Design of decoupling and tracking controllers for continuous-time transfer function matrices with multiple time delays

• A new decoupler is proposed.
• Sampled data from the unit-step response are used to obtain approximated delay-free/single-delay continuous-time models.
• A sliding mode tracking controller is developed to achieve reference model tracking and disturbance rejection.

This paper presents an extended adjoint decoupling method together with a reference model-based sliding mode tracking method, to design a decoupling and tracking controller for continuous-time transfer function matrices with multiple (integer/fractional) time delays in both denominators and numerators. First, for obtaining the diagonally decoupled subsystems, a decoupler is designed by utilizing the extended adjoint decoupling method. Then, by using sampled data from the unit-step response of the decoupled subsystems, the conventional balanced model-reduction method is carried out to obtain the approximated delay-free/single-delay continuous-time models for the decoupled subsystems with multiple time delays. For the integral of time multiplied by absolute error (ITAE) reference model tracking, a chain observer is designed to establish the virtual estimated states for the decoupled subsystems by utilizing the obtained approximated continuous-time models. At last, we develop a sliding mode tracking controller together with a disturbance observer (DOB), to achieve reference model tracking and disturbance rejection. Illustrative examples are given to demonstrate the effectiveness of the proposed method.