Robust pole placement by state-Pi feedback control for interval plants

In this paper, an interval analysis framework is applied to resolve the pole placement problem for interval plants, taking into consideration the robust state-PI feedback design for a linear time invariant system with uncertain parameters. Despite the fact that the state feedback technique through a gain matrix has been a familiar method for pole placement of a linear time invariant system, the technique might encounter a difficulty in eliminating the steady-state errors remained in some state variables. As a consequence, applying an integral element to such a gain matrix can virtually eliminate possible errors to zeros. The designed state-PI feedback controller shall place all coefficients of the closed-loop pole within an assigned closed-loop interval characteristic polynomial. The proposed method is adopted to generate robust controller for linear time invariant system in the presence of parametric uncertainty. This method is uncomplicated and advantageous that it requires no system canonical transformation and involves less computational complexity. Furthermore, it increases computational efficiency and simply helps applying linear programming methods. The effectiveness of the method is illustrated by means of numerical examples and experimental results.