PID control has been dominant as a control algorithm in process industry. To achieve high profitability, the tuning of PID controllers is still an important issue in practice. PID controllers are tuned usually on the basis of process models identified from operation data and empirical tuning rules. However, good identification is a difficult task. In addition, closed-loop identification is often required, especially when a process is unstable.

To avoid identification and optimize PID control parameters directly from closed-loop data, several techniques such as virtual reference feedback tuning (VRFT) and iterative feedback tuning (IFT) have been proposed. Without a process model, these methods can determine the PID control parameters so that the closed-loop response corresponds closely with that of the desired reference model. More recently, fictitious reference iterative tuning (FRIT) was proposed. FRIT can optimize the PID control parameters from a set of input-output data like VRFT, but its objective function is different from that of VRFT.

The objective of this research is to extend FRIT for improving its practicability. The problems of FRIT are: 1) there was a risk of obtaining a local minimum because the Gauss-Newton method is commonly used in FRIT and 2) it is difficult to properly determine a reference model without information on a process. The use of an inappropriate reference model deteriorates the control performance achieved. At the worst, the control system becomes unstable. The second problem is serious not only in FRIT but also in VRFT and IFT.

To solve these two problems, FRIT is extended. First, particle swarm optimization (PSO) is used to find a global minimum. Second, the objective function is modified to include the penalty for changes of the input variable. Third, the parameter in the reference model is optimized together with PID control parameters. The second and the third extensions are very useful to realize peaceful control responses, especially when the process is unstable. The proposed method is referred to as extended FRIT (E-FRIT).

E-FRIT is applied to two types of unstable polymerization processes, and its performance is compared with that of the conventional methods. The results clearly show that each extension plays an important role to derive better PID control parameters. In fact, conventional methods tend to make the control system oscillating or even unstable. The direct PID tuning via E-FRIT is promising for chemical process control.