Off-line tuning of PID controllers for systems subjected to random disturbances

An off-line method of tuning PID controllers used in process control applications is presented. The plant under consideration is of second order with delay and the loop is presumed to be operating at steady state under the influence of random disturbances. Tuning is performed by minimizing the cost function, namely the integral of squared error, with respect to the tuning parameters. To do this, a second order approximation of the cost function is obtained and minimized using the Newton-Raphson method. System identification is done without interrupting production by introducing test signals of low signal to noise ratio and using a Kalman filter to extract the response. The result is a model composed of Laguerre functions which emulates the frequency response of the system in question. The integral term is found to cause stability problems if left unconstrained because the lag it introduces is not beneficial in the case under consideration. On the other hand, the algorithm behaves well when tuning a PD controller if the Kalman filter yields accurate results because the model obtained is then very similar to the transfer function of interest. The Kalman filter presently used does not adequately model the noise, so its performance hampers proper tuning of the loop