Design of robust PID controller for an interval plant

In this paper, a method based on stability boundary plot is considered for an unstable second order process with dead time. All the controllers that satisfy the gain margin and phase margin requirements are found by plotting the Kp-Ki curve. The technique is based on Kharitonov theorem for stability of interval plants. Limiting values of the controller parameters that stabilize the given system are found using the curves obtained. In addition to this, an optimization based design of robust Proportional-Integral-Derivative (PID) controller that guarantees both the stability and performance of an interval plant is proposed. The controller design involves two steps. First, a controller setting is obtained for the nominal plant and then optimization is done to find a setting which will work on the entire range of the uncertainties specified. Optimization is based on the necessary and sufficient conditions for a system to be Hurwitz stable. A set of constraints are framed based on these conditions and it is used to minimize an objective function using non-linear programming (NLP). This technique is applied to i) Stable FOPTD process ii) Unstable FOPTD process. Further, Nonlinear simulation is performed for an unstable CSTR plant under three operating regions. The results obtained show the effectiveness of optimization taking into account the uncertainties associated with the plant.