Design of feedback control systems with a sector-bounded nonlinearity using Zakian's framework

Abstract

So far control systems design by Zakian’s principle of matching has been investigated extensively for linear time-invariant systems. For general nonlinear systems, this is still an open problem. In this regard, this thesis develops a practical method for designing a class of feedback control systems where the plant is a linear time-invariant (possibly uncertain) subsystem in cascade connection with a static memoryless nonlinearity. The design objective considered here is to ensure that the error function and the controller output stay within respective bounds for all time and for all possible inputs. The research conducted in the thesis comprises two parts. Part I considers the stability of Lur’e systems in the sense that the outputs are bounded whenever the magnitude and the slope of the input are bounded. It is shown by a straightforward extension of known results that if the Popov condition is satisfied, then the system is stable in the above sense for any nonlinearity lying in a sector bound. Based on this result, an inequality for determining stability points by numerical methods is developed. In Part II, since the original design criteria are computationally intractable, design inequalities that can be used for determining a controller satisfying the design objective are derived, thereby providing surrogate design criteria. The numerical examples are carried out and clearly illustrate the effectiveness of the systematic design approach developed here.