Plant models for nonlinear controller design

摘要

The main part of the author's presentation addresses the topic ofwhat information is needed about a nonlinear plant to design asatisfactory controller. The author cannot provide a definitive answer,but hopes to shed some light on the various possibilities and theirlimitations. First, however, the author looks at the problem in abroader context and defines precisely the problem under consideration.It is assumed that the objective is to design a controller for anonlinear plant so that the closed loop system will perform satisfactoryfor all inputs. These will typically be assumed to be step inputs ofvarying amplitude but obviously the system should not possessundesirable behaviour, for example subharmonic oscillations, whensubjected to other inputs. The plant is assumed to be nonlinear,continuous and time invariant It is quite easy to demonstrate usingsimple examples that typical specifications cannot in general be metusing a linear controller. It is therefore assumed that a time invariantnonlinear controller needs to be designed to meet the specifications.Use of a time varying controller seems inappropriate as it complicatesthe problem in the sense that the design now becomes one for anonlinear, continuous, time varying system. The author points outhowever, that there is an indirect linkage with time in the sense thatthe controller parameters in the nonlinear situation will vary with themagnitude of variables which are, of course, themselves time varying. Itmay also be the case that the variable which affects the gain or timeconstant of an element is not an input to that element in the systemblock diagram. Consideration is restricted to a SISO system althoughmost of the concepts may be extended to MIMO systems, some more easilythan others