Optimal PID control of double integrating processes

In this paper we investigate optimal PID control of a double integrating plus delay process and compare with the SIMC rules. What makes the double integrating process special is that derivative action is actually necessary for stabilization. In control, there is generally a trade-off between performance and robustness, so there does not exist a single optimal controller. However, for a given robustness level (here defined in terms of the Ms-value) we can find the optimal controller which minimizes the performance J (here defined as the integrated absolute error (iAE)-value for disturbances). Interestingly, the SIMC PID controller is almost identical to the optimal PID controller. This can be seen by comparing the pareto-optimal curve for J as a function of Ms, with the curve found by varying the SIMC tuning parameter τc.