Analytical decoupling control design for dynamic plants with time delay and double integrators

Two control schemes are proposed to control dynamic plants with time delay and double integrators. One adopts the H₂ optimal controller, whereas the other utilises a conventional derivative controller for the setpoint tracking in an open-loop control manner. Both of the proposed control schemes are of the two-degree-of-freedom control structure and use an identical disturbance estimator to construct the closed-loop between the plant input and output for load disturbance rejection. In consequence, the setpoint response is decoupled from the load disturbance response. The disturbance estimator is obtained by proposing a desired closed-loop complementary sensitivity function according to the H₂ optimal performance objective. The closed-loop robust stability is analysed and corresponding sufficient and necessary conditions are also provided in the presence of the plant multiplicative uncertainty. Consequently a rule-of-thumb for tuning the single adjustable parameter of the disturbance estimator is presented. Finally, illustrative examples are included to show that a good performance can be obtained using the two proposed control schemes, especially the proposed closed-loop for the load disturbance rejection, which can also be successfully utilised to reject ramp-type load disturbances in industrial and chemical processes with one integrator.