Analytical design 2 DOF IMC control based on inverted decoupling for non-square systems with time delay

Non‐square systems which have more inputs than outputs are difficult to control because of their special structure. In this article, inverted decoupling is extended to non‐square systems and an effective dynamic decoupling effect is achieved. The method to obtain realizable and stable decoupler matrices is provided. Based on the decoupled processes, the 2 DOF (degrees of freedom) controllers consisting of feedback filters and reference controllers are designed and then the performances for the reference response and the disturbance response are improved simultaneously. The feedback filters are designed based on the trade‐off between robustness and performance for input disturbance rejection. The reference controllers are designed in line with the IMC principle. To restrain overshoot, a requirement on the system maximum singular is proposed and the parameters of the reference controllers are determined based on the requirement. Simulation studies are provided to demonstrate the effectiveness of this method.