Optimal Generalized Predictive Functional Control with Applications to Extended PID Control for Quadruple Tank

Algorithm of optimal Generalized Predictive Functional Control is presented towards the control problem of linear discrete-time state-space multivariable systems. A quadruple tank system is simulated to demonstrate typical results. The proposed controller has been structured in a reduced order arrangement including a set of specified linear transfer-functions along with gains that are found to minimize a GPC cost-index. This approach enables a range of classical controller structures to be used in the feedback loop such as extended PI, PID or Lead-lag or a more general transfer function form. A MATLAB simulation was used to test the performance of the restricted structure controller for regulation and tracking problems and was compared against a classical PI Controller.