Optimal control open loop method

The human body is a remarkably complex biochemical process, and it shares many attributes with more traditional process control problems that have been discussed in earlier chapters. In the event that a body fails to achieve the robust level of self-regulation that occurs naturally (cf. Chapter 24), there are opportunities for medical intervention, often involving the administration of a therapeutic agent (or drug) in a prescribed manner. The therapy can be optimized using open-loop methods, but it is often advantageous to automate the process, thus removing the human from the feedback loop (much as a chemical plant removes the operator from the loop in the transition from manual control to... 

Several methods have been investigated to find correlations between physical properties of fuel gas mixtures and the excess air ratio to optimize the combustion procedure. In spite of the varying composition of natural gas it is said to be possible to control a heater system by measurements of the dynamic viscosity of the gas [7]. One explanation could be the correlation between Wobbe number and viscosity With increasing Wobbe numbers the viscosity decreases, and if the Wobbe number of a gas is known, the excess air ratio can be adjusted, resulting in an open loop control. 

You are required to design two cylindrical tanks in series to supply a chemical plant with a constant water feed of 35 m /h. The feed to the first tank keeps fluctuating, whereas the feed to the plant needs to be constant at 35 m /hr. Design a suitable control loop (PI control action) for this system. Draw appropriate block diagrams for both the open- (uncontrolled) and closed- (controlled) loop cases. Find the optimal control settings (gains) using the decay ratio criterion, and the Cohen and Coon criterion and compare the results of both methods. 

The first two points are valid for open-loop process nonlinearity measures as well. The third point is new in control-relevant nonlinearity quantification. In a more general context, one has not only to consider the performance criterion but additionally mention the controller design method. Following the idea of Ref 24, optimal control theory with an integral performance criterion will be used here as it represents a benchmark for any achievable performance. Considering nonlinear internal model control with different filter time constants is also possible, see for example Ref 23. 

Two broad approaches to dynamic operability analysis are the use of so-called open-loop indicators, and the solution of a suitably formulated optimization problem. Characteristics of the former are that they are based on steady-state or linear dynamic models, are relatively easy to compute and seek to provide indications of potential plant-inherent control problems independent of the choice of control system. Examples are the minimum singular value and the plant condition number which reflect sensitivity to input constraints and model uncertainty respectively. More detail may be found in [1] with a good overview of these methods given in [2]. 

While the main thrust of these analyses are to provide a plant that exhibits satisfactory closed-loop performance, the assumptions regarding the control system vary considerably across the various methods proposed. The open-loop indicators are largely based on factors that limit achievable closed-loop performance independent of controller type, whereas most of the optimization based integrated design formulations assume a specific controller type such as multiloop PI, LQG and so forth. While this is not considered to be a problem per se, it is important that the implications of these assumptions are clear so that appropriate deductions may be drawn. This chapter attempts to at least in part address this issue. 

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