Optimal control for high order systems with fixed PI controller based on model reduction and constrained optimization

This paper proposes a new semi-analytical robust mixed H₂/H_¿ method to design fixed-structure controllers (e.g. PI, PID) for high order systems. The method consists of two steps. Firstly, the model reduction determines reduced-order model, which is used for controller synthesis, with the guarantee of robustness margins obtained for full-order system. The reduced model will be validated a posteriori in term of closed-loop behavior by using the ¿-gap metric. Then, the parameters of a given structure controller will be determined to obtain optimal step load disturbance rejection with the respect of robustness constraints, i.e. maximum amplification of measurement noise, module margin and phase margin. The design objective and the robustness constraints are expressed as H₂ and H_¿ norms in function of unknown controller parameters. The controller design problem is then reformulated into a nonlinear optimization with constraints that can be efficiently solved numerically. We developed a controller design tool which provides, when it exists, an optimal controller that fulfills the design specifications. In this paper, to demonstrate the results, the proposed method is applied to a benchmark of common industrial systems controlled by PI controller.