输入具有齿隙非线性特性的周期系统的自适应控制

针对一类输入含齿隙非线性动态特性的周期时变系统, 在周期不确定性可时变参数化的条件下设计自适应控制器. 对周期时变参数进行傅里叶级数展开, 并采用微分自适应律估计未知傅里叶系数和齿隙动态特性参数, 通过鲁棒方法消除截断误差和齿隙模型的有界误差项对系统性能的影响. 采用双曲函数替代符号函数确保控制器可微, 同时能有效抑制颤振. 引入Δ函数, 避免参数估计发散, 并保证系统输出渐近跟踪理想轨迹. 理论分析与仿真结果表明, 闭环系统所有信号有界.

Adaptive control of a class of periodically time-varying nonlinear systems with input backlash

An adaptive controller is designed for a class of periodically time-varying systems with input backlash,when the periodical uncertainties can be parameterized.The unknown periodical parameters are expanded into a Fourier series;the coefficients of which and the unknown parameters of the backlash dynamics are estimated by using differential adaptive algorithms.A robust method is applied to eliminate the influences of truncation errors and bounded errors in the backlash model on the system performance.The sign function is replaced by the hyperbolic function to ensure the differentiability for the controller and to avoid the chattering.The introduction of △ functions ensures the boundedness for the parameter estimates and the asymptotical convergence for the desired trajectory.The theoretical analysis and the numerical experiment show that all the signals in the closed-loop system remain bounded.