Improved Optimization-based Design of PID Con- trollers Using Exact Gradients

Finding good controller settings that satisfy complex design criteria is not trivial, even for the simple three parameter proportional-integral-derivative (pid) controller. One strategy is to formulate the design problem into an optimization problem. However, when using gradient based optimization with finite differences to estimate the gradients, the algorithm often fails to converge to the optimal solution. This is thought to be a result of inaccuracies in the estimation of the gradients. In this paper we show exact gradients for a typical performance (iae) versus robustness (MS , MT ) design problem. We demonstrate increased accuracy in the optimization when using exact gradients compared with forward finite differences.