On direct PID controller tuning based on finite number of frequency response data

A nonlinear optimization technique is applied to tune a PID controller using a finite number of frequency response points of the process. The finite number of frequency response points are spaced at harmonics of a conceptual periodic trapezoidal waveform exciting the setpoint of the closed loop system. Using a Fourier series approach, the spectrum of the input waveform and the finite frequency response data of the process, the error between a desired closed loop output response and the output of the system is minimized in an integral least squares sense in the frequency domain to tune the PID gains. Gain and phase margin violation penalties are imposed on the function to be minimized to guarantee stability margins. The technique is illustrated by a simulation example and experimentally on a laboratory temperature control system. (C) 1997 Elsevier Science Ltd.