Real Time Implementation of Fuzzy Adaptive PI-sliding Mode Controller for Induction Machine Control

In this work, a fuzzy adaptive PI-sliding mode control is proposed for Induction Motor speed control. First, an adaptive PI-sliding mode controller with a proportional plus integral equivalent control action is investigated


INTRODUCTION
Sliding mode control (SMC) has for long been known for its capabilities in accounting for modeling imprecision and bounded disturbances. It achieves robust control by adding a discontinuous control signal across the sliding surface, satisfying the sliding condition. However, in SMC, the high frequency chattering phenomenon that results from the discontinuous control action is a severe problem when the state of the system is close to the sliding surface [1], [2].
To simplify the equivalent control of the classical SMC and ease the design task for practicing engineers [3], [4], an adaptive PI-sliding mode controller (APISMC) is used which the equivalent control action based on the proportional plus integral control law with generalized hard-switching parameters [5]- [7]. A potential advantage of this strategy is its ability of using the undistorted nonlinear model of the physical system in a simulation based design process [6]. In various nonlinear system control issues, fuzzy controller is recently a popular method to combine with sliding mode control method that can improve some disadvantages in this issue. Comparing with the classical control theory, the fuzzy control theory does not pay much attention to the stability of system, and the stability of the controlled system cannot be so guaranteed. In fact, the stability is observed based on following two assumptions: First, the input/output data and system parameters must be crisply known. Second, the system has to be known precisely. The fuzzy controller is weaker in stability because it lacks a  [8], [9]. Nevertheless, the concept of a sliding mode controller (SMC) can be employed to be a basis to ensure the stability of the controller [10]. The feature of a smooth control action of FLC can be used to overcome the disadvantages of the SMC systems (chattering phenomenon) [11], [12]. This is achieved by merging of the FLC with the variable structure of the APISMC to form Adaptive Fuzzy PI-Sliding Mode Controller (FAPISMC). In this hybrid control system, the strength of the sliding mode control lies in its ability to account for modeling imprecision and external disturbances while the FLC provides better damping and reduced chattering.
To demonstrate the effectiveness of the proposed control scheme, we apply the proposed scheme to the speed control of a three-phase induction motor using a dSPACE DS1104 digital signal processor (DSP) based real-time data acquisition control (DAC) system, and MATLAB/Simulink environment. The proposed controller has been achieved, fulfilling the robustness criteria specified in the sliding mode control and yielding a high performance in implementation to induction motor speed control. This paper is organized as follows: In section II, we present the indirect field-oriented control of the IM, the synthesis of the Adaptive PI-Sliding Mode Controller is outlined in section III. In section IV we present the synthesis of the Fuzzy Adaptive PI-Sliding Mode Controller. Experimental results and performance of the controllers are compared in section V. Finally, some remarking conclusions are summarized in Section VI.

INDIRECT FIELD-ORIENTED CONTROL OF THE THE INDUCTION MOTOR
The machine considered in this paper, is a three-phase squirrel-cage asynchronous machine. The dynamic model of the ∆-connected induction motor can be expressed in the d-q synchronously rotating frame as [13], [14]: where σ is the coefficient of dispersion and is given by The main objective of the vector control of induction motors is, to control independently the flux and he torque as DC machines, this is done by using a d-q rotating reference frame synchronously with the rotor flux space vector [6], [13]. In ideally field-oriented control, the rotor flux linkage axis is forced to align with the d-axes, and it follows that: Considering (3) and (4), the torque equation becomes analogous to that of the dc machine and can be described as: The decoupling control method with compensation is to obtain the inverter output voltages such that: By using, the placement poles method the proportional and integral gains of the PI speed controller ( p K and i K ) are determined by [6]: Where the desired poles are: , the value of ρ is given in appendix. The configuration of the overall control system is shown in Figure 1. It mainly consists of an induction motor, a ramp comparison current-controlled pulse width modulated (PWM) inverter, a slip angular speed estimator, an inverse park, an outer speed feedback control loop.

