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 simulatedexamples are used to demonstrate the utility of the proposed method.

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A constrained minimum ®ariance controller is deri®ed based on a mo®ing horizon approach that explicitly accounts for hard constraints on process ®ariables. A procedure for the performance assessment of constrained model predicti®e control systems is then de®eloped based on the constrained minimum ®ariance controller. The performance bound computed using the proposed mo®ing horizon approach con®erges to the unconstrained minimum ®ariance performance bound when the constraints on process ®ari-ables become inacti®e. The utility of the proposed method in the performance assessment of constrained model predicti®e control systems is demonstrated through a simulated example.

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