Fixed, Low-Order Controller Design with Time Response Specifications Using Non-Convex Optimization

In this paper, we present a new algorithm for designing a fixed, low-order controller with time response specifications for a linear time invariant (LTI) plant. For the two-parameter feedback configuration, the problem of finding a fixed or low-order controller to meet the desired time response specifications is reduced to the least square estimation (LSE) in the sense of partial model matching (PMM), which results in a quadratic cost function. The closed-loop stability condition imposed on controller parameters is formulated by polynomial function constraints associated with the cost function. When the cascade feedback structure is considered, the zeros of the controller may be a big obstacle to designing a good time response controller. This problem can also be formulated using polynomial constraints. Consequently, it is shown that the total problem here can be formulated as a global optimization problem with a quadratic objective function and polynomial function constraints in controller parameter space. We show that the software GloptiPoly [1] can be used as a simple algorithm to solve this problem. Finally, several illustrative examples are given.