Auto-tuning of multivariable PID controllers from decentralized relay feedback

A method for auto-tuning fully cross-coupled multivariable PID controllers from decentralized relay feedback is proposed for multivariable processes with significant interactions. Multivariable oscillations under decentralized relay feedback are first investigated, and, in particular, it is shown that for a stable m × m process the oscillation frequency will remain almost unchanged under relatively large relay amplitude variations. Therefore m decentralized relay feedback tests are performed on the process, with their oscillation frequencies close to each other so that the process frequency-response matrix can be estimated at that frequency. A bias is further introduced into the relay to additionally obtain the process steady-state matrix. For multivariable controller tuning, a new set of design equations are derived under the decoupling condition where the equivalent diagonal plants are independent of off-diagonal elements of the controller, and are used to design the controller diagonal elements first. The PID parameters of the controllers are determined individually by solving these equations at the oscillation and zero frequencies. The proposed method is applied to various typical processes, where significant performance improvement over the existing tuning methods is demonstrated.