator resistance 2.47[]

   7. Stator inductance 9[mH]

   8. Magnetic flux 0.066[Wb]

   9. -axis current 2.42[A]

   10. Bandwidth of current controller c 3000[rad/s]

   11. Bandwidth of speed controller sc 300[rad/s]

   12. Angular frequency of PI corner 60[rad/s]

   13. Sampling period of current control 100[s]

   14. Sampling period of speed control 200[s]

3. ANTI-WINDUP PI CONTROLLER CONSIDERING OUTPUT VARIABLE SATURATION

   Moreover, the equation for the control variable is defined in (7), and the equation for the PI controller is define in (8).

   = +( u) (6)

   u= s (7)

   sKp +Ki

   y = sKp +Ki(u*u) Ki F(s)(yy ) (8)

   s s

   The equations of a PI controller are defined as

   = +(u*u) (5)

   where * is the command, is the control variable, and

   is the PI controller output variable.

   The command is expressed by (7) and (8).

   u = u* 1 s+Ki F(s)(yy ) (9)

   Kp s+Ki /Kp

   1. Conventional method

      When the conditioning gain () = 1/Kps , the PI controller output variable is not saturated by the limiter, and is expressed as

      Fig 4: Block diagram of PI controller with limiter

      = u* 1

      (y ) (10)

      Fig 5: Block diagram of PI controller

      The anti-windup PI controller is applied to the speed controller and the -axis current controller. The actual motor speed becomes smaller than the speed command owing to the field forcing caused by -axis voltage saturation [10]. The integral state and the state variable of the PI controller are regulated as

      y = Kp . e+Ki . e (11)

      S

      When the PI controller output value exceeds the prescribed maximum value //, the PI controller output value / / is saturated at the prescribed maximum value / /. Then, the PI controller output variable is

      =

      Kp

   2. Proposed method considering motor dynamics

      (12)

      approximately equal to the plant input variable . However, when deviation is reduced to almost the same level as the prescribed maximum value / /, the PI controller output variable is not equal to the plant input variable . This problem may occur because the integral state accumulates control errors even while the output variable saturates, often leading to a wind-up phenomenon. Fig.4 shows the block diagram of a PI controller considering output variable y is saturated by using limiter. Then the difference between the controller output variable and the plant input variable is calculated. The calculated value is multiplied by the conditioning gain F(). Then, its calculated value is fed back to the integral state, and the state variable of the PI controller is regulated.

      The design of a limitation compensator considering the motor dynamics and current saturation is detailed in this section. The new conditioning gain F() in this design considers the state variable of a PI controller plus the motor dynamics. Accordingly, the speed servo system having the proposed algorithm can keep the response performance of the speed controller. The block diagram converts Fig.4 into Fig.6(a).

      In addition, the equivalent block diagram conversion by using block diagram reduction techniques are shown in Fig.6 .

      The transfer function 1 H () is given as

      1+( )

      Accordingly, occurring of the PI controller output variable prevents integrator windup.

      Here, a new PI controller is defined as shown in

      1-H(s) =

      1+

      (13)

      Fig.5. The PI controller output variable is not saturated by the limiter, and the equation for is defined in (6).

      In the conventional method, the speed response will

      overshoot owing to current saturation and the speed controller not keeping the response performance. Thus, the

      integral state and state variable of PI controller should be more regulated. The new conditioning gain F() is determined under the condition that the numerator of the transfer function 1 H() is small. In the proposed method, F() is designed under the condition that the numerator of the second term of the transfer function 1 H () is zero as

      The block diagram of a speed servo system in the proposed method consists of two anti-windup PI controllers. The anti-windup PI controller considering motor dynamics is applied to the speed controller, and the anti-windup PI controller is applied to the -axis current controller [10].

