Gain-bandwidth optimization of PID controllers

Many methods exist for the design of proportional-integral-derivative (PID) controllers. This paper describes a constrained optimization aimed at reducing the excess gain-bandwidth of an initial controller thereby improving its performance. Further reduction in the gain-bandwidth is possible even when the bandwidth is explicitly considered in the design such as is done using quantitative feedback theory (QFT). This procedure can ensure robustness of the PID controller if the parameter bounds are suitably specified. Also, a specific performance measure of the controller, such as the gain margin, can be improved by appropriate choice of the frequency interval over which the optimization is done.