Abstract
To create control systems, mathematical models of objects are required, which often have to be obtained experimentally. In this case, the numerical data of experiments on the identification of essentially nonlinear objects can be satisfactorily approximated only in certain areas, which leads to fragmentary models that are not analytical. In these cases, when only fragmentary models are adequate, it is proposed to apply the new Cut-Glue approximation method, which allows obtaining a model with analytical properties. The proposed approach to the unification of the Cut-Glue approximation method is demonstrated by solving the problem of synthesizing a nonlinear airship altitude control system and studying it.
Highlights
The development of modern automatic control systems (ACS) for various technological processes, in particular, transport, chemical, information, telecommunications objects and their systems is impossible without their mathematical models (MM)
Analytical methods for the synthesis of ACS are a developed tool and make it possible to find the laws of control of objects, including nonlinear ones, by solving systems of resolving equations, which take into account both the requirements for the quality of the ACS and the properties of control objects [1,2,3,4]
The complex problem of synthesizing nonlinear control laws for an essentially nonlinear control object is supposed to be solved by the example of synthesizing an airship altitude control system in the following sequence: first of all, the features of the method for solving the problem of synthesizing nonlinear ACS based on quasilinear MMs are considered in order to clarify the requirements for MM caused by this method; – the process of building a CGA model of the airship altitude control process and its transformation into a quasilinear form; synthesis of the law for controlling the height of the airship flight; and, numerical simulation of the synthesized ACS to confirm the results of the proposed approach, especially in the areas of fragments joining
Summary
The development of modern automatic control systems (ACS) for various technological processes, in particular, transport, chemical, information, telecommunications objects and their systems is impossible without their mathematical models (MM). Many analytical methods for the synthesis of nonlinear ACS have been developed, such as the method of linearization by feedback [9], the method of point transformations [1, 4, 10], the method of inverse step [11], the method of passivation [12], output control [13], method of quasilinear models [10] Application of these methods is possible after conversion of mathematical model of control object into one of many special forms of equation representation. The method of linearization by feedback involves the use of Lee algebra, which requires finding partial derivatives from the right parts of the differential equations of MM, similar requirements for MM occur in other methods The study of this problem showed that the process of synthesis of nonlinear control systems by analytical methods is well formalized, as well as for linear ones, but the initial MM must be analytical. Let us consider the main provisions of the ACS synthesis method based on quasilinear models of the control object, as well as the CGA method
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