Abstract
The interconnection between optimal control theory and the theory of energy-shaping control is described in our paper. For linear and nonlinear systems, the application of the theory of optimal control for the synthesis of parameters of energy-shaping control matrices is demonstrated in detail. The use of a Riccati equation allows us to form an optimality criterion and to synthesize the energy-shaping control system that provides the desired transient processes. The proposed approach was applied to the synthesis of control influences for electric vehicle subsystems, such as a two-mass system and a permanent magnets synchronous motor. The results of computer simulation studies, as well as those conducted on real experimental installations, are given in this paper.
Highlights
In recent decades, there has been a significant gap between the development of the theory of automatic control and the practical application of the established methods of the synthesis of control influences in technical systems
The mentioned methods of control systems synthesis are quite complex from a mathematical point of view, requiring specialist knowledge for their understanding and application; their widespread use has declined for the time being
A common feature of the above-mentioned methods is the formation of control influences based on state variables [1,7], which will ensure the stability of the synthesized system
Summary
There has been a significant gap between the development of the theory of automatic control and the practical application of the established methods of the synthesis of control influences in technical systems. Unlike the methods of feedback linearization and backstepping, the method of passivity-based control, as a representative of energy-based approaches, is based on the physical laws of energy transfer and conversion [11] This makes its application promising in electromechanical systems, in electric vehicles [12,13], where the energy flow control system is at the core. Considering the feasibility of passivity-based control in electromechanical systems, where providing optimal energy efficiency and energy flow management are key issues, this article aims to solve the problem of synthesis for control system interconnection and damping matrices with the use of the classical theory of optimal control
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