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Nonlinear feedback control of chaotic pendulum in presence of saturation effect. (English) Zbl 1142.93342
Summary: A feedback linearization control is applied to control a chaotic pendulum system. Tracking the desired periodic orbits such as period-one, period-two, and period-four orbits is efficiently achieved. Due to the presence of saturation in real world control signals, the stability of controller is investigated in presence of saturation and sufficient stability conditions are obtained. At first feedback linearization control law is designed, then to avoid the singularity condition, a saturating constraint is applied to the control signal. The stability conditions are obtained analytically. These conditions must be investigated for each specific case numerically. Simulation results show the effectiveness and robustness of proposed controller. A major advantage of this method is its shorter chaotic transient time in compare to other methods such as OGY and Pyragas controllers.
MSC:
93B52Feedback control
93C85Automated control systems (robots, etc.)
37D45Strange attractors, chaotic dynamics
93C10Nonlinear control systems
93B51Design techniques in systems theory