一类3阶非线性系统的非奇异终端滑模控制
Nonsingular terminal sliding mode control for a class of 3-order nonlinear systems

针对传统非奇异终端滑模控制方法不适用于3阶系统的问题,提出一类具有不确定和外干扰的3阶非线性系统的新型非奇异终端滑模控制方法.该方案首先结合Backstepping控制中的动态面方法和传统二阶非奇异终端滑模控制构造非奇异3阶终端滑模面,首次提出采用高阶滑模微分器估计值代替控制器中的负指数项.采用非线性干扰观测器任意精度地估计不确定和干扰,设计控制器中的补偿项.采用终端吸引子函数做趋近律避免抖振的同时能保证有限时间趋近滑模面.基于有限时间稳定李雅普诺夫定理证明了被控状态将在有限时间内收敛到任意小的闭球内.所提出方案快于传统的递阶线性滑模控制和其他非奇异终端滑模控制.仿真中与其他滑模控制方案对比,总误差减小18% 以上,超调及收敛时间也显著下降.
Traditional nonsingular terminal sliding mode control cannot be used for 3-order systems. To solve this problem, a novel nonsingular terminal sliding mode control for a class of 3-order nonlinear systems with uncertainties and disturbances is proposed. Firstly, the dynamic surface of Backstepping control is combined with 2-order nonsingular terminal sliding mode control (TSMC) to construct the 3-order nonsingular terminal sliding modes. Then, the approximations of negative fractional exponential terms are obtained by higher-order sliding mode differentiator (HOSMD) to eliminate the singularity. Then, nonlinear disturbance observer (NDO) is used to approximate unknown uncertainties and disturbance. Terminal attractor is used as reaching law to avoid controller chattering. Based on finite time stability Lyapunov theorem, it is proved that the proposed scheme will force system states into an arbitrary small neighborhood including the origin in finite time. The proposed scheme has faster convergence speed than recursive linear sliding mode control (RLSMC) and other nonsingular TSMC (NSTSMC). In simulation, the total error of the proposed method decreased at least 18% compared with other sliding mode controllers. Overshoot and convergent time are also decreased significantly.