Multiple inputs

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... 

Systems with multiple inputs 4.3.1 Principle of superposition... 

D. Pattern Recognition with Multiple Input Variables. . . . ... 

D. Pattern Recognition with Multiple Input Variables... 

The limitation of transfer function representation becomes plain obvious as we tackle more complex problems. For complex systems with multiple inputs and outputs, transfer function matrices can become very clumsy. In the so-called modem control, the method of choice is state space or state variables in time domain—essentially a matrix representation of the model equations. The formulation allows us to make use of theories in linear algebra and differential equations. It is always a mistake to tackle modem control without a firm background in these mathematical topics. For this reason, we will not overreach by doing both the mathematical background and the control together. Without a formal mathematical framework, we will put the explanation in examples as much as possible. The actual state space control has to be delayed until after tackling classical transfer function feedback systems. 

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. 

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. 

In CGP (which does not have development), a single node has a function (e.g., addition or multiplication), inputs (e.g., 2), and an output representing the result of the application of the node s function to its inputs. Each node has a number representing its position and each of its inputs has a number indicating its connectivity. 

These multiple input experiments can be carried out in a crossover fashion. 

When dealing with an entire fire detection system that utilizes more than one type of detector, a Detonator Module greatly expands the flexibility and capability of the system. An individual Detonator Module can accept multiple inputs from UV and IR controllers, other Detonator Modules, manual alarm stations, heat sensors, smoke detectors or any contact closure device. In the event of a fire, any of these devices will cause the internal fire circuitry of the module to activate the detonator circuit, sound alarms, and identify the zone that detected the fire. When properly used, a Detonator Module will add only one millisecond to the total system response time. See Figure 8 for an illustration of a fire detection system with a Detonator Module. 

The manufacturing pendant to process industry is the discrete industry e.g. automotive or engineering industry, where discrete products are assembled using other discrete components. Here, production is convergent, since multiple input components are assembled to one produced product resulting e.g. in built-to-order planning problems in the automotive industry (Meyr 2004a). 

RIO - Variable production processes, input and output planning Production processes have variable run times and throughputs as well as multiple input and output products as illustrated in fig. 49. 

Production planning in the chemical industry with processes, variable utilization, comprehensive recipes and multiple input and output products has been in the focus of research in the last years specifically optimization of production schedules and change-overs across resources... 

Production planning of quantities and campaigns described in subchapter 5.6 has to consider the variable production processes with multiple input and output and throughput smoothing as the planning of change-overs between campaigns. 

A probabilistic model will typically require distributions for multiple inputs. Therefore, it is necessary to consider the joint distribution of multiple variables as well as the individual distributions, i.e., we must address possible dependencies among variables. At least, we want to avoid combinations of model inputs that are unreasonable on scientific grounds, such as the basal metabolic rate of a hummingbird combined with the body weight of a duck. 

Identification of multiple input signals and several effector proteins underlines the high complexity of signal transduction via the Ras protein. The Ras pathway cannot be seen as a linear ordering of signal elements, by which information is conducted verti-... 

MINICOMPUTERS. The next step up is a minicomputer based integrator, which may service up to perhaps two to three dozen chromatographs simultaneously. Examples of this class are the 3352-B system of Hewlett-Packard and the PEP-2 system of Perkin-Elmer. The minicomputer may have multiple input/output devices to service two or more locations independently, and may make the computer available (through a language like BASIC) to do further calculations on chromatographic results or to do general laboratory calculations. 

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. 

---