“…The second case consists of a transfer function representing an industrial quench column with data collected after an open-loop pulse test. 20 It should be stressed that the extension of the approximation model methodology to the multiple-input-multiple-output case is straighforward from the results presented in Section 3. However, because we are concerned only with recycling processes with time delays, the worked examples are used to illustrate the ability of the finite-dimensional approximate model to describe some dynamic features of recycling processes.…”
Section: Illustrative Examplesmentioning
confidence: 97%
“…The first case study consists of a second-order system with zeros of nonminimun phase in the direct path and a first-order system in the recycle path, which can be used to represent chemical engineering prototype recycle systems. The second case consists of a transfer function representing an industrial quench column with data collected after an open-loop pulse test . It should be stressed that the extension of the approximation model methodology to the multiple-input−multiple-output case is straighforward from the results presented in Section 3.…”
Section: Illustrative Examplesmentioning
confidence: 99%
“…Emoto et al . conducted an open-loop step test on the process. When these data were used, the following models were obtained for the forward and recycle paths, respectively, It can be seen from the above transfer functions that there is a considerable time-delay separation between the direct and recycle paths.…”
Chemical processes with recycling commonly contain delays in both the forward and the backward paths. The characteristic equation of such systems is a quasipolynomial function, so that the corresponding transfer function contains an infinite number of poles. This feature precludes the use of classical stability analysis and control design techniques. In this work, a simple and effective methodology to derive an approximate discrete-time model for continuous-time recycling processes with delay is proposed. The method is based on the discretization, via a fictitious sampler and hold device, of the internal delayed signal, resulting in a finite-dimensional discrete-time version of the original continuous model. In this way, standard analysis methods, such as root locus and stability margin techniques, can be easily applied to the approximate model to obtain some conclusions on the stability of the original recycling process. Illustrative examples are used to show that some stability measures (e.g., stability margin) obtained with the approximate discrete-time model closely describe the behavior of the original recycling process.
“…The second case consists of a transfer function representing an industrial quench column with data collected after an open-loop pulse test. 20 It should be stressed that the extension of the approximation model methodology to the multiple-input-multiple-output case is straighforward from the results presented in Section 3. However, because we are concerned only with recycling processes with time delays, the worked examples are used to illustrate the ability of the finite-dimensional approximate model to describe some dynamic features of recycling processes.…”
Section: Illustrative Examplesmentioning
confidence: 97%
“…The first case study consists of a second-order system with zeros of nonminimun phase in the direct path and a first-order system in the recycle path, which can be used to represent chemical engineering prototype recycle systems. The second case consists of a transfer function representing an industrial quench column with data collected after an open-loop pulse test . It should be stressed that the extension of the approximation model methodology to the multiple-input−multiple-output case is straighforward from the results presented in Section 3.…”
Section: Illustrative Examplesmentioning
confidence: 99%
“…Emoto et al . conducted an open-loop step test on the process. When these data were used, the following models were obtained for the forward and recycle paths, respectively, It can be seen from the above transfer functions that there is a considerable time-delay separation between the direct and recycle paths.…”
Chemical processes with recycling commonly contain delays in both the forward and the backward paths. The characteristic equation of such systems is a quasipolynomial function, so that the corresponding transfer function contains an infinite number of poles. This feature precludes the use of classical stability analysis and control design techniques. In this work, a simple and effective methodology to derive an approximate discrete-time model for continuous-time recycling processes with delay is proposed. The method is based on the discretization, via a fictitious sampler and hold device, of the internal delayed signal, resulting in a finite-dimensional discrete-time version of the original continuous model. In this way, standard analysis methods, such as root locus and stability margin techniques, can be easily applied to the approximate model to obtain some conclusions on the stability of the original recycling process. Illustrative examples are used to show that some stability measures (e.g., stability margin) obtained with the approximate discrete-time model closely describe the behavior of the original recycling process.
“…To design a feedback PID controller for TC105, Emoto et al 20 conducted an open-loop step test on the process. The data collected from the step test are shown in Figure 8.…”
Section: Case Studiesmentioning
confidence: 99%
“…Hence, we expect that a recycle compensator will not be needed and that the feedback controller could be tuned on the basis of the forward-path model alone. In fact, Emoto et al did obtain good closed-loop control of the TC105 loop using a feedback-only control structure and PID controller settings based on the forward-path model. 9 Recycle effect index plot for the quench column system.…”
Systems with material and/or energy recycles are quite common in the chemical industry.
Modeling and DCS-level controller design are quite challenging for such processes because
separation of the overall process response into a direct (forward-path) response and an indirect
(recycle-path) response is often difficult. Even when this is possible, one needs to know whether
a feedback-only control structure is sufficient or an advanced control structure that employs a
recycle compensator is necessary. Using control loop performance assessment concepts, this paper
proposes a quantitative measurethe recycle effect index (REI)to help determine whether a
simple feedback control system can provide the desired quality of control.
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