基于Lyapunov能量函数的倒立摆稳定控制

倒立摆是一种复杂的非线性控制系统.通过对其进行控制能够检验控制器的鲁棒性.基于一个能量形式的Lyapunov函数设计了倒立摆稳定控制器使得摆趋于上平衡位置,并且使得小车位移和角度都收敛于零.该控制策略基于系统的总能量,利用其耗散特性设计了Lyapunov函数,并证明了控制系统的稳定性.理论分析及仿真试验表明该控制器对于倒立摆控制具有很强的鲁棒性.

Lyapunov-energy based stability control for inverted pendulums

The inverted pendulum is a complicated nonlinear control system.The robustness of a control can be verified by controlling it effectively.A stability controller was first designed for inverted pendulums based on a Lyapunov function with the form of energy,the pendulum was then raised to its upper equilibrium position and the cart displacement and angle were both brought to zero.The control scheme was based upon the total energy of the system,and the dissipative characteristic was used to design a Lyapunov function,the stability of the control system was also proved.Through the analysis and simulation,it was (manifested) that the controller has strong robustness.