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Analysis and Synthesis of Control Systems
Nonlinear control laws based on linear ones using odd functions
I. B. Furtat, P. Gushchin, E. Kopisova Institute of Problems of Mechanical Engineering RAS, St.Peterburg
Abstract:
The paper investigates nonlinear control laws obtained from linear one by two types of coordinate change by using odd functions. The first coordinate change consists in passing each component of the state vector through a nonlinear function, the second coordinate change is in passing the entire linear control law through a nonlinear function. To study such systems, it is proposed to represent nonlinear functions as linear ones with a nonlinear slope. Such a representation will allow using the methods of linear matrix inequalities (LMI) to study the stability of the closed-loop systems. The stability domains and the domains for the initial conditions are found, obtained as a result of a multi-step solution search procedure using LMI. It is shown that the use of the proposed nonlinear control laws makes it possible to reduce the steady-state error compared to the linear one. The simulations illustrate the theoretical conclusions.
Keywords:
dynamical system, nonlinear control law, linear matrix inequalities.
Received: December 6, 2022 Published: March 31, 2023
Citation:
I. B. Furtat, P. Gushchin, E. Kopisova, “Nonlinear control laws based on linear ones using odd functions”, UBS, 102 (2023), 58–75
Linking options:
https://www.mathnet.ru/eng/ubs1146 https://www.mathnet.ru/eng/ubs/v102/p58
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Statistics & downloads: |
Abstract page: | 51 | Full-text PDF : | 36 | References: | 12 |
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