Decoupling Proportional-Integral-Derivative Controller Design for Multivariable Processes with Time Delays

In this article, the decoupling proportional-integral-derivative (PID) controller is designed for multi-input multi-output (MIMO) processes with time delays. Three basic issues on the decoupling control are restudied here: the computation of the decoupler, the selection of the decoupled matrix, and the design of the controller. Considering the difficulty of computing the inverse-based dynamic decoupler, especially for nonsquare processes, here, we introduce a new concept of nyquist set to describe the dynamic of the decoupler. Then, based on the nyquist set, the decoupler is approximated as a low order transfer function matrix though the complex-curve fitting technique. In addition, some rules are proposed to reselect the decoupled matrix if it cannot produce a feasible decoupler. With the proposed decoupler, a model reduction technique and a new robust internal model control (IMC) principle are employed to design the decentralized PI controller. The decoupler and the decentralized PI controller are implemented by a centralized PID controller, which is the desired decoupling controller. Simulation studies demonstrate the effectiveness and merits of the presented methodology.