PID controller design for disturbed multivariable systems

A linear-quadratic-regulator-based design methodology is proposed to design proportional-integral-derivative (PID) controllers for multivariable systems with load disturbances. Except for a few parameters that are preliminarily selected, most of the PID parameters are systematically tuned using the developed plant state-feedback and controller state-feedforward LQR approach, such that satisfactory performance with guaranteed closed-loop stability is achieved. In order to access the plant state variables and carry out disturbance rejection, an observer-based disturbance rejection technique is proposed, which through an ‘equivalent disturbance’ concept, retains the observation error to be used for disturbance compensation. This makes disturbance measurement unnecessary and the disturbance rejection tuning independent of the set-point response adjustment. A robust stability analysis is also included for the modelling error. An illustrative example is given for comparison with alternative techniques.