相对阶数为2的机械非线性采样数据模型

Sampled-data Model of Nonlinear Mass-spring-damper Mechanical Vibration Systems with Relative Degrees Two

针对相对阶数为2的非线性多变量质量-弹簧-阻尼机械振动系统,导出了近似的采样模型和离散性质.采用比Euler模型更复杂的离散采样方式,分析了该近似采样模型的局部截断误差和全局截断误差.特别地,通过研究导出近似离散时间控制模型的采样零动态,给出了相应的渐近特性,还分析设计了离散采样控制器.将线性质量-弹簧-阻尼机械模型情形推广到了非线性系统,在非线性系统辨识方面有应用价值.

The approximate sampled-data models and discretization properties are derived for nonlinear multivariable mass-spring-damper mechanical vibration systems when the corresponding relative degrees of continuous plant are both two. The proposed sampled-data models use a more sophisticated derivative approximation than the simple Euler approach, and the local truncation error and global truncation error are also represented, respectively. An insightful interpretation of the given sampled-data models can be made in terms of an explicit characterization of nonlinear sampling zero dynamics which have no continuous-time counterpart. More importantly, nonlinear discrete-time controller design is also represented based on the above sampled-data model and zero dynamics. The ideas presented here generalize well-known results from the linear case to nonlinear plants. Finally, we also explore the implications of these results in nonlinear system identification.