A New Class of Nonlinear PID Controllers

摘要

This paper introduces a new class of simple nonlinear PID-type controlers comprised of a sector-bounded nonlinear gain in cascade with a linear fixed-gain P, PD, PI, or PID controller. Two simple nonlinear gains are proposed: the sigmodial function and the hyperbolic function. The systems to be controlled are assumed to be modeled or approximated by second-order transfer-functions, which can represent many robotic applications. The stability of the closed-loop systems incorporating nonlinear P, PD, PI, and PID controllers are investigated using the Popov Stability Criterion. A numerical example is given for illustration.