New Design Method for Fractional Order Proportional Integral (FO-PI) Controller of 3x3 Multivariable Systems

This paper presents a new design method of Fractional Order Proportional Integral Controller (FO-PI) for 3x3 multivariable system (three-input-three-output). The Optimal parameters of the FO-PI controllers are tuning by minimizing performance index criterion as objective function. The irrational transfer function of the fractional operator is performed by means of diffusive representation and allows to formulate the optimization problem as a function of fractional order. The simulation results show that the performance of the response obtained by diffusive approach -based FO-PI are better than whose obtained by the classical controllers.

A Innovation Identification Approach of Control System by Irrational (Fractional) Transfer

<p>In this paper, an innovative algorithm of identification of control system, described by irrational transfer function with distributed parameter characteristics - with irrational components, is proposed. Algorithm is based on real interpolation method (RIM). Parameters of irrational transfer function can be identified by its experimental transient responses. Each of them can be represented by an analytic expression, table or graph. The proposed method is computationally efficient, simple and practical, as is illustrated by numerical examples. In the furure, the method can be used for tuning the controller and for direct application construction of adaptive controllers, working on the identification principle.</p>

Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer Function

Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer FunctionThis paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems for a given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase error between the irrational transfer function and its rational approximation. A simple analog circuit which can serve as a fundamental analog fractional system is obtained. Illustrative examples are presented to show the quality and usefulness of the approximation method.

Noncollocated passivity-based PD control of a single-link flexible manipulator

The passivity property of a noncollocated single-link flexible manipulator with a parameterized output is studied. The system can be characterized by either the irrational transfer function of an infinite-dimensional model or its truncated rational transfer functions. Necessary and sufficient conditions for these transfer functions to be passive are found. It is also shown that a non-passive, marginal minimum-phase, truncated transfer function can be rendered passive by using either the root strain feedback or the joint angular acceleration feedback. For the noncollocated truncated passive transfer function, a PD controller suffices to stabilize the overall system. Numerical results are given to show the efficacy of the proposed approaches.