Authors A.R. Gaiduk, E.A. Plaksienko
Month, Year 05, 2016 @en
Index UDC 681.5.013
Abstract Many technological and industrial processes are multivariable as they are characterized several controlled variable and several control actions – controls. The problem of automation of such processes is complicated that they are nonlinear and are described by the several nonlinear equations, and requirements to the differe nce automated variables can be various. In view of the extremely big variety of the nonlinearities the problem of construction of the automation systems for the nonlinear multivariable processes is very difficult. The article is devoted to develop of the analytical design method of the optimal automation algorithms of the nonlinear multivariable technological processes. The method development is based on the idea of academician A.A. Krasovsky – to use uncertain qualities criteria, some functions and parameters of which are appointed during the decision of the optimization problem. For the decision of the problem the method of transformation of the set nonlinear equations of an automation system are involved in special, Jordan controlled form also. This form allows analytically finding, socalled, linearization control which the nonlinear equations of the process, without loss of accuracy of the description, become linear and the initial uncertain nonlinear-quadratic functional passes in usual the quadratic criterion. The final kind of optimal algorithm of automation is defined as a result of the decision with help MATLAB of known Riccati equation. The basic scientific results of this article are conditions of resolvability of the optimal automation problem of multivariable nonlinear technological process both at absence of connections between subsystems, and at presence of these connections. The received conditions consist in restrictions on derivatives of the automation process nonlinearities. The conditions of asymptotic stability of the steady-state process of the multivariable nonlinear automation systems both in domain and global are found also. The developed design method can be applied to construction of the systems of automation of chemical, power and other technological processes and also processes of the special purpose, because the nonlinear equations of many of these processes can be converted to the Journal controlled form. The method allows providing desirable properties of optimal nonlinear automation multivariable systems by a choice of the corresponding values of the parameters of uncertain nonlinear-quadratic criteria.

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Keywords Technological process; multivariable; nonlinearity; automation; Jordan controlled form; design; uncertain nonlinear-quadratic criteria; stability; transient.
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