Novel approach to direct adaptive fuzzy control applied to the asynchronous machine

. This paper presents an advanced direct adaptive fuzzy control for asynchronous machine which uses the theory of approximation and the theory of Lyapunov to establish a parametric adaptation law ensuring the stability and boundedness of all the control signals and the tracking error. In the direct approach, the fuzzy system is used to describe directly the control law and the parameters of the fuzzy system are directly adjusted to achieve the control objectives. Through the obtained results, stable direct adaptive fuzzy control generalized has proved a great effectiveness and a strong robustness in the presence of parameter variations and disturbances.


INTRODUCTION
The pragmatic use of scientific developments has led to the appearance of modern electric variable speed drive industrial processes. Its optimal operation and its control characteristics directly influence the cost and quality of production.
In this context industrial currently are opting for static converter -asynchronous motor squirrel cage sets because of there robustness, there low cost, and also for the availability of static converters with very high switching frequencies and very sophisticated signal processing means. These technologies allow the implantation of enough complex control strategies.
Nowadays, a large number of publications were dedicated to the problem of nonlinear systems control. The control of complex systems runs up against several difficulties such us the presence of nonlinearities, uncertainties and the computational complexity. This requires intelligent controllers with large capacity for learning and decision making in uncertain environments. Since conventional regulators require a perfect knowledge of the system model to deal with, which does not give a great performance, especially in the presence of modeling errors and / or parametric variations of the system.
The fuzzy logic control find significant interest from researchers, because the fuzzy systems have the ability to deal with fuzzy variables and induce a control law based on approximate reasoning, as an approximate reasoning we refer to a type of reasoning that is not very accurate or very inaccurate [8] -[9]. This type of system is very useful when the process control presents some uncertainties or unknown variables.
However, to keep a consistent performance in the presence of true uncertainties, the use of adaptive control is in most cases inevitable. Adaptive fuzzy control has been the subject of intensive research during the last decade [10] - [11] -[12] - [13] - [14] - [15] - [16]. Therefore, the combination of adaptivity and uncertainty has enabled researchers to derive adaptive fuzzy controllers.
In most work on fuzzy control of the asynchronous machine, the control laws are fixed parameters.
These control techniques have shown their limits during parametric variations of the system. To overcome this drawback, we propose to work with an approach to adaptive control based on fuzzy systems.
There are two approaches to adaptive fuzzy control which are indirect and direct adaptive fuzzy control [17] - [18] - [19] -[20] - [21]. The application of the indirect approach on the asynchronous machine does not guarantee the convergence of the tracking error to zero and the control calculation is performed in two stages, which requires a relatively high [7] computation time.
To overcome these drawbacks, we propose a stable direct adaptive fuzzy generalized control; this technique uses the theory of approximation and the theory of Lyapunov to establish a parametric adaptation law ensuring the stability and boundedness of all the control signals and the tracking error.
In the direct approach, the fuzzy system is used to describe directly the control law and the parameters of the fuzzy system are directly adjusted to achieve the control objectives.

STABLE DIRECT ADAPTIVE FUZZY CONTROLGENERALIZED
There are several types of direct adaptive fuzzy controller. Among them the adaptive fuzzy control linearized or application the direct control strategy requires the measurement of the derivative of flow and of speed [7]. To overcome this problem, we propose a new type of control namely the stable direct adaptive fuzzy control generalized or the control law is based on Lyapunov stability theory and the theory of approximation by fuzzy systems.

Structure of the control
Consider a system with a dynamic model of the controller is described by the following equation: Our objective is to generate a control law for the output to be able to follow its reference y d . For this, we assume that the derivative of the function F (X) satisfies the following condition [20] - [21].
where  c  nn subspace is a state where in the path may vary as a result of the control F 0i is a positive constant and known.
To synthesize the control law we assume that the nonlinear functions F (X)and G i (X)are replaced by fuzzy systems of Takagi-order, based on the M-rules. where  fi ,  gi are the optimal parameters and  f ,  g are errors reconstructions of functions F (X) and G i (X)such that: According to the fuzzy system parameters used W ,  fi and  gi are organized as follows:

Control synthesis
In this work, our goal is to develop a fuzzy adaptive control law for the direct dynamic system represented by (1). We first determine the dynamics of the error filtered according to the fuzzy model, the desired trajectory and the input vector. Then the Lyapunov approach is used to ensure the convergence of the filtered error, the boundedness of adaptive parameters and all control signals [20] - [21].

APPLICATION TO THE ASYNCHRONOUS MACHINE
In the fixed reference relative to the rotating field. The flow dynamics  r and the rotating speed pulsation  r of three-phase asynchronous motor are given by the following equations: Adaptive fuzzy controllers speed and flow provide currents i dsref and i qsref providing regulation of i ds and i qs respectively. The reference currents are obtained by the passage of i dsref and i qsref by a coordinate transformation. Comparison of current references to real currents provides control of each arm of the inverter. By the application of the direct adaptive fuzzy control generalized for regulating the speed of the asynchronous machine, the system is put in the following form:

International Letters of Chemistry, Physics and Astronomy Vol. 55
Where the dynamics of the flow depends only on the control input i dref and flow  r then, the dynamic of the speed depends mainly on the input control i qref and speed. The implementation of this control requires the approximation of functions F and G i by fuzzy systems:

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ILCPA Volume 55 Figure (2) schematically illustrates the principle of the adaptive fuzzy control generalized when setting the asynchronous machine.
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SIMULATION RESULTS
Given the nature of the "sign" function contained in the term of the sliding mode, the control is discontinuous in the vicinity of the origin (S = 0), this can cause nuisance switching (chattering) command. To overcome this problem, we replaced the "sign" function by a continuous "smooth" function: Figures (3), (4) respectively illustrates the responses obtained when starting of the asynchronous machine for a set point speed 209rad / s and load change on reversal of the direction of travel. We can see that the speed perfectly follows its reference, rejection of the disturbance is fast, the stator current is limited during the transitional regime and the rotor flux is maintained, it follows its reference value according to the axis (d) with a quadrature component (q) zero.

ROBUSTNESS
To test the robustness of the generalized fuzzy adaptive control, we made a parametric change on the rotor resistance, on the rotor and stator inductances well as the mutual inductance. We can conclude from the results illustrated in Figure (5), the direct adaptive fuzzy control stability generalized exhibits strong robustness in the presence of parametric variations. Dynamic tracking of the setpoint and the decoupling of the machine are not affected by these changes, which shows the adaptation of the proposed control capacity.
International Letters of Chemistry, Physics and Astronomy Vol. 55

CONCLUSION
The non-linear characteristic and variation of parameters of the asynchronous machine during operation poses a control problem. The use of modern control methods allows to obtain good performance. This work relates setting the speed of the asynchronous machine powered by an inverter controlled voltage current. Thus we are interested in fuzzy control systems that are capable of treating imprecise, uncertain and vague.
In this case, we presented a stable direct adaptive fuzzy control generalized. or control laws with easy structure to implement and does not require a structural or parametric information of the dynamic model of the asynchronous machine and fuzzy systems are involved to approximate the model of the system to adjust. This control technique using approximation theory and the Lyapunov to establish a law parametric adaptation ensuring boundedness of all system signals and error parameters of fuzzy systems, and to offset the effects of reconstruction errors is introducing a term of sliding mode. From the results obtained, stable direct adaptive fuzzy control generalized has good performance as well as in the presence of disturbance that upon reversal of the direction of rotation. The techniques of direct adaptive fuzzy control generalized is tested by the parametric variations of the system, and the results recorded, have allowed us to determine that this technique exhibits strong robustness in the presence of parametric variations.