A multivariable IMC-PID method for non-square large time delay systems using NPSO algorithm

• We present a novel IMC-PID controller design method for non-square system based on the concept of equivalent open-loop transfer function (EOTF).
• The new NPSO algorithm and the incremental PID with first-order lag filter structure are combined to determine the desired controller parameters.
• This controller can offer superior dynamic performance and robustness in the control of non-square system with multiple time delays.

Multiple time delays and strong interactions among different loops are the main problems in the design of multivariable controller for non-square systems. In this paper, the concept of effective open-loop transfer function (EOTF) is extended to non-square systems. By applying the internal model control (IMC) method, the controllers with equivalent models are designed. For practical applications, the NPSO algorithm is used to obtain the parameters of the incremental PID with first-order lag filter. This new method does not only avoid the complex computation caused by the procedure of decoupling first and then designing controllers but also employs the advantages of IMC-PID's suitable for large time delay systems and strong robustness. Simulation is carried out to demonstrate the effectiveness of the proposed method; also significant performance improvement has been achieved with the proposed method compared with other methods.