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Nonlinear Control for Rotational Movement of Cart-pendulum System Using Homoclinic Orbit
Hiroya Oka,Yuji Maruki,Haruo Suemitsu,Takami Matsuo 제어·로봇·시스템학회 2016 International Journal of Control, Automation, and Vol.14 No.5
In this paper, we deal with the control method for rotational movements of a pendulum using a separatrix. We design a controller that attains a homoclinic motion or a heteroclinic motion of the pendulum and the asymptoticstability of the cart by using a kind of forwarding control design. First, we derive a controller that converges toa homoclinic orbit via a Lyapunov function of the pendulum subsystem. Next, we give a nonlinear stabilizingcontroller via another Lyapunov function of the cart subsystem. Moreover, using the third Lyapunov function andadding a complementary control input, we guarantee that the pendulum converges to the homoclinic orbit and thecart is stabilized. Finally, the simulation and the experiment using the rapid controller prototyping system based onMATLAB/Simulink are performed to demonstrate the forward upward circling and the giant swing of the pendulum.
Forwarding Control of Cart-Pendulum System by Following Homoclinic Orbit and Stabilizing Cart
Yuji Maruki,Hiroya Oka,Haruo Suemitsu,Takami Matsuo 제어로봇시스템학회 2014 제어로봇시스템학회 국제학술대회 논문집 Vol.2014 No.10
In this paper, we design a controller that attains a homoclinic motion of the pendulum and the asymptotic stability of the cart by using a kind of forwarding control design. First, we derive a controller that converges to a homoclinic orbit via a Lyapunov function of the pendulum subsystem. Next, we give a nonlinear stabilizing controller via another Lyapunov function of the cart subsystem. Moreover, using the third Lyapunov function and adding a complementary control input, we guarantee that the pendulum converges to the homoclinic orbit and the cart is stabilized. Finally, the simulation with MATLAB/Simulink is performed to demonstrate the validity of the proposed control law.