Closed-Loop Tuning of Controllers

The tuning of process control loops can have a significant effect on the variability and robustness of the control of a process system. This chapter teaches methods of tuning controllers while they are running in automatic output mode, that is, closed loop. The pattern recognition methods are highly effective. 

---

Foxboro developed a self-tuning PID controller that is based on a so-called expert system approach for adjustment of the controller parameters. The on-line tuning of K, Xi, and Xo is based on the closed-loop transient response to a step change in set point. By evaluating the salient characteristics of the response (e.g., the decay ratio, overshoot, and closed-loop period), the controller parameters can be updated without actually finding a new process model. The details of the algorithm, however, are proprietary... 

The Bode stability criterion indicates how we can establish a rational method for tuning the feedback controllers in order to avoid unstable behavior by the closed-loop response of a process. 

They tuned simple PI controllers and found that the closed-loop response of the overall system became faster and less oscillatory when they increased the controller gains. Use the dynamic RGA to explain this observation. 

The two main types of disturbances introduced into a controller for closed loop tuning are ... 

Robbins reported the development of a closed-loop tuning methodology that does not require any of the loops to be run with sustained cycling. The steps for the Robbins tuning method for self-regulating control loops are as follows ... 

The development of the Robbins closed-loop tuning methodology was the result of about 11 years of development with collaboration and feedback of comments from others. A number of different methods for tuning process control loops were tested along the way, and this new closed-loop method using pattern recognition was determined to be the most cost-effective. 

The closed-loop stability of the batch motion can be established with the application of the standard singular perturbation [25] or small gain theorems [8, 10] available in the nonlinear dynamical systems literature, in eonjunction with the definition (7) of finite-time motion stability. In a chemical process context this closed-loop stability assessments can be seen in the cascade control of a continuous reactor [22], the cascade control of a continuous distillation [21, 24], and in the calorimetric estimation [15] of a batch polymer reactor. The closed-loop motion stability is ensured if the observer gain ( o) is tuned slower than the characteristic frequency ( j) of the fastest unmodeled dynamics, and the observer ( ), secondary ( ,.), and primary ( p) gains are sufficiently separated. This is. 

Compared with model I, model II performs considerably better during simulation (Fig. 30.21). The manipulated variable i follows the measurements closely, which indicates that the closed loop dynamics of the simulation approximates the actual experimental setup. However, when the controller is switched on, the reflux fraction is increased and becomes larger than one, before it is decreased. This was found to be independent of controller tuning and is caused by the fuzzy model. The result is that there is a slight inverse response in the production curve the production first becomes negative before it increases, which is not possible in practice. The net effect is that the simulated production lags behind the measurements (Fig. 30.21c). Model III performs better than models I and II. Quality control is good and the simulation matches the measurements of i closely. The simulated production curve approximates the measured production well. 

In earlier chapters, Simulink was used to simulate linear continuous-time control systems described by transfer function models. For digital control systems, Simulink can also be used to simulate open- and closed-loop responses of discrete-time systems. As shown in Fig. 17.3, a computer control system includes both continuous and discrete components. In order to carry out detailed analysis of such a hybrid system, it is necessary to convert all transfer functions to discrete time and then carry out analysis using z-transforms (Astrom and Wittenmark, 1997 Franklin et al., 1997). On the other hand, simulation can be carried out with Simulink using the control system components in their native forms, either discrete or continuous. This approach is beneficial for tuning digital controllers. 

Compare the closed-loop performance of a discrete PI controller using the ITAE (disturbance) tuning rules in Table 12.3. Ajpproximate the sampler and ZOH by a time delay equal to Ar/2. Use Simulink to check the effect of samphng period for different controllers, with Af = 0.05, 0.25,0.5, and 1.0 min. 

The developed control system exhibited good performance in all the tested conditions however, it was necessary to perform a more rational choice of the controller parameters so as to obtain improved closed-loop responses of the present membrane system. The Ziegler-Nichols tuning technique was initially used. The value of the proportional gain providing an oscillatory response was equal to 4.508, whereas the oscillation period... 

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

The tuning of the controller in the feedback loop can be theoretically performed independent of the feedforward loop (i.e., the feedforward loop does not introduce instability in the closed-loop response). For more information on feedforward/feedback control appications and design of such controllers, refer to the general references. 

The PI controller, even when optimally tuned, is also unable to prevent surge. Furthermore, it is unable to stop surge once it occurs. In the above situation, the operator would correctly identify the problem as instability of the closed-loop PI controller. The only viable action would be to open the closed control loop by placing the controller in manual, thereby freezing the valve open. In this scenario, open-loop control will stop surge. 

Fig. 4.35 Closed-loop step response of temperature control system using PID controller tuned using Zeigler-Nichols process reaction method.

In the present study, we propose a tuning method for PID controllers and apply the method to control the PBL process in LG chemicals Co. located in Yeochun. In the tuning method proposed in the present work, we first find the approximated process model after each batch by a closed-loop Identification method using operating data and then compute optimum tuning parameters of PID controllers based on GA (Genetic Algorithm) method. 

---