Advanced Control of Industrial Processes: Structures and by Piotr Tatjewski

By Piotr Tatjewski

This e-book provides the ideas and algorithms of complicated business technique keep watch over and online optimization in the framework of a multilayer constitution. It describes the interplay of 3 separate layers of technique regulate: direct regulate, set-point keep an eye on, and fiscal optimization. The booklet good points illustrations of the methodologies and algorithms by way of labored examples and by means of result of simulations in response to business technique versions.

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The structure of a single rule can thus be presented as follows: IF THEN The antecedent defines the condition, and the consequent – the conclusion which will be implemented if the condition is true. The antecedent of a fuzzy rule consists, in the simplest case, of a single condition. Then the rule takes the following form: IF x is A THEN where x is a linguistic variable, while A is a fuzzy set defined by a membership function µA (x). , [155]): 1. Crisp consequent: IF THEN y = ya where ya is a numerical value or a symbolic value, 40 2 Model-based Fuzzy Control 2.

Optimal constant set-point values are obtained through the solution of the steady-state (static) optimization problem which takes the form min Q(c,y) subj. 21) In this problem formulation actual (measured or estimated) disturbance values w are used as constant parameters. However, the disturbances are usually varying, more or less slowly, or changing rarely but abruptly. Therefore, the set-point values should be adapted to these changes, to keep the process close to optimal operation. 21) at regular time intervals corresponding to dynamic properties of the disturbances, or after each significant change of the disturbance values if these changes are irregular but can be measured or estimated on-line.

4. Generalized bell membership functions of slopes and αi influences the width of the “bell”. 7. Let us note that the bell function is symmetric with respect to the vertical axis x = ci . In order to obtain a two-sided asymmetric function, it should be built from two halves of bell functions with different parameters. , [58, 155, 111]. The linguistic variables (fuzzy variables) allow to capture roughly defined phenomena better than numerical variables, defined also as crisp variables. For example, the description of a linguistic variable “temperature”, presented in Fig.

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