Optimal PID-Control on First Order Plus Time Delay Systems & Verification of the SIMC Rules

Optimal PID-settings are found for first-order with delay processes for specified levels of robustness (MS-value) and compared with an extended SIMC-rule. Optimality (performance) is defined in terms of the integrated absolute error (IAE) for combined step changes in load output and input disturbances. The SIMC-rules gives a PI-controller for first order systems and no recommendation are given for tuning the derivative part. We propose an extended SIMC-rule where the the time delay is counteracted by introducing derivative action with τD = θ/3. The modification was found to give surprisingly good settings with near Pareto-optimal performance. However, to obtain the improvement over PI control τc should be reduced to about half of the recommended value τc = θ.