Designing of Adaptive Model-Free Controller Based on Output Error and Feedback Linearization

S Pezeshki,M A Poor,S Ghaemi,M A Badamchizadeh

doi:10.1155/2013/461907

S Pezeshki, M A Poor + Show 2 more

Open Access

https://doi.org/10.1155/2013/461907

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Abstract

This paper introduces a new approach to design Model-Free Adaptive Controller (MFAC) using adaptive fuzzy procedure as a feedback linearization based on output error. The basic idea is to transfer the control signal to an appropriate surface and then, depending on the output error of system, the control signal changes around this surface. Some examples are provided as well to illustrate the efficiency of the proposed approach. The obtained simulation results have shown good performances of the proposed controller.

Highlights

Classical control method is based on mathematical equations of the system; this method suffers from some drawbacks
Notice that the initial values of A(t) can be chosen as A(0) = 0 or any selected value by information that is acquired from system dynamic or even can be determined from another available control approach; for instance, the columns of A(0) can be taken as kf or, for example, if we want to estimate f(x) function, the columns of A(0) are better to contain coefficients of system states of f(x) [7]
If the bigger kv is opted, better performance of output and quick tendency to the desired value are achieved while increasing the control signal u; it should be noted that if kv is chosen very large, it can make the system unstable

Summary

Introduction

Classical control method is based on mathematical equations of the system; this method suffers from some drawbacks. In 1996, this controller was used for general class of nonlinear system in the form of x(k + 1) = f(x(k)) + g(x(k))u(k) [5] Another idea is introduced in 2000 [6], which uses a neural network as an adaptive controller for stabilization of system. Their proposed algorithm does not need any complex tuning and can be applied to any controllable multiinput systems. The MFAC has been successfully implemented in many practical applications, for example, chemical industry, linear motor control, injection modeling process, PH value control, and so on [4]. The proposed model-free adaptive controller and its Lyapunov stability are represented in Sections 3 and 4, respectively; in Section 5 simulation results are given to highlight advantages of MFAC method.

Feedback Linearization by Means of Adaptive Fuzzy Controller

Proposed Approach

Lyapunov Stability for the Proposed ModelFree Adaptive Controller

Implementation of MFA Controller

Conclusion