CASE STUDIES IN OPTIMAL CONTROL

This section illustrates a set of case studies in which root-finding plays an important role in chemical engineering including the calculation of the volume of a nonideal gas, bubble point, and zero-crossing. However, these scenarios also crop up in several other areas. For instance, the calculation of the volume of a nonideal gas is a typical problem in fiuid dynamics, whereas the zero-crossing problem is very common in all disciplines involving differential and differential-algebraic systems as convolutions models, such as the optimal control for electrical and electronic purposes. 

For the case study in this work with Ntray = 30 and NC = 2, there are 1316 DAEs in 1324 variables (101 states). The remaining eight variables consist of the three continuous design variables for optimization (column diameter, surface areas of the reboiler and the condenser), and the five manipulated variables (reflux, distillate, cooling water, steam and bottoms flow rates), whose values are determined by the tuning parameters and the set-points of the control scheme used. 

Nowadays many companies have adopted a policy of continuous improvement of working conditions. Therefore, it is desirable to create target levels for those who want to pursue more efficient control by applying the best available control technologies. There are also endeavors to create optimal working conditions in order to improve the performance and the innovativeness of a staff, and hence enhance productivity. A series of laboratory and case studies show that employee productivity is higher when the work environment is appropriate for the tasks being done.- Such efforts are typical in the advanced sector of industry. One can say that there is a transition from blue-collar to white-collar work. ... 

The definition of the cost model is of crucial importance for controlling the behavior of the S N P optimizer. One of the central questions is whether to maximize service level, which usually means using high penalties for non and late delivery, or to maximize profits, which requires the use of realistic sale prices. In the case study scenario, the nondelivery cost levels reflect real sale prices sufficiently close to enable a profit maximization logic. 

This paper presents a general mathematical programming formulation the can be used to obtain customized tuning for PID controllers. A reformulation of the initial NLP problem is presented that transforms the nonlinear formulation to a linear one. In the cases where the objective function is convex then the resulting formulation can be solved easily to global optimality. The usefulness of the proposed formulation is demonstrated in five case studies where some of the most commonly used models in the process industry are employed. It was shown that the proposed methodology offers closed loop performance that is comparable to the one... 

Optimal control theory aims to maximize or minimize certain transition probabilities, called objectives, such as the production of a specified wave function at a specified time tf, given a wave function F(t0) at time f0. The general principles of OCT are best understood via a case study due to Rice and coworkers [104, 119], illustrated in Figure 4.2, in which the objective is to concentrate the wave function in one of the exit channels of a bifurcating chemical reaction ... 

Numerical results using this technique were obtained [471] for the pump-dump photodissociation of Na2 to optimize the production of either Na(3s) + Na(3p) or Na(3s) + Na(4s). In this case optimal control often required pulses that were fairly heavily structured in laser phase and frequency. A more detailed study [471] indicated that this structure was necessary for the dissociation pulses, but not necessary for the excitation pulse. Further, as is often the case with OCT, pulses with very different structures were found to achieve similar control objectives in different ways. 

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