Feedback strategies

Thyroid hormone release is subject to the negative feedback strategy that is typical of endocrine systems controlled by the hypothalamic-pituitary axis. Increased circulating levels of the thyroid hormones (T4, T3) serve to limit their own production by inhibiting TRH release from the hypothalamus and TSH release from the anterior pituitary.30,35 This negative feedback control prevents peripheral levels of thyroid hormones from becoming excessively high. 

Table 9.8. Comparison of Nominal and Worst-case Algorithm based Optimum Design of Operating Policies (Feedback Strategy)...

Figure 9.17. Optimum Temperature Trajectories (Feedback Strategies)...

Gramopadhye, A. K., Drury, C. G., and Sharit, J. (1997b), Feedback Strategies for Visual Search in Airframe Structural Inspection, bUemational Journal cf Industrial Ergonomics, Vol. 19, No. 5, pp. 333-344. 

The open-loop strategy implies that each players control is only a function of time, Ui = Ui t). A feedback strategy implies that each players control is also a function of state variables, ui = Ui t Xi t) Xj(t)). As in the static games, NE is obtained as a fixed point of the best response mapping by simultaneously solving a system of first-order optimality conditions for the players. Recall that to find the optimal control we first need to form a Hamiltonian. If we were to solve two individual non-competitive optimization problems, the Hamiltonians would be Hi = fi XiQi, i = 1,2, where Xi t) is an adjoint multiplier. However, with two players we also have to account for the state variable of the opponent so that the Hamiltonian becomes... 

Notice that the difference is captured by an extra term on the right when we compare (2.10) and (2.13) or (2.11) and (2.14). The difference is due to the fact that the optimal control of each player under the feedback strategy depends on Xi t), i = 1,2. Hence, when differentiating the Hamiltonian to obtain equations (2.13) and (2.14) we have to account for such dependence (note also that two terms disappear when we use (2.12) to simplify). 

The third configuration (Fig. 5.21) is feedback control strategy, but it is different from the first feedback configuration. The inflow Fj is used as the control variable rather than the outlet flow, but still measuring the level (h), which is an output variable. This is the reason it is still a feedback strategy. 

Rgab, O., D. L. Yu and J. B. Gomm. Polymer electrolyte membrane fuel cell control with feed-forward and feedback strategy. International Journal of Engineering, Science and Technology 2(10) 56-66, 2010. 

Most of the current MFC research is based on state-space models, because they provide an important theoretical advantage, namely, a unified framework for both linear and nonlinear control problems. State-space models are also more convenient for theoretical analysis and facilitate a wider range of output feedback strategies (Rawlings, 2000, Maciejowski, 2002 Qin and Badgwell, 2003). 

In their simplest form, mathematical models have been developed that describe the interactions of healthy CD4+ T cells, infected CD4+ T cells, and free viruses in the form of three coupled ordinary differential equations (Craig and Xia, 2005). Such a model can be the basis of simple model-based feedback strategies for control and can also be extended to generate more complex models suitable for a model predictive control strategy (Zurakowski et al., 2004). 

Generic Control Strategies. The two generic strategies for process control are feedback and feedforward control. Most process control strategies are based on one or a combination of these strategies (1 3). 

Some of the inherent advantages of the feedback control strategy are as follows regardless of the source or nature of the disturbance, the manipulated variable(s) adjusts to correct for the deviation from the setpoint when the deviation is detected the proper values of the manipulated variables are continually sought to balance the system by a trial-and-error approach no mathematical model of the process is required and the most often used feedback control algorithm (some form of proportional—integral—derivative control) is both robust and versatile. 

The main disadvantage of the feedback control strategy is that no corrective action is taken until after a deviation between the measured controlled... 

The feedforward control strategy (Fig. lb) addresses the disadvantages of the feedback control strategy. The feedforward control strategy measures the disturbance before it affects the output of the process. A model of the process determines the adjustment ia the manipulated variables(s) to compensate for the disturbance. The information flow is therefore forward from the disturbances, before the process is affected, to the manipulated variable iaputs. 

The primary advantage of the feedforward over the feedback control strategy is that corrective action is initiated before the controlled variable is upset. Feedforward control, however, has its own drawbacks, ie, variables used to characterize the disturbances must be measurable a model of the response of the controlled variable to the disturbance must be available (when the feedforward strategy is used alone, the control performance depends on the accuracy of the model) and the feedforward control strategy does not compensate for any disturbance not measured or modeled. 

In most process plant situations where feedforward control is appropriate, a combination of the feedforward and feedback control is usually used. The feedforward portion reduces the impact of measured disturbances on the controlled variable while the feedback portion compensates for model inaccuracies and unmeasured disturbances. This control strategy is referred to as feedforward control with feedback trim. 

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. 

Regulatory Control For most batch processes, the discrete logic reqmrements overshadow the continuous control requirements. For many batch processes, the continuous control can be provided by simple loops for flow, pressure, level, and temperature. However, very sophisticated advanced control techniques are occasionally apphed. As temperature control is especially critical in reactors, the simple feedback approach is replaced by model-based strategies that rival if not exceed the sophistication of advanced control loops in continuous plants. 

Chang, C.-T. and Epstein, M.A.F. 1987. Simulation studies of feedback control strategy for batch crystallizers. American Institute of Chemical Engineers Symposium Series, 83(253), 110-119. 

The dotted lines in the diagram indicate the various feedback paths that exist to enable the individual to identify if a particular stage of the processing chain was executed correctly. Thus, if the operating team had planned a strategy to handle a complex plant problem, they would eventually obtain feedback with regard to whether or not the plan was successful. Similar feedback loops exist at the rule and skill-based levels, and indicate opportunities for error correction. The application of the stepladder model to a process industry example is given in Appendix 2A at the end of this chapter. 

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