      This implies that

      s (

      ) = 0 (14)

   3. Comparison between proposed and conventional methods

      Here, the conditioning gain in conventional method F()

      F(s) =

      / (15)

      =1/ substitutes to the transfer function C() and the transfer function 1 H () as

      C() = (16)

      The conditioning gain in proposed method F() =/ Kp substitutes to the transfer function C () as

      C(s) = Kps+ (

      ) (17)

      +

      (a)

      Moreover, the equivalent block diagram converts Fig.6(c) into Fig.6(e). The -axis current iqp in proposed method is given in (18).

      iqp =

      (18)

      +

      (b)

      3500

      3000

      Rotor speed (rpm)

      2500

      2000

      1500

      Step input

      Rotor speed

      (c)

      1000

      500

      0

      -500

      2

      1.5

      1

      d axis current(Amp)

      0.5

      0

      -0.5

      -1

      -1.5

      -2

      -2.5

      0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

      Time (seconds)

      1. Rotor speed Vs Time

         (d)

         -3

         0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

         Time (seconds)

      2. d- axis current Vs time

         4

         3

         q axis current(Amp)

         2

         1

         0

         -1

         -2

         -3

         (e)

         Fig 6: Equivalent block diagram of PI controller considering with limiter plus motor dynamics

         -4

         0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

         Time (seconds)

      3. q- axis current Vs time

         20

         15

         Output variable

         10

         5

         0

         -5

         -10

         -15

         p element I element

         REFERENCES

         1. D. W. Novotny and T. A. Lipo:Vector Control and Dynamics of AC Drives, Oxford (1996)

         2. R. Hanus, M. Kinnaert and J. L. Henrotte:Conditioning Technique, a General Anti-windup and Bumpless Transfer Method, Automatica, Vol.23, No.6, pp.729-739 (1987)

         3. M. V. Kothare, P. J. Campo, M. Morari and C. N. Nett:A Unified Framework for the Study of Anti-Windup Design,

            -20

            0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

            Time (seconds)

      4. output variable Vs time

   Fig 7: Simulation results of step speed response

4. SIMULATION RESULTS

   The simulation and experimental results of step speed response of the proposed method as shown in Fig.7 . In conventional method, the speed response has the overshoot caused by current saturation at the deceleration area and the speed controller not keeping the response performance. In contrast, the speed servo system having the proposed anti-windup control method regulates the motor speed smoothly and stably. In addition, the proposed method can keep the response performance of the speed controller and the settling time is shortened. With step load torque, the proposed anti-windup control method regulates the motor speed smoothly and stably. The proposed anti- windup control method regulates the motor speed smoothly and stably.

5. CONCLUSION

This paper proposes a design method for a limitation compensator in order to keep the response performance for speed servo system. The proposed anti- windup algorithm applied to the speed controller considers the motor dynamics and current saturation. In this paper, The simulation results confirm that the proposed method regulates the integral state of the speed controller and the motor speed of the speed servo system smoothly and stably. Hence, the proposed method can keep the response performance of the speed controller and the settling time is shortened.

Automatica, Vol.30, (1994)

1. Y. Peng, D. Varncic and R. Honus:Anti-windup, Bumpless, and Conditioned Transfer Techniques for PID Controllers, IEEE control System Magazine, Vol.16, No.4, pp.48-57 (1996)

2. S. Tarbouriech, M. Turner:Anti-windup design: an overview of some recent advances and open problems, Control Theory and Applications, IET, Vol.3, pp.-19 (2009)

3. Hwi-Beom Shin, Jong-Gyu Park:Anti-Windup PID Controller With Integral State Predictor for Variable-Speed Motor Drives, IEEE Trans.on Industrial Electronics, Vol.59, No.3, (2012)

4. K. Ohishi, E. Hayasaka, T. Nagano, M. Harakawa, T. Kanmachi:Highperformance speed servo system considering Voltage saturation of a vector-controlled induction motor, IEEE Trans. on Industrial Electronics, (2006)

5. M. Sazawa, T. Yamada, K. Ohishi, S. Katsura:Robust High Speed Positioning Servo System Considering Saturation of Current and Speed,IEEE International Conference on Industrial Technology, pp.866-871 (2006)

6. K. Takahashi, K. Ohishi, High-performance Inverter Based on Shaft Acceleration Torque for AC Drives, IEEE Trans. On Industrial Electronics, Vol.PP, No.99, pp.1-12 (2012)

7. Muhammad Rehan,Abrar Ahmed, Naeem Iqbal, Sk Shahi mohammed Experimental comparison of different antiwindup schemes for an AC motor speed control System.2009 International Conference on Emerging Technologies .