(96d) A PID Tuning Method Using MINLP with Nonparametric Process and Disturbance Models

Since the invention of PID control in 1910 for the steering of ships, numerous patents, papers, and commercial software have addressed the need for determining PID tuning parameters that achieve satisfactory closed-loop performance. The behavior of the vast majority of PID controllers can be accurately predicted with tuning software and the tuning results implemented satisfactorily. However, there is no shortage of incidences where PID controllers perform poorly when derivative action is applied despite the use of tuning software. In these cases, the failure of the software is often due to the neglect of including actual process imperfections in calculating PID tuning parameters. Frequently occurring imperfections include measurement noise, disturbances, instrument resolution, and control valve hysteresis.

This paper presents a PID tuning method where most of the real world imperfections are included in the nonlinear optimization routine. The imperfections, which are often times readily available but has been underutilized or not utilized at all by commercial tuning software, are formulated as a time domain step response model similar to nonparametric models used in DMC multivariable model predictive controllers. Excel GRG2, a mixed integer non-linear programming (MINLP) routine, is used to obtain optimal filter time, scan time and P-on-PV/P-on-Error selection along with PID controller gain, integral, and derivative constants.

This paper demonstrates that tuning results with derivative action can be much improved when process and loop imperfections are formulated in the optimization problem. It also shows the capability of MINLP system in many ways. First, the optimal filter time can be obtained through the trade off between IAE and control valve movement. Second, the PID controller scan time for modern DCS systems can be optimized as an integer with minimal sacrifice of loop performance. Third, the selection of P-on-PV or P-on-Error can be automatically determined based on the objective function. The implementation of a temperature controller for a high purity Benzene/Toluene column is presented to illustrate the effectiveness of this approach.