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By Leigh, James R

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It will be discussed only briefly. Problem (b) is the so-called observer problem. The solution involves using the process model to produce a reconstructed state vector. Problem (c) can be solved completely under very restrictive conditions (linearity, independence, Gaussian statistics) using the Kalman filter. However, as we shall indicate, with perseverance and engineering compromise, the Kalman filter can be made to work very satisfactorily in industrial situations. The Kalman filter is an algorithm that allows optimal estimation of the internal variables of a process from noisy measurement.

Of course, most sequential process routes are not so simple as in the example. The process route will often fork or even have closed loops but with care the approach advocated here will still be useful in deciding how much to invest in control and how to balance the investment between the different stages in the sequence. 8 Post-implementation checks on economic benefits Checks to ensure that the hoped-for benefits of an automation scheme are, in fact, obtained may be carried out by techniques similar to those described earlier as suitable for the pre-implementation justification.

1 illustrates the operation. Notice in particular the simple actuator arrangement. A two-speed gearbox is all that is required. A controller with a continuous output would have required an infinitely variable-speed drive for the worm, with consequent increase in cost. 3 One-, two- and three-term controllers From a theoretical standpoint, the simplest controller of all is one that compares a measured value with the desired value and, multiplying by a gain k, closes the control loop. Such a controller is called a one-term controller or a ?

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