Feedback controllers worked example

Example 14.9 This example cites a real study of a laboratory CSTR that exhibits complex d5mamics and limit cycles in the absence of a feedback controller. We cite the work of Vermeulen, and Fortuin, who studied the acid-catalyzed hydration of 2,3-epoxy-1-propanol to glycerol ... 

Ve do not require any sophisticated mathematics to use these generalized functions such as the delta function. We introduce them here ibecause they make our work simpler, not more complicated. You will also find these functions useful in the process control course when you analyze the dynamics and feedback control of processes. Moreover, empirical tests, such as the step- and impulse-response experiments, provide a general method for modeling the dynamic behavior of many processes. Using these methods to determine a reactor RTD is just one small example of their uses in chemical process modeling. 

Accumulation of macromolecules has to be modeled as a dynamic process with time constants in the range of minutes to hours or days. Furthermore, macromolecules act as feedback controller on the metabolic flux pattern. The following paragraphs give examples for some of these microalgal capabilities. Comprehensive models are often not available but some model ideas, bricks, or lumped approaches. Much more work can possibly be done in this field. An example for combined temperature/light kinetics is given below ... 

Input variables are not state variables they are external to the system, but they affect the system or, in other words, work on the system. For example, the feed temperature and composition of the feed stream to a distillation tower or a chemical reactor or the feed temperature to a heat exchanger are the input variables. They affect the state of the system, but are not affected by the state of the system (except when there is a feedback control, and in this case, we distinguish between control variables and disturbances or input variables). 

It is probably apparent that most overrides are really feedback control loops. They therefore are subject to stability considerations. In many cases they are also subject to truly hard constraints, as, for example, maximum column-base pressure. Since any feedback control system must have some room within which to work, the overrides must be so designed that the process does not normally approach the hard constraints too closely. 

The first four criteria are derived from feedback-control theory. A SHE performance indicator must be observable and quantifiable, i.e. it must be possible to observe and measure performance by applying a recognised data-collection method and scale of measurement. The nominal scale is the simplest type. This means that we must be able to tell whether the result represents a deviation from a norm or not. Usually, the SHE performance indicators are expressed on a ration scale of measurement. A typical example is the LTI-rate, i.e. the number of lost-time injuries per one million hours of work. 

We first focus on criteria developed from feedback-control theory. Efficient control requires a reliable measurement and feedback of performance. Reliability is here defined as the extent to which repeated measurements give the same results. A reliable reporting and counting of accidents is important if the frequency of accidents (number of accidents per one milHon hours of work) is used as a measure of the SHE performance of the company or department in qnestion. Another example has to do with whether different investigators who look into the same accident will come up with the same results concerning causal factors (intra-observer reliability). 

Over time, a large number of traditional laboratory instruments have been morphed to meet industrial needs for QC applications. Example applications include raw material, product QC and also some environmental testing. In such scenarios laboratory instruments appear to work adequately. Having said that, there are issues the need for immediate feedback and the need for smaller, cheaper, and more portable measurements. There is a growing interest in the ability to make measurements in almost any area of a process, with the idea that better production control can lead to a better control of the process and of the quality of the final product. The cost of implementation of today s (2004) process analyzers is still too high, and it is impractical to implement more than a couple of instruments on a production line. Also, there is growing concern about the operating environment, worker safety, and environmental controls. 

Our initial studies of dynamics in biochemical networks included spatially localized components [32]. As a consequence, there will be delays involved in the transport between the nuclear and cytoplasmic compartments. Depending on the spatial structure, different dynamical behaviors could be faciliated, but the theoretical methods are useful to help understand the qualitative features. In other (unpublished) work, computations were carried out in feedback loops with cyclic attractors in which a delay was introduced in one of the interactions. Although the delay led to an increase of the period, the patterns of oscillation remained the same. However, delays in differential equations that model neural networks and biological control systems can introduce novel dynamics that are not present without a delay (for example, see Refs. 57 and 58). 

Where complex properties occur in living systems, as for example in chaotic cardiac arrhythmias, they are characteristic of pathological failure of the normal controls— in this case in some kinds of heart disease—not of health. Even at the level of an individual enzyme, the enzyme peroxidase from horseradishes, an example of chaotic behavior has been known for many years, but we have no idea how its properties benefit the horseradish, and they contribute nothing to our present understanding of how metabolic systems are controlled in general. The sort of positive feedback loops that account for the complex behavior of economic systems, political relations, and indeed some aspects of biology such as the extravagant overdevelopment of the peacock s tail, are conspicuously absent from the major pathways in the metabolic economy. There is no reason, therefore, to see any contradiction in the claim that classical economic theory works much better in metabolism than it does in the domain in which it was developed. 

At each level of the hierarchical structure, inadequate control may result from missing constraints (unassigned responsibility for safety), inadequate safety control commands, commands that were not executed correctly at a lower level, or inadequately communicated or processed feedback about constraint enforcement. For example, an operations manager may provide unsafe work instructions or procedures to the operators, or the manager may provide instructions that enforce the safety constraints, but the operators may ignore them. The operations manager may not have the feedback channels established to determine that unsafe instructions were provided or that his or her safety-related instructions are not being followed. 

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