基于Backstepping的板球系统自适应神经网络H_(∞)控制

Backstepping-based Adaptive Neural Network H_(∞) Control of Ball and Plate System

针对一个同时考虑了小球离心加速度及小球与板之间的未知摩擦力的非严格反馈形式的板球系统模型,基于Backstepping方法和H_(∞)控制理论首次研究了系统受到外部扰动时的H_(∞)跟踪控制问题。提出了一种自适应神经网络H_(∞)控制方法,获得了板球系统的自适应神经H_(∞)控制器。在控制器设计中,先借助一种变量分离方法对板球系统数学模型中的非严格反馈项进行处理,而后对于设计过程中出现的未知函数用神经网络进行近似逼近,并借助动态面技术避免了Backstepping方法的计算复杂性。所设计的控制器能够保证闭环板球系统内所有信号半全局一致最终有界,且系统具有对外部干扰的抑制能力。系统仿真实验证明了所设计控制器的有效性。

Based on backstepping method and H_(∞) control theory,the H_(∞) tracking control problem is first studied for a nonstrict-feedback ball and plate system model considering the centrifugal acceleration of the ball and unknown frictions between the ball and plate as well as external disturbances.An adaptive neural network H_(∞) control method is proposed so that the adaptive neural network H_(∞) controller is obtained for the ball and plate system.In the controller design,the nonstrict-feedback term in the mathematical model of the ball and plate system is handled by a variable separation method.Then the unknown functions appearing in the design process are approximated by neural networks,and the computing complexity of backstepping method is avoided by virtue of the dynamic surface technique.The designed controller can ensure that all the signals in the closed-loop ball and plate system are semi-globally uniformly ultimately bounded,and the system has the ability to attenuate external disturbances.The effectiveness of the designed controller is proved by a simulation experiment.