Implementation of the New Control Methods in Simplification of a Multidimensional Control and Optimization of a Control System Parameters




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Wydawnictwo Politechniki Łódzkiej ; Katedra Dynamiki Maszyn - Wydział Mechaniczny Politechniki Łódzkiej
Lodz University of Technology. Press ; Division of Dynamics - Faculty of Mechanical Engineering, Lodz University of Technology


The main purpose of this text is to present application of the Largest Lyapunov Exponent (LLE) as a criterion for optimization of the new type of simple controller parameters. Investigated controller is the part of numerically simulated control system. The calculation of LLE was done with a new method [2]. Introduction contains reference to previous publications on inverted pendulum control and Lyapunov stability. Application of the new simple formula for LLE estimation in control systems is discussed. In the next part simulated dynamical system is described and new type of simple controller allowing to control multidimensional system is introduced. In the last part results of the simulation are shown along with conclusions to whole dynamics analysis. Comparison of the proposed regulator with the linearquadratic regulator (LQR) was verified and its better effectiveness with respect to LQR was proved.


Słowa kluczowe

largest Lyapunov exponent, robot control, stability, nonlinear dynamics, największy wykładnik Lapunowa, sterowanie robotem, stabilność, dynamika nieliniowa


Mechanics and Mechanical Engineering, Vol. 19, No. 2, 2015, s. 127-139