Abstract
The stabilization of a Rotary Inverted Pendulum based on Lyapunov stability theorem is investigated in this paper. The key of designing control laws by Lyapunov control method is the construction of Lyapunov function. A logarithmic function is constructed as the Lyapunov function and is compared with the usual quadratic function theoretically. The comparative results show that the constructed logarithmic function has higher numerical accuracy and faster convergence speed than the usual quadratic function. On this basis, the control law of stabilizing Rotary Inverted Pendulum is designed based on the constructed logarithmic function by Lyapunov control method. The effectiveness of the designed control law is verified by experiments and is compared with LQR controller and the control law designed based on the quadratic function. Moreover, the system robustness is analyzed when the system parameters contain uncertainties under the designed control law.
Highlights
The Rotary Inverted Pendulum, which was proposed by Furuta et al [1], is a well-known test platform to verify the control theories due to its static instability
The control law of stabilizing Rotary Inverted Pendulum is designed based on Lyapunov stability theorem
A logarithmic function is constructed as the Lyapunov function, based on which the control law is designed by Lyapunov control method
Summary
The Rotary Inverted Pendulum, which was proposed by Furuta et al [1], is a well-known test platform to verify the control theories due to its static instability. Considering the mentioned facts, Rotary Inverted Pendulum is selected as the controlled system and lots of control problems are concerned by researchers, such as stabilizing the pendulum around the unstable vertical position [7,8,9], swinging the pendulum from its hanging position to its upright vertical position [10,11,12,13], and creating oscillations around its unstable vertical position [14, 15]. For the swing-up and stabilizing control of Rotary Inverted Pendulum, a variety of control methods had been applied. Hassanzadeh and Mobayen used particle swarm optimization (PSO) method to search and tune the controller parameters of PID in the control of balancing the pendulum in an inverted position [19]
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