Plant models for nonlinear controller design

The main part of the author´s presentation addresses the topic of what information is needed about a nonlinear plant to design a satisfactory controller. The author cannot provide a definitive answer, but hopes to shed some light on the various possibilities and their limitations. First, however, the author looks at the problem in a broader context and defines precisely the problem under consideration. It is assumed that the objective is to design a controller for a nonlinear plant so that the closed loop system will perform satisfactory for all inputs. These will typically be assumed to be step inputs of varying amplitude but obviously the system should not possess undesirable behaviour, for example subharmonic oscillations, when subjected to other inputs. The plant is assumed to be nonlinear, continuous and time invariant It is quite easy to demonstrate using simple examples that typical specifications cannot in general be met using a linear controller. It is therefore assumed that a time invariant nonlinear controller needs to be designed to meet the specifications. Use of a time varying controller seems inappropriate as it complicates the problem in the sense that the design now becomes one for a nonlinear, continuous, time varying system. The author points out however, that there is an indirect linkage with time in the sense that the controller parameters in the nonlinear situation will vary with the magnitude of variables which are, of course, themselves time varying. It may also be the case that the variable which affects the gain or time constant of an element is not an input to that element in the system block diagram. Consideration is restricted to a SISO system although most of the concepts may be extended to MIMO systems, some more easily than others