Feedback control loop concepts

Prior to attempting this workshop, you should review Chapter 3 in the book. 

Process systems respond to various disturbances (or stimuli) in many different ways. However, certain types of response are characteristic of specific types of process. The characteristic response of a process can be described as its personality. Process control engineers have developed a range of terms and concepts to describe different process personalities, and they use this knowledge to develop effective control systems. 

There are two main differences between first- and second-order responses. The first difference is obviously that a second-order response can oscillate, whereas a first-order response cannot. The second difference is the steepness of the slope for the two responses. For a first-order response, the steepest part of the slope is at the beginning, whereas for the second-order response the steepest part of the slope occurs later in the response. 

First- and second-order systems are not the only two types of system that exist. There are higher-order systems, such as third- or fourth-order systems. However, these higher-order systems will not be discussed. 

1 Understand the components of the loop and how these components interact. 

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In the following example the effect of the various fixed parameter control modes on the stability of a simple feedback control loop are examined using the Bode stability criterion and the concept of gain and phase margins. 

The Smith predictor is a model-based control strategy that involves a more complicated block diagram than that for a conventional feedback controller, although a PID controller is still central to the control strategy (see Fig. 8-37). The key concept is based on better coordination of the timing of manipulated variable action. The loop configuration takes into account the facd that the current controlled variable measurement is not a result of the current manipulated variable action, but the value taken 0 time units earlier. Time-delay compensation can yield excellent performance however, if the process model parameters change (especially the time delay), the Smith predictor performance will deteriorate and is not recommended unless other precautions are taken. 

The notion of quantum feedback control naturally suggests a closed-loop process in the laboratory to stabilize or guide a system to a desired state. In addition, feedback is important in the design of molecular controls. These points will be made clear below, starting with considerations of design followed by a discussion of its role in the laboratory and finally leading to feedback concepts for the inversion of laboratory data. 

The controllability tools presented in here are based on the theory of linear systems, which is valid for relatively small disturbances around the stationary state. A non-linear approach, more suited for investigating the effect of large variations, will be developed in Chapter 13. The chapter starts with a brief introduction in process dynamics, followed by the properties of linear systems. The controllability analysis begins with SISO (single input/single output) systems and reviews the major concepts in feedback control. Then, the analysis is extended to MIMO (multi input/multi output) systems, with emphasis on decentralised control systems (multi SISO control loops), which is the most encountered in plantwide applications. 

Open loop control (non-feedback control) is a procedure by which one or several input variables influence output variables based on a concept of system behaviour (model) and the current status of its parameters. Characteristic is the open chain, i.e. no feedback from the system is integrated into the control process. 

Chapters 2, 3, and 4 deal with the distillation variables, and Chapter 5 covers distillation process control strategies. Chapter 6 describes some of the constraints on distillation variables and separation capabilities. Chapter 7 introduces the concepts that are critical to product quality and the measurements that evaluate performance criteria such as frequency of failure. Chapter 8 describes the concepts and nomenclature that are fundamental to PID control loops. Chapter 9 covers the concepts of tuning process controllers when they are operating in automatic output mode. Chapter 10 is about measuring the response of process variables when the controller is in manual output mode, that is, with no feedback from the process variable. 

The problem of information of documents is compounded by the fact that there is so much information in system and software specifications, while only a small subset of it may be relevant in any given context (Leveson 2000). Risk management should be considered as a control function focused on maintaining a particular hazardous, productive process within its boundaries of safe operation and that a systems approach based on control theoretic concepts should be applied to describe the overall system functions (Rasmussen 1997). Systems are viewed as interrelated components that are kept in a state of dynamic equilibrium by feedback loops of information and control (Dulac and Leveson 2004). The management of risk requires that there is a comprehensive, structured plan in place with clear responsibilities and authority, which consistently reduces risk to an acceptable level that can be tolerated by all concerned and insures that the integrity of risk reduction is maintained throughout the life of the process (Mostia 2009). 

The cybernetic description of systems of different types is characterized by concepts and definitions like feedback, delay time, stochastic processes, and stability. These aspects will, for the time being, be demonstrated on the control loop as an example of a simple cybernetic system, but one that contains all typical properties. Thereby the importance of the probability calculus and communication in cybernetics can be clearly explained. This is then followed by a general representation of cybernetic systems. 

Frequency response techniques are powerful tools for the design and analysis of feedback control systems. The Bode and Nyquist stability criteria provide exact stability results for a wide variety of control problems, including processes with time delays. They also provide convenient measures of relative stability, such as gain and phase margins. Closed-loop frequency response concepts such as sensitivity functions and bandwidth can be used to characterize closed-loop performance. 

Summary. In this chapter the control problem of output tracking with disturbance rejection of chemical reactors operating under forced oscillations subjected to load disturbances and parameter uncertainty is addressed. An error feedback nonlinear control law which relies on the existence of an internal model of the exosystem that generates all the possible steady state inputs for all the admissible values of the system parameters is proposed, to guarantee that the output tracking error is maintained within predefined bounds and ensures at the same time the stability of the closed-loop system. Key theoretical concepts and results are first reviewed with particular emphasis on the development of continuous and discrete control structures for the proposed robust regulator. The role of disturbances and model uncertainty is also discussed. Several numerical examples are presented to illustrate the results. 

However, design constraints may limit our ability to exercise this strategy concerning fresh reactant makeup, An upstream process may establish the reactant feed flow sent to the plant. A downstream process may require on-demand production, which fixes the product flowrate from the plant. In these cases, the development of the control strategy becomes more complex because we must somehow adjust the setpoint of the dominant variable on the basis of the production rate that has been specified externally. We must balance production rate with what has been specified externally. This cannot be done in an open-loop sense, Feedback of information about actual internal plant conditions is required to determine the accumulation or depletion of the reactant components. This concept was nicely illustrated by the control strategy in Fig. 2.16, In that scheme we fixed externally the flow of fresh reactant A feed. Also, we used reactor residence time (via the effluent flowrate)... 

Calmodulin has been reported to stimulate membrane-bound adenylate cyclase in the presence of Ca ". Some reports suggest that Ca " " is required for the stimulation of dopamine-dependent adenylate cyclase and that the sensitivity of adenylate cyclase to a neurotransmitter is regulated by the presence of membrane-bound calmodulin, which binds the Ca required for dopamine stimulation of the enzyme. Furthermore, these reports present data that support the concept that cAMP-dependent phosphorylation of the plasma membrane leads to a release of membrane-bound calmodulin, thereby providing a feedback loop for the control of adenylate cyclase activity. The appearance of calmodulin in soluble fractions of the cell would also result in the activation of phosphodiesterase, which would further attenuate cAMP activity. 

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