Optimal control of first 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 (i.e. PID, the most widely used structure in industry). Precisely, the method consists in determining the parameters of a given structure controller that minimizes the influence of a step load disturbance to the process output with the respect of 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 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, the unique optimal controller that fulfills the design specifications. The method is based on generic models that can represent common industrial plants. Further, the proposed method enables a graphical representation of the different design tradeoffs. To demonstrate the results, we apply this method for first order processes controlled by PI controller.