Abstract
This paper describes a design scheme for terminal sliding mode controllers of certain types of non-linear dynamical systems. Two classes of such systems are considered: the dynamic behavior of the first class of systems is described by non-linear second-order matrix differential equations, and the other class is described by non-linear first-order matrix differential equations. These two classes of non-linear systems are not completely disjointed, and are, therefore, investigated together; however, they are certainly not equivalent. In both cases, the systems experience unknown disturbances which are considered bounded. Sliding surfaces are defined by equations combining the state of the system and the expected trajectory. The control laws are drawn to force the system trajectory from an initial condition to the defined sliding surface in finite time. After reaching the sliding surface, the system trajectory remains on it. The effectiveness of the approaches proposed is verified by a few computer simulation examples.
Highlights
The first class of systems considered in the paper is described by non-linear matrix differential equations of the second order
The paper [22] investigated applications of terminal sliding mode control system (TSMC) strategies to rigid robotic manipulators, whose dynamics were described by a second-order non-linear matrix differential equation
This paper is based on the results presented in [41], for the class of non-linear systems described by second-order matrix differential equations with external disturbances
Summary
Stabilization of non-linear systems finds applications in many areas of engineering, in the fields of mechanics, robotics, electronics, and so on [1,2]. In some non-linear systems, such as Chua’s circuit, a phenomenon called chaos can be observed [8,9]. This chaotic behavior can be caused, for example, by uncertainties and non-idealities of the electronic circuit elements [10]. The first class of systems considered in the paper is described by non-linear matrix differential equations of the second order. The second class of the systems can be mathematically modeled by non-linear matrix differential equations of the first order. All systems considered in the analysis can be affected by some unknown external disturbances
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