PID Controller Design with Specifications on the Infinity-Norm of Sensitivity Functions

A controller design method using a frequency criterion is proposed in this paper. The frequency criterion is defined as the weighted sum of squared errors between the specified and computed values of the design parameters. These are the infinity-norm of the sensitivity and complementary sensitivity functions and the crossover frequency. The criterion is then minimized iteratively using the Gauss-Newton method. Robustness against the model uncertainties are also investigated by including uncertainty profiles in the criterion. Simulation examples show the effectiveness and simplicity of the proposed method.