PID control performance assessment: The single‐loop case

Abstract

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.

An industrial application of a performance assessment and retuning technique for PI controllers

“…The stochastic performance is usually addressed by considering the minimum variance control [9,10]. On the other side, deterministic performance assessment techniques consider more traditional design specifications such as those related to the set-point following and load disturbance rejection tasks [11].…”

On the Impact of Plant Model and Controller Sophistication on Performance of Disturbance Attenuation and System Robustness

“…This differs from related papers [8], [11], [13], where the discrete-time MV or LQG indices are chosen. In [11] the quadratic index is only used for LQG benchmark, and PID controller is tuned using a deterministic approach with assumed level of robustness.…”

“…The decision to retune or replace any of these controllers should be preceded by an investigation whether and to what extent this would improve performance. Such procedure is referred to benchmarking or control performance assessment [3]- [5], [8]- [13]. Most of research done so far assume MV control as the performance lower bound and variance of the system output as basic quantity for control quality assessment.…”

“…Moreover, instead of typical random walk [8],[1 1], [13], a stationary model of disturbance is chosen to better characterize real-world stationary disturbances. In this case, whenever the system allows open loop identification, the closed loop system PSD function [8] can be compared with PSD function of disturbance itself to give more insight into control quality.…”

Deterministic Performance Assessment and Retuning of Industrial Controllers Based on Routine Operating Data: Applications

“…In this context, even though the proposed techniques can be actually viewed under the same framework (see [6] and the references therein), they are often conveniently divided into two categories [7]: stochastic performance monitoring and deterministic performance monitoring. In the former case, it is important to assess the capability of the control system to deal with stochastic disturbances, and therefore, the control system benchmark is based on the minimum variance concept [8][9][10]. In the latter case, more traditional design specifications, such as set-point and load rejection disturbance step response parameters, are considered [11].…”