Relative control optimization

The chapter is organized as follows. We describe the criterion that will drive the control optimization in Section 9.1. We then present the concept of synchronization redundancy in Section 9.2, and show how they can be used to reduce the control cost Finally, we present in Section 9.3 a technique called control synchronization that introduces redundancies by lengthening and serializing the constraint graph hardware model. 

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Relative control optimization a technique, called control resynchronization, that reduces the control implementation costs while still satisfying the required timing and synchronization constraints. 

Relative control optimization by resynchronization. The control circuit resulting om control synthesis can be optimized further to reduce its size, with the requirement that the optimized hardware is still a valid implementation of its behavioral model. Most approaches to control optimization use a finite state machine model, where operations are bound to control slates. Howevo, when synthesizing circuits from a higher, more abstract level of hardware specification that supports concurrency, synchronization, and timing constraints, these approaches may be overly restrictive. 

Finally, we have developed a novel optimization strategy for control synthesis that operates on the sequencing graph abstraction. This approach, called relative control optimizations, departs from more conventional control optimizations that are based on the FSM model in that it takes advantage of the degrees of freedom present at the behavior level. In particular, it minimizes the size of the control... 

Relative and absolute MIP gap mixed integer programming parameter for controlling optimization accuracy e g. MIP gap of 1% leads to an algorithm stop, if the objective value cannot be improved within a tolerance interval of 1%. 

The amplitude of temperature fluctuations was controlled in a feedback loop by adjusting the relative phase between the primary and secondary forced air flows. A demonstration of the closed-loop performance is illustrated in Fig. 24.12. The controller converged on the optimum phase with a 1/e rise time of approximately 30 control steps (Fig. 24.12a). Figure 24.126 illustrates the difference between the power spectra with control off (i.e., neither primary nor secondary drivers) and control optimized. The response time necessary to reach the optimum phase was slowed by the large variations in the measured coherence (examples shown in Fig. 24.12a) which are attributed to the complex interactions between the inlet mode, the combustor modes, and the preferred mode of the jet. 

In another example of application of the simplex method, McMullen et cd. [38] demonstrated the rapid optimization and scaling of a Heck reaction using an automated microreactor system with HPLC monitoring and feedback control. Optimal reaction conditions in the microreactor were determined after 19 automated experiments and required a relatively small amount of starting material. The reaction was then successfully scaled up 50-fold from a microreactor to a Coming meso-scale glass reactor using the optimal conditions determined by the microreactor system. 

Conflict resolution, relative scheduling, relative control synthesis and optimization are formulated on a constraint graph model that is derived from the sequencing graph model under detailed timing constraints. Descriptions and analyses of these formulations are presented in subsequent chapters. 

The sequencing graph model is the underlying representation for design space exploration, which is described in the next chapter. Relative scheduling, constrained conflict resolution, and relative control synthesis and optimization are all formulated based on the constraint graph model. 

For ease of presentation, relative scheduling is first described in Chapter 6, where resource conflicts are assumed to be resolved. Resource conflict resolution by appropriately serializing the operations subject to the timing constraints is presented in Chapter 7. Control generation from relative scheduling is described in Chapter 8. A novel approach to control optimization called resynchronization is described in Chapter 9. 

These secondary goals may be conflicting, i.e., the schedule that minimizes the latency may be different than the schedule that minimizes the control cost We address in this chapter the first goal of finding the minimum latency schedule the second goal is the topic of Chapter 9 on control optimization. Therefore, the term relative schedule in the remainder of this chapter refers to the minimum relative schedule, unless otherwise stated. 

It turns out that there is another branch of mathematics, closely related to tire calculus of variations, although historically the two fields grew up somewhat separately, known as optimal control theory (OCT). Although the boundary between these two fields is somewhat blurred, in practice one may view optimal control theory as the application of the calculus of variations to problems with differential equation constraints. OCT is used in chemical, electrical, and aeronautical engineering where the differential equation constraints may be chemical kinetic equations, electrical circuit equations, the Navier-Stokes equations for air flow, or Newton s equations. In our case, the differential equation constraint is the TDSE in the presence of the control, which is the electric field interacting with the dipole (pemianent or transition dipole moment) of the molecule [53, 54, 55 and 56]. From the point of view of control theory, this application presents many new features relative to conventional applications perhaps most interesting mathematically is the admission of a complex state variable and a complex control conceptually, the application of control teclmiques to steer the microscopic equations of motion is both a novel and potentially very important new direction. 

Most aroma chemicals are relatively high boiling (80—160°C at 0.4 kPa = 3 mm Hg) Hquids and therefore are subject to purification by vacuum distillation. Because small amounts of decomposition may lead to unacceptable odor contamination, thermal stabiUty of products and by-products is an issue. Important advances have been made in distillation techniques and equipment to allow routine production of 5000 kg or larger batches of various products. In order to make optimal use of equipment and to standardize conditions for distillations and reactions, computer control has been instituted. This is particulady well suited to the multipurpose batch operations encountered in most aroma chemical plants. In some instances, on-line analytical capabihty is being developed to work in conjunction with computer controls. 

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