平面二级倒立摆自适应滑模控制器设计

Design of Adaptive Sliding Mode Controller for Planar Double Inverted Pendulum

研究平面二级倒立摆系统稳定性和速度特性优化问题,由于倒立摆系统的外界扰动的不确定性,建立平面二级倒立摆的数学模型,应用变结构控制理论(SMC)和模糊逻辑系统设计了自适应滑模控制器,把趋近律和切换控制的模糊化相结合,采用模糊系统调整趋近速率的大小,在加快趋近速度的同时用模糊逼近切换控制,为减少控制量的抖振和优化控制系统,同时倒立摆控制具有了滑模控制对外界扰动和参数摄动的不变性。进行仿真的结果验证了控制器的稳定性,表明控制器系统能保证在不同的运行条件下具有快速性和鲁棒性。

The mathematical model of planar double inverted pendulum was established by means of analytical dynamics method. Taking into account the uncertainty of inverted pendulum system external disturbances, adaptive sliding mode controller was proposed based on sliding mode control （SMC） theory and fuzzy logic system. Based on the reach law and fuzzification of the switch control, the controller can adjust the convergence rate and approximate switch control via fuzzy system. Then the chattering of control action exerted on the pendulum was weakened, and the output of the controller was improved. At the same time, inverted pendulum system has the features that SMC can keep invariance to the external disturbance and parameter perturbation. Lyapunov function was used to prove the stability of the controller. Simulation results also show that this controller can ensure the fast responses under different operating conditions and good stability and robustness.