Control of MIMO Time-Delay Processes Having Disturbances with Time Delays

This work deals with the control of continuous-time MIMO (Multiple Input Multiple Output) time-delay processes having multiple disturbances acting on the process outputs. Such disturbances possess time delays that can be modeled using the Laplace operator. A discrete-time PI (Proportional Integral) LQG (Linear Quadratic Gaussian) controller is designed to control such time-delay processes. As a matter of fact, an LQG controller results from the combination of an LQR (Linear Quadratic Regulator) controller with a Kalman filter to estimate process states. An LQR controller is selected for the following reasons. First, such a controller secures an infinite gain margin and a phase margin of about 60 ^∘ C. Consequently, robustness and disturbance rejection ability are some of the characteristics of an LQR controller. Intensive simulation studies related to the application of the proposed approach on benchmark time-delay processes demonstrate that the outputs of MIMO processes can be controlled simultaneously despite the presence of disturbances possessing time delays, which are acting on the process outputs.