Automatic tuning of multivariable controllers with adaptive relay feedback

A new method for automatic tuning of multivariable PI controllers using adaptive hysteresis relay feedback is proposed for multivariable processes with significant interactions. It is shown that for a stable m x m process it is possible to estimate an m x m transfer function matrix at two points in the frequency domain. Therefore, a minimum of m/sup 2/ adaptive relay feedback tests are performed in the process. For each test, if a limit cycle exits, it will correspond to a single critical point of the process. By varying the relay parameters, different critical points can be determined. The resulting oscillations frequencies are allowed to be close to each other by means of an adaptive relay, so that the process frequency response matrix can be estimated at that point. The method developed here also identifies steady state matrix of the multivariable process during the same adaptive relay feedback tests. The results of the identification procedure are used to tune a multivariable PI controller by the Maciejowski rule. Comparative results are shown to demonstrate that the new auto-tuning method has the best set-point response performance.