Generalized control problem

Controllers for closed-loop systems 4.5.1 The generalized control problem... 

Dual fuel firing was cited in Chapter 6 as an example of bias feedforward control. Here we will expand on this technique. The general control problem is illustrated in Figure 10.8. 

Generally speaking, temperature control in fixed beds is difficult because heat loads vary through the bed. Also, in exothermic reactors, the temperature in the catalyst can become locally excessive. Such hot spots can cause the onset of undesired reactions or catalyst degradation. In tubular devices such as shown in Fig. 2.6a and b, the smaller the diameter of tube, the better is the temperature control. Temperature-control problems also can be overcome by using a mixture of catalyst and inert solid to effectively dilute the catalyst. Varying this mixture allows the rate of reaction in different parts of the bed to be controlled more easily. 

A. E. Broderick (Union Carbide). HEC did not become a viable commercial product until the early 1960s. In addition to the general production problems and market development costs, new products face a variety of environmental controls in the 1990s that add more constraints to market development. None the less two more recentiy developed water-soluble polymers have achieved limited market acceptance and are described below. 

In order to assure control of the reaction, the vapor-phase inhibitor concentration must be closely controlled in the ppm range. Although several compounds have been claimed to be useful, it is likely that commercial processes use only ethylene dichloride or some of the simpler chlorinated aromatics (102). In general, the choice between inhibitors is not based on their differences in performance, but rather on the designers preference for dealing with the type of control problems each inhibitor system imposes (102). 

RGA Method for 2X2 Control Problems To illustrate the use of the RGA method, consider a control problem with two inputs and two outputs. The more general case of N X N control problems is considered elsewhere (McAvoy, Interaction Analysis, ISA, Research Triangle Park, North Carohna, 1983). As a starting point, it is assumed that a linear, steady-state process model is available. 

Introduction The model-based contfol strategy that has been most widely applied in the process industries is model predictive control (MFC). It is a general method that is especially well-suited for difficult multiinput, multioutput (MIMO) control problems where there are significant interactions between the manipulated inputs and the controlled outputs. Unlike other model-based control strategies, MFC can easily accommodate inequahty constraints on input and output variables such as upper and lower limits or rate-of-change limits. 

The current widespread interest in MFC techniques was initiated by pioneering research performed by two industrial groups in the 1970s. Shell Oil (Houston, TX) reported their Dynamic Matrix Control (DMC) approach in 1979, while a similar technique, marketed as IDCOM, was published by a small French company, ADERSA, in 1978. Since then, there have been over one thousand applications of these and related MFC techniques in oil refineries and petrochemical plants around the world. Thus, MFC has had a substantial impact and is currently the method of choice for difficult multivariable control problems in these industries. However, relatively few applications have been reported in other process industries, even though MFC is a veiy general approach that is not limited to a particular industiy. 

A generalized closed-loop control system is shown in Figure 4.22. The control problem can be stated as The control action u t) will be such that the controlled output c t) will be equal to the reference input r t) for all values of time, irrespective of the value of the disturbance input riit) . 

An optimal control system seeks to maximize the return from a system for the minimum cost. In general terms, the optimal control problem is to find a control u which causes the system... 

The actual noise levels produced by HVAC systems can var) considerably, and it is not possible to generalize the problems that may be encountered. From a safety point of view, it is advisable to start hearing conservation programs for workers. Permanent hearing damage will result when the noise levels exceed 80 dB(A) for a given time period. Whenever possible, it is desirable to control noise pressure levels to meet the requirements of speech communication in this case noise should not exceed 65-70 dB(A). 

We now review the Laplace transform of some common functions—mainly the ones that we come across frequently in control problems. We do not need to know all possibilities. We can consult a handbook or a mathematics textbook if the need arises. (A summary of the important ones is in Table 2.1.) Generally, it helps a great deal if you can do the following common ones... 

Generally, we can write the transfer function as the ratio of two polynomials in 5.1 When we talk about the mathematical properties, the polynomials are denoted as Q s) and P(s), but the same polynomials are denoted as Y(s) and X(s) when the focus is on control problems or transfer functions. The orders of the polynomials are such that n > m for physical realistic processes.2... 

In techniques such as MBE and VPE, surface limited reactions are generally controlled by the temperatures of the reactants and substrate. In general, the temperature is kept high enough so that any deposition over a monolayer sublimes, leaving only the atomic layer, forming the compound. Problems are encountered when the temperatures needed to form atomic layers of different elements are not the same, as changing the temperature between layers is difficult. 

The experimental identification of the regime that controls the extraction kinetics is, in general, a problem that cannot be solved by reference to only one set... 

Therefore, for large optimal control problems, the efficient exploitation of the structure (to obtain 0(NE) algorithms) still remains an unsolved problem. As seen above, the structure of the problem can be complicated greatly by general inequality constraints. Moreover, the number of these constraints will also grow linearly with the number of elements. One can, in fact, formulate an infinite number of constraints for these problems to keep the profiles bounded. Of course, only a small number will be active at the optimal solution thus, adaptive constraint addition algorithms can be constructed for selecting active constraints. 

---