Application of Predictive Control to Optimize Dynamic Processes in a Given Range
Abstract
The problem of digital control of controlled variables for a dynamic process with their retention in a given range is considered. It is assumed that the change of variables within the range can be arbitrary, but the values of variables must remain within the established boundaries. At the same time, if all the constraints are met, then the control should either be turned off or have as little intensity as possible. This formulation of the problem requires the development of special methods for the synthesis of control laws, different from traditional approaches in which the control goal is set by a command signal.
A formalized formulation of the control synthesis problem is performed for a nonlinear object model specified in discrete time, taking into account constraints on the control signal. A method of synthesis of the digital control law based on the use of predictive models in the feedback loop is proposed. The goal of object control is achieved by introducing a quadratic quality functional, including a penalty for violation of a specified range by controlled variables. In addition, this functionality characterizes the intensity of the control operation and allows adjusting energy costs using a weight multiplier. It is shown that the implementation of the control law in real time in the general case is reduced to solving the problem of nonlinear programming at each sample instant of discrete time. The effectiveness of the developed approach is illustrated by an example of controlling the oil refining process in a distillation column.
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