Optimization of fixed-order controllers using exact gradients. (November 2018) - Grimholt, Chriss; Skogestad, Sigurd
Highlights: We derive exact gradients for optimizing performance with constrained robustness. We demonstrate increased accuracy and better convergence than with forward finite differences. The exact gradients were presented in such a way that they can easily be implemented in Matlab. Evaluating gradients consist of combining and evaluating defined transfer functions. Abstract: Finding good controller settings that satisfy complex design criteria is not trivial. This is also the case for simple fixed-order controllers including the three parameterpid controller. To be rigorous, we formulate the design problem into an optimization problem. However, the algorithm may fail to converge to the optimal solution because of inaccuracies in the estimation of the gradients needed for this optimization. In this paper we derive exact gradients for the problem of optimizing performance (iae for input and output disturbances) with constraints on robustness ( M S, M T ). Exact gradients give increased accuracy and better convergence properties than numerical gradients, including forward finite differences. The approach may be easily extended to other control objectives and other fixed-order controllers, including Smith Predictor andpidf controllers.