A fast closed-loop process dynamics characterization

Stable, integrating and unstable processes, including dead-time, are analyzed in the loop with a known PI/PID controller. The ultimate gain and frequency of an unknown process Gp(s), and the angle of tangent to the Nyquist curve Gp(iω) at the ultimate frequency, are determined from the estimated Laplace transform of the set-point step response of amplitude r0. Gain Gp(0) is determined from the measurements of the control variable and known r0. These estimates define a control relevant model Gm(s), making possible the use of the previously determined and memorized look-up tables to obtain PID controller guaranteeing desired maximum sensitivity and desired sensitivity to measurement noise. Simulation and experimental results, from a laboratory thermal plant, are used to demonstrate the effectiveness and merits of the proposed method.