On Self-Tuning Control of Nonminimum Phase Discrete-Time Systems Using Approximate Inverse Systems

Abstract

This paper presents a new method for self-tuning control of nonminimum phase discrete-time stochastic systems using approximate inverse systems obtained from the least-squares approximation. We show how unstable pole-zero cancellations can be avoided, and that this method has the advantage of being able to determine an approximate inverse system independently of the plant zeros. The proposed scheme uses only the available input and output data and the stability using approximate inverse systems is analyzed. Finally, the results of computer simulation are presented to show the effectiveness of the proposed method.

A New Method for the Self-Tuning Control of Nonminimum Phase Discrete-Time Systems in the Presence of Disturbances

“…Statement Consider the following SISO discrete-time system where Furthermore, d is a delay of the system, A(z) and B(z) are coprime polynomials, bo 0 and z is a difference operator, u(t) is the input and y(t) is the output and w(t) is the disturbance expressed by (2) Moreover, the plant is a nonminimum phase system and the coefficients of A(z) and B(z) are unknown.…”

“…It has long been known that such plants are not easy to control [1]. There exists fundamental limitation to the controlled perfor mance, because boundedness of all signals is not assured due to the unstable pole-zero cancellation in the adaptive control systems [2].…”

An Optimal Adaptive Flight Control System

“…Sliding Mode Control of Pitch Rate for an F-16 is proposed in [6]. An adaptive controller design method based on back-stepping neural network is proposed for reconfigurable flight control systems in the presence of variations in aerodynamic coefficients or control effectiveness deficiencies caused by control surface damages [7].Adaptive control schemes are used to overcome difficulties connected with the ignorance of system structure, where the parameters of the plant are not known exactly or slowly time varying [8], [9], [10]. For the control of plants different approaches have been adopted to design the adaptive controllers.…”

Time Varying Back Propagating Algorithm for MIMO Adaptive Inverse Controller

“…Finally, the disturbance affecting the plant is canceled by an adaptive feedback disturbance canceler. These controllers approximately compensate the effect of numerator polynomial at the output with the help of approximate inverse of the plant [4], [10]. The desired trajectory is approximately followed by the output of the plant with some delay which can be estimated.…”

“…To overcome these difficulties, the adaptive control methods were developed. Because it can work even if the system structure and critical parameters are unknown [6], [10]. There are several approaches are proposed to develop the adaptive controllers [8] and already been implemented for different robotic applications.…”