PID control performance assessment: The single‐loop case

An iterative solution is developed for the calculation of the best achievable (minimum variance) PID control performance and the corresponding optimal PID setting in an existing control loop. An analytic expression is derived for the closed‐loop output as an explicit function of PID setting. The resulting benchmark allows for realistic performance assessment of an existing PID control loop, especially when the control loop fails to meet the minimum variance performance. A PID performance index is then defined based on the PID performance bound, and its confidence interval is estimated. A series of simulated examples are used to demonstrate the utility of the proposed method.