采用幂次趋近律的滑模控制稳态误差界

Sliding mode control approach based on nonlinear integrator

对一类不确定非线性系统采用幂次趋近律的滑模跟踪控制,分别推导了采用Slotine形式的传统滑模面和积分滑模面时的稳态跟踪误差的界.首先,基于Lyapunov方法求出了滑模误差的最终界和系统不确定性、幂次趋近律参数之间定量的数学关系.其次,利用有界输入有界输出稳定的方法,分别求出了采用Slotine形式的传统滑模面和积分滑模面时滑模误差界与稳态误差界之间定量的数学关系.最后,综合得到了稳态跟踪误差界的数学表达式.并且根据给定的稳态跟踪误差要求,设计出适合的幂次趋近律来抑制抖振.仿真算例验证了上述理论结果的正确性.

For the sliding mode tracking control of a class of uncertain nonlinear systems using power rate reaching law,the steady-state error bounds are respectively derived when using the Slotine-form conventional sliding surface and the integral sliding surface.Mathematical relations among the sliding error bounds,system uncertainties,and parameters of the power rate reaching law are investigated by means of the Lyapunov method.Based on the BIBO stability,the relationship between the steady-state error bounds and the sliding error bounds is obtained.Finally,the mathematical expressions of the steady state tracking error bounds are derived.Moreover,for the specified steady-state error bounds,an appropriate power rate reaching law to suppress the chattering is designed.Simulation results are given and the validity of the conclusions is confirmed.