Design of discrete-time adaptive PID controllers for a class of linear integrator systems

摘要

Proportional, Integral and Derivative (PID) controllers are widely employed in control applications. The Ziegler-Nichols method is one of the most widely used PID parameter tuning methods, even though it is known to have some drawbacks. Automatic or self-tuning of PID controllers has been extensively studied. However, the stability of the resulting system with the PID controller is not considered in most PID auto-tuning methods and the tuned PID parameters may not guarantee the stability of the control system after changes in the system. This paper presents a new method to design discrete-time stabilizing PID controllers with time varying (or adaptive) gains for a special class of MIMO linear systems. The technique, based on appropriate choices of control Lyapunov functions (CLF), determines the optimal values of the parameters, with respect to the CLF choice, which guarantee the asymptotic stability of the equilibrium of the considered system.