Optimal control of second-order linear systems with fixed proportional-integral structure controller

This paper proposes a new semi-analytic robust mixed H2/H-infinity design method for fixed-structure controllers. Precisely, the method consists in determining the parameters of a controller with given structure such that it minimizes the influence of a step load disturbance to the process output with respect to robustness constraints, i.e. constraints on maximum amplification of measurement noise, minimum module margin and minimum phase margin. The design objective and the robustness constraints are first expressed as H2 and H-infinity norms in function of unknown controller parameters. The controller design problem is then reformulated into a nonlinear optimization problem with a set of inequality constraints that can be efficiently solved numerically. Finally, we obtain a controller design tool which provides, when it exists, an optimal controller that fulfills the design specifications. Furthermore, the proposed method enables also a graphical representation of the different design tradeoffs. In this paper, to demonstrate the results, this method is applied to second-order processes controlled by PI controller.