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 parameter PID 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 and PIDF controllers. (C) 2018 Elsevier Ltd. All rights reserved.