Design of Fixed Structure Pid Controller for Nonlinear System with Saturation

Abstract

An approach is presented to design a PID controller for a given plant with saturation. Based on the describing function models of saturation and the method of determining the sets of stabilizing a PID controller for a linear plant with time delay or one that is delay free, the new equivalent inverse Nyquist plots are given for different sinusoidal input amplitudes of saturation. The PID controller parameters are selected from intersecting sets of stabilizing PID parameter regions for different input amplitudes. The controller can effectively mitigate the saturation effect. For an open-loop unstable plant, a prefilter is added on the reference input. Within the proposed framework, this approach can improve the stability of the system and reduce the degree of saturation. The simulation examples demonstrate the validity of the proposed approach.

The Synthesis of the Proportional‐Differential Regulators for the Systems with Fixed Ends of Trajectories Under Two‐Sided Constraints on Control Values

“…A detailed review of models and the methods used in the modern theory of optimal control can be found in works [8,9]. Works [10][11][12][13][14][15][16][17][18][19][20] contain references to a large number of studies of theoretical and applied characters which are devoted to problems of optimal control. The linear-quadratic (LQ) problem of optimal control by dynamic systems with convex functional and constraints on values of control is investigated in [13].…”