Tuning of the Controller Parameters

P, I, D system (Figure 9.10). This type of temperature control requires careful tuning of the control parameters, in order to avoid oscillations, which may lead to loss of control of reactor temperatures in cases where an exothermal reaction is carried out. The main advantage of the isothermal control is to give a smooth and reproducible reaction course, as long as the controller is well tuned. 

When noise is present in the measured process output, any derivative action should be accompanied by a filter. However, the problem is often that, as the time constant of the derivative filter is increased to cope with the measurement noise, the closed-loop performance degrades, requiring re-tuning of the controller parameters. This problem is illustrated using the IMC-PID rules appUed to Process A with fd = 0.67. Figure 7.7 shows the closed-loop responses to a negative unit step load disturbance with a derivative filter time constant equal to O.lrp. Figure 7.8 shows the closed-loop responses... 

The purpose of a controller is to keep the controlled variable at its setpoint or bring it to setpoint. The determination of the behaviour of the controlled system is essentially not different from the determination of the behaviour of the uncontrolled system. The controlled behaviour depends strongly on the controller parameters and the type of controller that is used. Tuning of the controller parameters should lead to a matching of the behaviour of the controlled process to desired and/or specified behaviour for changes in setpoint or disturbances that act on the process. 

Adaptive Control Process control problems inevitably require on-hne tuning of the controller constants to achieve a satisfactory degree of control. If the process operating conditions or the environment changes significantly, the controller may have to be retuned. If these changes occur quite frequently, then adaptive control techniques should be considered. An adaptive control system is one in which the controller parameters are adjusted automatically to compensate for changing process conditions. 

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... 

We first assume that initial values of the controller parameters have been obtained using any classical control technique. We then introduce tuning factors <>]. j and 9f as well as the binary variables 8P, Sj., and 5° to denote the selection l-th term of the proportional, integral and derivative term of the PID controller, i.e. 

What is the objective of the adaptation procedure Clearly it is not to keep the controlled variable at the specified set point. This will be accomplished by the control loop, however badly. We need an additional criterion, an objective function that will guide the adaptation mechanism to the best adjustment of the controller parameters. To phrase it differently, we need a criterion to guide the adaptive tuning of the controller. Any of the performance criteria we discussed in Chapters 16 and 18 could be used ... 

The advantage of feedback control is that corrective action is taken regardless of the source of the disturbance. Its chief drawback is that no corrective action is taken until after the controlled variable deviates from the set point. Feedback control may also result in undesirable oscillations in the controlled variable if the controller is not tuned properly that is, if the adjustable controller parameters are not set at appropriate values. Although trial-and-error tuning can achieve satisfactory performance in some cases, the tuning of the controller can be aided by using a mathematical model of the dynamic process. 

There are several approaches that can be used to tune PID controllers, including model-based correlations, response specifications, and frequency response (Smith and Corripio 1985 Stephanopoulos 1984). An approach that has received much attention recently is model-based controller design. Model-based control requires a dynamic model of the process the dynamic model can be empirical, such as the popular first-order plus time delay model, or it can be a physical model. The selection of the controller parameters Kc, ti, to) is based on optimizing the dynamic performance of the system while maintaining closed-loop stability. 

As discussed in Chap. 6, strategies based on 7r-pulse techniques require a rather fine tuning of the laser parameters to achieve a high-degree of control. Further studies will be needed to overcome this major drawback and to be able to propose robust control strategies, e.g. based on adiabatic passage, in complex realistic systems such as polyatomic molecules. 

Step 1. Adjust Kf. The effort required to tune a controller is greatly reduced if good initial estimates of the controller parameters are available. An initial estimate of Kf can be obtained from a steady-state model of the process or from steady-state data. For example, suppose that the open-loop responses to step changes in d and u are available, as shown in Fig. 15.15. After Kp and K have been determined, the feedforward controller gain can be calculated from the steady-state version of Eq. 15-21 ... 

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... 

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