Abstract
The work uses the method of standard characteristic polynomials, based on the Lyapunov theorem on adaptive control systems, the theory of flexible and robust control, methods of the theory of nonlinear systems. When modeling an internal combustion engine, methods of identification theory were additionally involved. When obtaining theoretical results, the method of Lyapunov functions, the method of standard characteristic polynomials, methods of the theory of adaptive and robust control, methods of the theory of nonlinear systems were used. When constructing a model of an internal combustion engine, methods of identification theory were additionally involved. For the synthesis of control systems in conditions of uncertainty, one of the topical directions is adaptive systems. These are control systems that compensate for parametric, signal, functional, or structural uncertainties of the control object by automatically adjusting the controller during the system's working operation, i.e., adaptive systems make up for the lack of a priori information about the control object during operational operation. To solve the problem of managing undefined objects, for example, classical methods are used. In such methods, when state variables are immeasurable, it becomes necessary to use additional dynamic filters. Classical methods are more often used for a limited class of objects. In the case of class extension, the structure of the control algorithm becomes more complicated.
Highlights
One of the current directions of the modern theory of adaptive and robust control is the search for ways to build sufficiently simple control algorithms for objects with uncertainties
To state the idea underlying the method of synthesis of adaptive regulators, let us consider a simple example of the problem of stabilizing the output of a nonstationary scalar object of the form: x x u where x is the controlled variable; u is the control signal, (t) is the bounded unknown function; – perturbation, const 0)
For the synthesis of control systems in conditions of uncertainty, adaptive systems are one of the topical directions. They are such control systems that provide compensation of parametric, signal, functional, or structural uncertainties of the control object due to automatic adjustment of the regulator in the course of operation of the system, i.e., adaptive systems compensate for the lack of a priori information about the control object in the course of operation [1]
Summary
One of the current directions of the modern theory of adaptive and robust control is the search for ways to build sufficiently simple control algorithms for objects with uncertainties. By simplifying the control algorithm, we understand both the reduction of its dynamic order and the reduction of the number of arithmetic operations in the regulator structure, the reduction of the number of adjustable parameters, and the number of measurable variables. The relevance of this direction is due to the problem of complexity of existing solutions, even for simple object models. The main subject of research reflected in the article is to obtain a simple, practically realizable solution of the control problem for a nonstationary parametrically indeterminate object of arbitrary order and arbitrary relative degree
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