Design of an H(lemniscate) PI controller with given relative stability and its application to the CSTR problem

H ¥ control theory has achieved a very high level, which is not followed by appropriate application in industry. Some reasons are: synthesis of H ¥ controllers is complex and based on the numerical Nevanlinna-Pick procedure, high order of controllers (higher than the order of the process) and sensitivity to deviation of controller coefficients (fragile controller). On the other hand, PI (PID) controllers are still dominant in industry, which places the problem of design of fixed structure controllers at the forefront. The mentioned problem is very difficult. This paper proposes a simple interactive procedure for design of H ¥ PI controllers with the presence of constraints (given relative stability) based on D-decomposition. The catalogue of responses to references, suppression of disturbances and minimum of H ¥ criteria of control is created. The selection of controllers, based on the catalogue, is left to the user. The application of H ¥ PI controllers to a CSTR (continuous stirred-tank reactor) is demonstrated.