Processes with Large Dead Time

Compensatory control for processes with large dead time or inverse response... 

Proportional-plus-integral control is the most generally useful control mode and therefore the one usually applied to automated process-control. Its major limitation is in processes with large dead-time and capacitance if reset time is faster than process dead-time, the controller-response changes are faster than the process, and cycling results. In these cases, derivative control is beneficial. 

All the chapters of Part IV were devoted to the analysis and design of feedback control systems for rather simple processes. In this chapter we are concerned with the feedback control of two special types of systems those with large dead times or inverse responses. We will see that for such systems, conventional P, PI, or PID controllers may not be sufficient to yield the desired response. 

There are different schemes to handle systems with a large dead time. One of them is the Smith predictor. It is not the most effective technique, but it provides a good thought process. 

Part V (Chapters 19 through 22) deals with the description, analysis, and design of more complex control systems, with one controlled output. In particular, Chapter 19 introduces the concept of feedback compensation with Smith s predictor, to cope with systems possessing large dead times or inverse response. Chapter 20 describes and analyzes a variety of multiloop control systems (with one controlled output) often encountered in chemical processes, such as cascade, selective, and split-range. Chapter 21 is devoted exclusively to the analysis and design of feedforward and ratio control systems, while Chapter 22 makes a rather descriptive presentation of adaptive and inferential control schemes why they are needed and how they can be used. 

Proportional-Plus-Derivative Control. Here, derivative action is added to proportional controllers for processes with large capacitance and appreciable dead-time. Control action is now proportional to the rate of change (the time derivative) of the error signal. The response equation is written as... 

Varying the flow of a compressible fluid controls the pressure in a large volume. This process is dominated by a single large capacitance with no dead time. The measurement is normally noise free and, owing to its capacitive nature, is characterized by a slow response and a small process gain. As shown for liquid level control, a proportional controller is more than adequate for gas pressure control. 

Acts before the effect of a disturbance has been felt by the system Is good for systems with large time constant or dead time Does not introduce instability in the closed-loop response Requires direct measurement of all possible disturbances Cannot cope with unmeasured disturbances Is sensitive to process/model error... 

The order of the postulated model is a very important factor. For a well-known process such as a stirred-tank heater, it is not a problem. On the other hand, it is not obvious what order of dynamics we should assume for a fluid catalytic cracker (see Example 4.15). Also, it is not obvious what type of low-order model we should use to approximate the high-order models of even simple distillation columns (see Example 4.16). As a general starting point one could employ first- or second-order models with or without dead time. There exist a surprisingly large number of processes which could be effectively described by such low-order models. 

The TAC is started when a photon is detected. It is, however, not stopped with the delayed laser pulse that produced this photon, but with the next one. The signal processing starts with this pulse. The TAC/ADC dead time turns the system blind for a large part of the next laser period. The blind interval of the next period is in fact the interval where a new signal photon is most likely to be expected. Consequently, the system can be considered to be blind for the next signal period after the detection of a photon. The probability of losing a photon in the blind period is... 

Two-Position Control. The simplest case is two-position (on-off) control. Here, any deviation of the measured value from a set point drives the final control-operator to either a full-on or full-off position. This forces the measured value back and forth across the set point, and the measurement signal cycles about this point. The amplitude and frequency of this cycle depend on the response characteristics of the process. As the process dead-time becomes small, the frequency of the cycle becomes high likewise, as the process capacitance becomes high, the amplitude of the cycle becomes small. This mode of control is used only for processes in which this cycling effect can be tolerated it is most successful with those having large capacitance. 

Monomer conversion can be adjusted by manipulating the feed rate of initiator or catalyst. If on-line M WD is available, initiator flow rate or reactor temperature can be used to adjust MW [38]. In emulsion polymerization, initiator feed rate can be used to control monomer conversion, while bypassing part of the water and monomer around the first reactor in a train can be used to control PSD [39,40]. Direct control of surfactant feed rate, based on surface tension measurements also can be used. Polymer quality and end-use property control are hampered, as in batch polymerization, by infrequent, off-line measurements. In addition, on-line measurements may be severely delayed due to the constraints of the process flowsheet. For example, even if on-line viscometry (via melt index) is available every 1 to 5 minutes, the viscometer may be situated at the outlet of an extruder downstream of the polymerization reactor. The transportation delay between the reactor where the MW develops, and the viscometer where the MW is measured (or inferred) may be several hours. Thus, even with frequent sampling, the data is old. There are two approaches possible in this case. One is to do open-loop, steady-state control. In this approach, the measurement is compared to the desired output when the system is believed to be at steady state. A manual correction to the process is then made, based on the error. The corrected inputs are maintained until the process reaches a new steady state, at which time the process is repeated. This approach is especially valid if the dominant dynamics of the process are substantially faster than the sampling interval. Another approach is to connect the output to the appropriate process input(s) in a closed-loop scheme. In this case, the loop must be substantially detuned to compensate for the large measurement delay. The addition of a dead time compensator can... 

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