NON-LINEAR SYSTEM - CONTROL USING FEEDBACK LINEARIZATION

Abstract

In the work documented here first a nonlinear control technique, feedback linearization is discussed. Feedback linearization is a method of designing a nonlinear control law for controlling nonlinear systems. It eliminates the limitation of small operating range which is posed in linear control approach of nonlinear system based on small perturbation theory. The control task is discussed here mainly in tracking context. Tracking problem by inverse dynamics is also discussed using feedback linearization. Feedback linearization, however, has the drawback that it requires an intensive online calculation for real time tracking control and this may become very huge and unrealistic in case of higher order plants. In view of this demerit, another method of nonlinear control is also discussed which is based on neural networks. This method is very appropriate for tracking problems. The method breaks the whole control problem in two parts, one is offline identification and other is online tracking. For the identification a nonlinear model of the input-output behavior of the system known as NARMA-L2 model is used. The control method using NARMA-L2 model is called NARMA-L2 control. It provides a faster tracking requiring much less online calculations. The non-ability of non-minimum phase system in tracking a reference trajectory is also discussed and a technique called output redefinition is discussed which provides approximate tracking with some finite tracking error. Application of NARMA-L2 control to MIMO system is discussed by applying it to an aircraft control system. The dynamics of the aircraft are derived and its control by the NARMA-L2 control is discussed in the context of automatic control i.e. unmanned control of the aircraft. Aircraft dynamics are identified using neural networks according to the NARMA-L2 model and the identified model is validated by comparing the outputs from the identified model with that obtained from the actual mathematical model upon application of the same input.