# Nonlinear Control System

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CHAPTER 1 INTRODUCTION Nonlinear control deals with the modelling, analysis and design of control systems containing at least one non-linear component. Modelling aims in developing mathematical model for a given system. Characteristics of system behavior along with stability issues are addressed by analysis of a given system. In design part main objective is to design a controller such that the closed loop system exhibits desired characteristics for a given non-linear plant[1]. In this chapter a brief introduction to nonlinear systems is given. This Chapter explains the necessity of nonlinear control along with characteristic properties of nonlinear system. It describes chaotic systems and multi-scroll systems. Objectives are discussed. The…show more content…
This is a priori paradoxical result comes from the fact that nonlinear controller designs are often deeply rooted in the physics of the plants. Take an example, consider a swinging pendulum attached, in the vertical plane. Starting from some arbitrary initial angle, the pendulum will oscillate and progressively stop along the vertical axis. Although the pendulum’s behaviour could be analysed close to equilibrium by linearising the system, physically its stability has very little to do with the eigenvalues of some linearised system matrix: it comes out from the fact that the total mechanical energy of the system is progressively dissipated by various friction forces (e.g. at the hinge) so that the pendulum comes to rest at a position of minimal…show more content…
Accordingly, the behavior of the system changes due to change in the number of equilibrium points. Thus we can say bifurcation means “quantitative change in the system parameter leads to qualitative change in the system properties”. Values of these parameters at which qualitative nature of the system changes are known as critical or bifurcation values. Chaos For stable linear systems, small differences in initial conditions can only cause small difference in output. Nonlinear system, however, can display a phenomenon called chaos, by which we mean that the system is extremely sensitive to initial conditions. Even if we have an exact model of a chaotic system, the system’s response in long run cannot be well predicted without knowing the initial conditions. Other behaviours Other interesting behaviour, such as jump resonance, sub-harmonic generation, asynchronous quenching, frequency-amplitude dependence of free vibrations, can also occur and are important in some system