Abstract
A self-tuning PID controller is proposed for regulation and tracking problems of first and second order lag systems. A PID self-tuning problem is defined by introduction of a first-order-lag reference model. Structural differences in PID and adaptive controllers are pointed out. A differential equation is derived for self-tuning of PID gain parameters. Output error convergence to zero is proven together with boundedness of relevant parameters and variables. A persistent excitation condition is given for PID gain parameter convergence to the exact model matching value. Robustness for a typical type of additive disturbance is proven. A numerical simulation and a temperature regulation experiment for an existing incinerator demonstrate the proposed self-tuning PID controller.
