SVPWM Variable Structure Control of Induction Motor Drives P. Alkortaȥ, O. Barambones, A. J. Garrido and I. Garrido E.U.I.T.I. de Eibarȥ / E.U.I.T.I. de Bilbao University of the Basque Country Eibar, Spain Email:
[email protected],
[email protected]
Abstract— This paper presents a new proposal of speed vector control of induction motors based on robust adaptive VSC (Variable Structure Control) law and its experimental validation. The presented control scheme incorporates the SVPWM (Space Vector Pulse Width Modulation) instead of the traditional current hysteresis comparator. The SVPWM improves the quality of the stator currents, reducing the harmonics, while maintains the main characteristics that is usual in this kind of algorithm, like the fast response and good rejection to uncertainties and measurement noises. This regulator is also compared with the PI (Proportional Integral) controller designed in the frequency domain, in order to prove the good performance of the proposed controller. The two controllers have been tested using various simulation and real experiments, taking into account the parameter uncertainties and measurement noise in the loop signal, in the rotor speed and in the stator current. This work shows that the VSC regulator is more efficient than the traditional PI controller in both adverse conditions and suitable conditions. Finally, some practical recommendations for real experiment implementations are also given.
I.
INTRODUCTION
AC induction motors have been widely used in industrial applications such machine tools, steel mills and paper machines owing to their good performance provided by their solid architecture, low moment of inertia, low ripple of torque and high initiated torque. Some control techniques have been developed to regulate these induction motors servo drives in high-performance applications. One of the most popular technique is the indirect field oriented control method [1], [2], [3]. The field-oriented technique guarantees the decoupling of torque and flux control commands of the induction motor, so that the induction motor can be controlled linearly as a separated excited D.C. motor. However, the control performance of the resulting linear system is still influenced by uncertainties, which are usually composed of unpredictable parameter variations, external load disturbances, and unmodelled and nonlinear dynamics. Therefore, many studies have been made on the motor drives in order to preserve the performance under these parameter variations and external load disturbances, such as nonlinear control, optimal control, variable structure system control, adaptive control and neural control [4], [5], [6].
1-4244-0755-9/07/$20.00 '2007 IEEE
In the past decade, the variable structure control strategy using the sliding-mode has been focussed on many studies and research for the control of the AC servo drive systems [7], [8], [9], [10].
Fig. 1. Diagram of PI speed control of induction motor.
The sliding-mode control offers many good properties, such as good performance against unmodelled dynamics, insensitivity to parameter variations, external disturbance rejection and fast dynamic response [11]. These advantages of the sliding-mode control may be employed in the position and speed control of an AC servo system. Since V. Utkin proposes in 1993 [11] the sliding mode design principles and applications to electric drives, a lot of authors have used this advanced technique in induction motors speed control. The most important characteristics that may offer this control algorithm are the good rejection to parameter uncertainties and to measurement noises, good behavior with non-modeled dynamics and fast response. Recently, it has been proposed [12] an induction motor speed control based on VSC algorithm that may eliminate the speed tracking error in spite of the presence of important uncertainties and measure noises. However, the control scheme proposed in [12] uses a current control based on a hysteresis-band which may cause an undesirable harmonics generation. In the present paper the author proposes a SVPWM control that improves the quality of the stator currents and reduces the harmonics generation that is usual in the traditional current hysteresis comparator. This report is organized as follows. The PI speed controller design is introduced in Section II. Then, the proposed variable structure robust speed control is presented in Section III. In the
1195
Section IV, the variable structure speed control with current PI controller is introduced. The induction motor speed control simulation and experimental results are presented in Section V. Finally some concluding remarks are stated in the last Section. II. PROPORTIONAL INTEGRAL SPEED CONTROLLER DESIGN The PI control algorithm is well known classic control algorithm. This control strategy has a great popularity, and a extended use in the industry because its simple design and good performance. Moreover, many times the PI control is used as a reference in order to compare other controllers with it. As it is well know, the closed loop stability of the motor with the PI controller is guaranteed if the PMȦ margin phase has a positive and suficiently high value. Therefore, the gains of the PI controller may be calculated ussing the frequency domain [13].
From the Fig. 2 diagram the open loop transfer function is obtained as: Ki · 1 § (3) TFOL ( s ) Zm ¨ Kp ¸ s ¹ sJ © Considering that in the cross frequency the system has a unit gain (4) TFOL ( s ) Z 1 m
s jZc
and that the system phase is
arg TFOL ( s ) Zm
180º PM Z
s jZc
It is obtained the following expressions for the PIȦ controller parameter’s tg( PM Z ) Ki (6) Kp
Zc
JZ c
Ki
2
1 tg( PM Z )
Fig. 2. Diagram for speed loop PI controller design
Figure 1, shows the PI clasic control for a induction motor and the function of the blocks that appear in this diagram are: The ABCÆdq block get the is space vector from the iA, iB e iC motor stator currents, using the Park’s transformation [3], while the dqÆABC block makes the reverse Park’s transformation. It should be noted that this transformations make use of the rotor flux angular position, șe and therefore this angle should be calculated using an indirect method. The design of the PI controller is quite easy but in this control scheme the induction motor parameters should be precisely know. The design consists on the one hand, in calculating the PI controller parameters, Kp and Ki, for the Zm mechanical rotor speed loop, and on other hand, in calculating the PI controllers parameters, Kpi and Kii. for the two current loops, isd and isq . The calculation of the PI controller parameters for the speed loop is based on the diagram shows in Fig. 2. We may choose a band width of Ȧc rad/s and a margin phase of PMȦ dB in open loop. The motor electromagnetic torque [3] has the following expression (1) in stationary state, taking into account that the torque and rotor flux components are decoupled in the rotating reference frame,
Te
3 p Lm \ rd isq 4 Lr
K T isq
(1)
where KT is the torque constant (2) and
