Abstract
The paper presents a design scheme of the linear dynamic feedback controller for some non-linear systems. These systems are mathematically described by matrix non-linear differential equations of the first and second orders. A first-order form of the studied systems includes some types of differential-algebraic equations. The stability property of the non-linear systems with the linear controller is assured by an appropriate definition of the system output, and the linear dynamic compensator is an important part of the feedback control system. The order of the dynamic part is equal to the size of the system input and is independent of the size of the system state vector. The asymptotic stability in the Lyapunov sense is analysed and proved by the use of Lyapunov functionals and LaSalle’s invariance principle. Stabilisation in a wide range of controller parameters improves the system’s robustness.
Highlights
Almost all real systems are non-linear by nature and it is well known that non-linearity needs complex analysis
Non-linear systems have a wide range of uses in mechanics, electronics and robotics
The order of the dynamic part is equal to the size of the system input vector and is independent of the size of the system state vector
Summary
Almost all real systems are non-linear by nature and it is well known that non-linearity needs complex analysis. The controller itself, should be, if possible, linear, robust to the parameters’ uncertainties and external disturbances, with the lowest possible order of the dynamic part, and implemented in real-time embedded platforms This is because, in modern applications, the controller is a system that can be considered as a combination of computer hardware and software designed to perform a dedicated control function. The stabilisation of non-linear second-order systems finds applications in mechanics, electronics and robotics. The aim of the paper is to design a linear dynamic feedback controller, able to asymptotically stabilise some classes of non-linear systems. The purpose of this paper is to utilise classical version of the principle where it appears straightforward and conclusive Both methods, both in classical and non-classical versions, are widely recognised as the most powerful techniques for analysing the stability of the systems whose dynamics is described by nonlinear differential equations. The stability of the closed-loop systems is assured in a wide range of the controller’s parameters, which definitely improves the system’s robustness
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