Minimum Variance Benchmark and Performance Assessment for PID Controllers

Abstract

A lot of controller tuning algorithms have been proposed since the middle of the last century. Linear controllers, especially proportional integral derivative (PID) controllers and their sub-class proportional integral (PI) controllers, are the most common type of controllers used in the process industry. When the control structure is established, existing methods can be used to tune the controller parameters. After this stage, the closed-loop performance may deteriorate due to uncertain dynamics and changing operating conditions. Regardless where the controllers have been applied, automatic online performance monitoring is essential to check the controllers to detect significant performance degradation. Therefore a performance monitoring tool could bring peace of mind to the operation group, whether a considerable performance degradation happens or not. An explicit explanation for the minimum variance benchmark is proposed to be applicable in industrial cases as the current online performance monitoring methods for PID controllers were inadequate. Control performance assessment (CPA) compares the actual output variance with the minimum variance (MV) for the non-restricted linear controller. MV describes the most fundamental performance limitation of a system due to time delays or infinite zeros. MV is estimated with-out disturbing the system and just needs the time delay of a process and its closed-loop operational data. Since the PID controller structure is quite different from the MV controller, the performance index for the MV controller is not suitable for a PID controller. Thus, the CPA benchmark needs to be more relevant for real applications where the PID controller regulates the loop. However, for estimation of minimum variance benchmark for PIDs (MVPID), full information of the system is needed, e.g. the process, disturbance model and time delay. Thus, system identification effort is usually required. In addition to all the afore-mentioned problems for estimation of the PID benchmark, the non-convex optimization problem also arises. There is no direct method to solve non-convex optimization problems and usually convex methods with iterations are used to find the optimum result for these cases. Most identification methods had been used to find the open-loop model. Both the non-convex optimization and system identification sets of methods are time-consuming. However, the estimation of the performance benchmark is to be used for online monitoring purposes; thus, the procedure should be without any considerable delay. This thesis presents an overview of the current status of control performance monitoring using minimum variance principles. The thesis also explores extending these principles to PID-achievable performance assessment through multivariable assessment. The univariate CPA concepts for PID controllers have been developed for multivariate cases. Prior knowledge of interactor matrices in multivariate cases is essential to estimating a performance benchmark. The thesis proposes an integrated approach for PID control loop performance assessment. Fast and reliable algorithms for PID performance assessment are developed and evaluated by simulations as well as applications on real industrial processes. A loop that indicates poor performance compared to the MV benchmark does not certainly demonstrate a poor controller, as the MV benchmark does not consider the controller structure. In this thesis, an algorithm for estimating the PID benchmark with fast calculation time is developed without requiring the model of noise as one of the benchmark estimation requirements. We used the feedback control invariant (a portion of the output variance, which estimates minimum variance term) to estimate the unknown disturbance model. It is shown that this requirement can be assessed from routine operating data, thus avoiding the need to disrupt the process.