Same controller in all loops controller design for multivariable systems with multiple time delays based on ideal decoupler

In this paper, a two-degree-of-freedom (TDOF) control scheme for multi-input/multi-output (MIMO) systems with multiple time delays is proposed. First, a novel inversing decoupler design method based on the ideal decoupling is proposed for decoupling the MIMO system with multiple time delays into several same independent single-input/single output (SISO) systems. Then the H2 proportion-integral-derivative (PID) controller based on the internal model control (IMC) is applied to the obtained SISO systems. Finally, the second controller is developed according to the decoupled closed-loop transfer function. Since the decoupled SISO systems are the same, only one PID controller should be designed for the independent SISO systems. The proposed method can simplify the design task significantly. Moreover, because the TDOF control structure can isolate the disturbance from the reference, the controller of the reference loop can be used to improve the reference response independently. Simulations are provided to illustrate the effectiveness of the proposed design approach.