By Leigh, James R
Motion imaginative and prescient: layout of compact movement sensing suggestions for navigation of independent structures - ISBN 0863414532
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The derivation of the filter can be found in the original references (Kalman, 1960, Kalman and Bucy, 1961). 7. Applications of the filter are described in Davies (1978), Litchfield et al (1979), Page (1979) and Wick (1978). 5 The Kalman filter — principle of operation From our point of view, the Kalman filter is a realistic tool that allows reliable estimates of unmeasurable process variables to be made on-line. Such estimates can then be used for closed-loop control or for operator guidance. The filter also allows inaccurate measurements to be processed to give a more accurate data set on which to base control actions.
However, we can search for the minimum cost value of C that will achieve such a g n . Basically, this 18 The economics of industrial control requires a substitution of all possible values of k for each value of/. Readers will recognize the influence of dynamic programming in the nested equation for qn and the computation can be achieved efficiently using a dynamic programming technique. At the end of the exercise, management can be given a set of possible product qualities q'ni q'n, q'n, • • • , and for each, the optimum configuration for its realisation and the total cost can be quoted.
For instance, in a continuous chemical process where the internal composition is impossible to measure, the approach might be to produce a single variable from suitable weighted gas flow, gas temperature and gas analysis information. All that is required is to correlate this single artificial variable with the variables of importance. The advantage of this rather vague-sounding method is that it can achieve good results in return for only moderate expenditure of effort. Of course, if the continuous process is allowed to depart far from its desired state, then the method advocated here cannot be expected to achieve very good correction of such large deviations.