SPEED CONTROL OF THE IM BY THE ADAPTIVE PI-SLIDING MODE CONTROLLER
A Sliding Mode Controller is a Variable Structure Controller (VSC). Basically, a VSC includes several different continuous functions that can map plant state to a control surface, and the switching among different functions is determined by plant state that is represented by a switching function [1], [2]. The following is a possible choice of the structure of a sliding mode controller [3], [6]: where e u is called equivalent control which is used when the system state is in the sliding mode [5], [15]. k is a constant and it is the maximal value of the controller output. s is called switching function because the control action switches its sign on the two sides of the switching surface 0 = s is defined as [5], [16]: e e s ⋅ + = λ  (11) where: e is the error between the speed reference and real speed of the IM ( λ is a constant ) sgn(s is a sign function, which is defined as: The control strategy adopted here will guarantee the system trajectories move toward and stay on the sliding surface 0 = s from any initial condition if the following condition meets: where η is a positive constant that guarantees the system trajectories hit the sliding surface in finite time [17]. Using a sign function often causes chattering in practice. One solution is to introduce a boundary layer around the switch surface [6], [17]: (15) ψ is the constant factor defines the thickness of the boundary layer, ) / ( ψ s sat is a saturation function that is defined as: The function between k u s / and ψ / s is shown in the Figure 2. This controller is actually a continuous approximation of the ideal relay control [5], [17], [18]. The consequence of this control scheme is that invariance of sliding mode control is lost. The system robustness is a function of the width of the boundary layer. To simplify the equivalent control and ease the design task for practicing engineers, Nandam and Sen [6] have proposed an equivalent control action based on the proportional plus derivative control law. A potential advantage of this strategy, which the authors did not address, is its ability of using the undistorted nonlinear model of the physical system in a simulation based design process. Y. Li and al [19] extends this control strategy by incorporating an integration term and to form a generic controller structure. In this study,  (17) With generalized hard-switching parameters are:

SPEED CONTROL OF THE IM BY THE FUZZY ADAPTIVE PI-SLIDING MODE CONTROLLER
In this section, a fuzzy sliding surface is introduced to develop a sliding mode controller, which the expression ) / ( ψ s sat k u s ⋅ − = is replaced by an inference fuzzy system for eliminate the chattering phenomenon. The if-then rules of fuzzy sliding mode controller can be described as [6], [20] Figure 4 and Figure 5. Figure 6 is the result of defuzzified output us for a fuzzy input s. The block diagram of the fuzzy adaptive sliding mode controller for induction motor speed control is shown in Figure 7.

EXPERIMENTAL RESULTS
The Figure 8 shows the photo of the experimental banc test which consist of the following elements: a) Three-phase cage induction motor with the following characteristics: ∆connected, four poles, 1.5 kW, 1426 min−1, 230/400 V, 50 Hz with the 1024 points integrated incremental coder. b) Three-phase rectifier, c) Electrical insulation and adaptation card and current sensor LEM LA25-NP for measuring stator currents (realized in the laboratory), d) Brushless rotary torque sensor, e) Powder brake, f) Measuring device for mechanical quantities, g) Measuring device for electrical quantities, h) Load mechanical torque simulator, i) Three-phase power supply, j) Relay card for automatic brake control with dSPACE, k) The dSPACE DS1104 with ControlDesk GUI software for release 6.2.   Figure 10. Experimental results of the control of the IM by the FAPISMC under reference variation

CONCLUSION
In this paper a new adaptive fuzzy PI-sliding mode controller is proposed for induction motor speed control, which combines the fuzzy logic with sliding mode control. In this proposed controller, the fuzzy sliding surface is introduced to develop a sliding mode controller, which the expression ) / ( ψ s sat k u s ⋅ − = is replaced by an inference fuzzy system for eliminate the chattering phenomenon. The proposed scheme has not only attenuate the chattering extent of the adaptive fuzzy PI-sliding mode controller but has presented satisfactory performances (minimal overshoot, minimal rise time, best disturbance rejection) for different operating regimes of the IM. Experimental results show that the performance and disturbance rejection with the adaptive fuzzy PI-sliding mode controller is significantly improved as compared to a system with adaptive PI-sliding mode controller.