The SIMC method by Skogestad (J. Process Control
2003, 13, 291–309) to tune the PID controller is revisited, and a
new method (K-SIMC) is proposed. The proposed K-SIMC method includes
modifications of model reduction techniques and suggestions of new
tuning rules and set point filters. Effects of such modifications
are illustrated through simulations for a wide variety of process
models. The proposed modifications permit the SIMC method to be applied
with more confidence.
The proportional-integral-derivative (PID) controller is the dominant type of controller used in current industrial practice. The behavior and capabilities of the PID controller are familiar to both the design engineer and the field operator, and it is relatively easy to tune manually by a variety of open-loop methods (Seborg et al., 1989). An important recent improvement in the PID controller tuning method is a self-tuning capability (Astrom and Hligglund, 1,984; Seborg et al., 1989), while the control loop is closed. Here we propose a new closed-loop tuning method for the PID controller plus dead-time models, the control performances for some processes are very poor. Here we improve the YS method by identifying processes with a second-order plus dead-time model under closed-loop conditions. We also employ a more elaborate frequency domain tuning method. To obtain a second-order plus dead-time model, a Taylor series expansion of the dead-time term is combined with the ultimate data matching technique of Chen (1989). To tune the PID controller, a frequency domain method based on methods of Edgar et al. (1981) and Harris and Mellichamp (1985) is applied, yielding controller settings much superior to the ZN method or the first-order methods.
Second-Order Plus Dead-Time Model IdentificationTo identify a model of a process, Gp(s), a control system under proportional control [G,(s) = KJ is tested. We choose a proportional controller with a sufficiently large gain so that the closed-loop system is underdamped. From a response curve to step change in set point of magnitude A, we can obtain an approximate model of the closed-loop system G,,(s) as (Yuwana and Seborg, 1982;Chen, 1989);
Very simple proportional-integral-derivative (PID) controller tuning rules for a wide range of stable processes are available. However, for unstable processes, the design trend is for controllers to be more complex for better performances. Here, the design concept of "simplicity" is extended to unstable processes. Simple desired closed-loop transfer functions for the direct synthesis method and simple approximations of the process time delay are utilized for unstable processes. Very simple tuning rules for PID controllers and set-point filters are obtained, yielding similar or even improved performances over previous more complicated PID controller tuning methods.
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