 Open Access
 Total Downloads : 542
 Authors : D. Balachandra, K. Mani, B. Ramesh
 Paper ID : IJERTV3IS071286
 Volume & Issue : Volume 03, Issue 07 (July 2014)
 Published (First Online): 01082014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Antiwindup 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 PIcontroller is designed and implemented in order to control the AC motor speed. Windup affect due to actuator saturation is removed by implementing antiwindup compensator. When PI controller output variable is saturated by a current and/or voltage limiter, a windup phenomenon and an unstable response often occur. We have already proposed an antiwindup 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 antiwindup 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 antiwindup 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: Antiwindup controller, robust control, Servo Permanent Synchronous Motor, PI controller.

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 variablespeed 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 windup 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 antiwindup 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 antiwindup design having a coprime factorization for a feedback controller has been presented [3]. The design criteria are as follows: 1) The nonlinear closedloop 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 closedloop performance should degrade gracefully from the linear performance.
For ideal antiwindup 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 antiwindup 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 outerloop 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 antiwindup 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.

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 antiwindup 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 openloop transfer function Gos() in this speed control system is approximated as
Gos s Kps Kt
sJ
(2)
ps is calculated such that the openloop 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)

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.

Rated speed 3000[min1]

Rated torque 0.64[Nm]

Number of pole pairs 4

Inertia 2Ã—105[kgm2]

Stator resistance 2.47[]

Stator inductance 9[mH]

Magnetic flux 0.066[Wb]

axis current 2.42[A]

Bandwidth of current controller c 3000[rad/s]

Bandwidth of speed controller sc 300[rad/s]

Angular frequency of PI corner 60[rad/s]

Sampling period of current control 100[s]

Sampling period of speed control 200[s]


ANTIWINDUP 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

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 antiwindup 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

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 windup 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
1H(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 antiwindup PI controllers. The antiwindup PI controller considering motor dynamics is applied to the speed controller, and the antiwindup PI controller is applied to the axis current controller [10].
This implies that
s (
) = 0 (14)

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)

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)

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)

q axis current Vs time
20
15
Output variable
10
5
0
5
10
15
p element I element
REFERENCES

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

R. Hanus, M. Kinnaert and J. L. Henrotte:Conditioning Technique, a General Antiwindup and Bumpless Transfer Method, Automatica, Vol.23, No.6, pp.729739 (1987)

M. V. Kothare, P. J. Campo, M. Morari and C. N. Nett:A Unified Framework for the Study of AntiWindup 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)


output variable Vs time

Fig 7: Simulation results of step speed response


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 antiwindup 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 antiwindup control method regulates the motor speed smoothly and stably. The proposed anti windup control method regulates the motor speed smoothly and stably.

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)

Y. Peng, D. Varncic and R. Honus:Antiwindup, Bumpless, and Conditioned Transfer Techniques for PID Controllers, IEEE control System Magazine, Vol.16, No.4, pp.4857 (1996)

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

HwiBeom Shin, JongGyu Park:AntiWindup PID Controller With Integral State Predictor for VariableSpeed Motor Drives, IEEE Trans.on Industrial Electronics, Vol.59, No.3, (2012)

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

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.866871 (2006)

K. Takahashi, K. Ohishi, Highperformance Inverter Based on Shaft Acceleration Torque for AC Drives, IEEE Trans. On Industrial Electronics, Vol.PP, No.99, pp.112 (2012)

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 .