Robust Control Applied to Multiple-Input Multiple-Output Nonlinear Systems

Abstract

Many of practical systems (for example: robotic systems, power systems and electronic circuits) are multiple-input multiple-output nonlinear systems and some of them have coupling between inputs and outputs. Besides all that, these systems can suffer with parametric uncertainties and external disturbances. Any control techniques applied to these systems are complex. This work presents a control structure, based on the union between a modified version of the variable structure model reference adaptive control and a left-inverse decoupling technique, to transform a multiple-input multiple output nonlinear system into a set of single-input single-output linear systems. In that case each input affects only one output and with a desired closed-loop performance. The proposed structure transforms the variable structure model reference adaptive control, which is usually applied to single-input single-output linear systems, into a controller to be applied to a class of multiple-input multiple-output nonlinear systems. It is important to note that proposed structure, using only input/output measurements, presents fast transient performance, reduces the output “chattering” and it is robust to parametric uncertainties and disturbances. All these features are verified by simulation results of an electronic circuit that exhibits chaotic behavior (Chua’s circuit).