Multiplicity, output input

Multivariable control strategies utilize multiple input—multiple output (MIMO) controUers that group the interacting manipulated and controlled variables as an entity. Using a matrix representation, the relationship between the deviations in the n controlled variable setpoints and thek current values,, and the n controUer outputs, is... 

Watt, Universal AC Input, Multiple-output Flyback Converter... 

Reduce >f minimal cui failure data Mathematical combination of uncertainties output includes two moments of minimal cutsets and the lop event Johnson, empirical C le multiple. sy.siem fiiiJLuizjn with multiple data input descriptions can fit Johnsem-type distribution to the top event 1 t brnia... 

Unlike the preceding discussion, hydraulic systems can provide mechanical advantage or a multiplication of input force. Figure 40.12 illustrates an example of an increase in output force. Assume that the area of the input piston is 2 square inches. With a resistant force on the output piston, a downward force of 20 pounds acting on the input... 

In the next two examples, we illustrate how state space models can handle a multiple-input multiple output (MIMO) problem. We ll show, with a simple example, how to translate information in a block diagram into a state space model. Some texts rely on signal-flow graphs, but we do not need them with simple systems. Moreover, we can handle complex problems easily with MATLAB. Go over MATLAB Session 4 before reading Example 4.7A. 

The next task is to seek a model for the observer. We stay with a single-input single-output system, but the concept can be extended to multiple outputs. The estimate should embody the dynamics of the plant (process). Thus one probable model, as shown in Fig. 9.4, is to assume that the state estimator has the same structure as the plant model, as in Eqs. (9-13) and (9-14), or Fig. 9.1. The estimator also has the identical plant matrices A and B. However, one major difference is the addition of the estimation error, y - y, in the computation of the estimated state x. 

There are many advanced strategies in classical control systems. Only a limited selection of examples is presented in this chapter. We start with cascade control, which is a simple introduction to a multiloop, but essentially SISO, system. We continue with feedforward and ratio control. The idea behind ratio control is simple, and it applies quite well to the furnace problem that we use as an illustration. Finally, we address a multiple-input multiple-output system using a simple blending problem as illustration, and use the problem to look into issues of interaction and decoupling. These techniques build on what we have learned in classical control theories. 

In this section, we analyze a multiple input-multiple output (MIMO) system. 

Here p is the set of characteristic values of the parameters i.e. p(x) = p co(jt) where w(x) has values centered on 1. Often we can set p = / p(x) g(x) dx. The proof is really a statement of what linearity means, for if g(x)djt is the input concentration, g(x)dx.A(p(x)) is the output when the parameter values are p(x). Here x serves merely as an identifying mark, being truly an index variable and the integration in equation (14) follows from the superposition principle for linear systems. The same principle allows an obvious extension to multiple input, multiple output linear systems. A becomes a matrix whose elements are the response at one of the out-ports to a unit input at one of the in-ports, the input at all the others being zero. The detail of this case will not be elaborated here, but rather shall we pass to an application. 

A distillation column provides a good example of multiple input/multiple output (MIMO) control and illustrates well the qualitative methodology involved in determining a suitable control strategy for a process. The first requirement is to decide the primary objective of the process, i.e. what is its principal purpose Let us suppose that, for the column shown in Fig. 7.9, it is required to produce an overhead product D of a particular specification xD without attempting to control... 

Fic. 7.9. Multiple input/multiple output (M1MO) control of a distillation column... 

Interaction can be between two or more processes or between actions produced by different control loops applied to a single process. The former has already been discussed in Section 1.53. Some degree of interaction between control loops will nearly always occur in a multiple-input/multiple-output (MIMO) system. For example, consider the distillation process described in Section 7.3 (Fig. 7.9). Suppose it is desired to control simultaneously the compositions of both the overheads product stream (by manipulating the reflux flowrate) and the bottoms product stream (by regulating the steam flowrate to the reboiler). A typical arrangement is shown in Fig. 7.73. 

The most general heat-balance equation for multiple-reactions, multiple-input and multiple-output system is obtained by summing the enthalpies of the input streams and the output streams. If we have F input streams and we use / as the counter for the input streams and if we have K output streams and use k as their counter with M components and N reactions, then we obtain the most general heat-balance equation in the form F / M K / M N... 

This is the most general heat-balance equation for a multiple input, multiple output, multiple reactions (and of course multi-components) system. 

For the sake of generality, we now develop most general mass-balance equations for a two phase system in which each phase has multiple inputs and multiple outputs and in which each phase is undergoing reactions within its boundaries. 

A two-phase heterogeneous system with multiple inputs, multiple outputs, and multiple reactions in each phase and with mass transfer between the two phases... 

This simplifies the problem of multiple inputs. One can proceed similarly for multiple outputs. 

The results from a MINTEQA2 calculation are read to an output file which can be viewed by a text editor. The format of this file can be pre-selected to vary the amount of detail given. Multiple output files can be created in which one of the inputs is systematically varied by selecting the use of the sweep option. 

Empirical Model Identification. In this section we consider linear difference equation models for characterizing both the process dynamics and the stochastic disturbances inherent in the process. We shall discuss how to specify the model structure, how to estimate its parameters, and how to check its adequacy. Although discussion will be limited to single-input, single-output processes, the ideas are directly extendable to multiple-input, multiple-output processes. 

In designing networks for the case of multiple outputs, two possible strategies can be adopted. One is to develop a single model that connects all the inputs to all the outputs. The other, which can be more useful if optimization is the end goal, is to develop a separate network for each of the properties, in effect by having only one output node, corresponding to that property, in the network. 

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