The Pareto optimal robust design of generalized-order PI Controllers based on the decentralized structure for multivariable processes

This paper proposes an optimal tuning approach for designing robust generalized-order proportional integral (PI) controllers based on the multi-objective optimization problem for multivariable processes. Generalized-order means that the order of the integral term could be an integer order or a fractional one. Due to the sophistication of an MIMO process, the decentralized structure based on the simplified decoupling is addressed to reduce the full matrix controller (n(2) controllers) to the diagonal form (n controllers). Multi-objective particle swarm optimization (MOPSO) is adopted to design a generalized-order PI controller for each diagonal element of the decoupled matrix. The objective functions are to minimize the integrated absolute error (IAE) for both servomechanism and regulator problems which are normally conflicting in terms of system performance. In the first stage, a Pareto front (PF) including the optimal solutions is obtained, then in the second stage, the most appropriate control parameters are chosen from the PF based on the maximum peak of the sensitivity function (M-s). The robustness stability of the whole system (the MIMO one) is finally evaluated to guarantee the applicability of the control structure. Some simulation examples in comparison with other well-known methods are presented to demonstrate the effectiveness of the proposed method.