Four-Point ZeaD (Zhang et al Discretization) Formula Applied to Output Tracking of Mass-Spring-Damper Mechanical System

The discretization of continuous-time models is an important topic. To solve the problem (especially, Zhang dynamics models), a ZeaD (Zhang et al discretization) method has been proposed and applied. In order to achieve the discretization of higher precision, a four-point ZeaD (FPZeaD) formula with cubic model precision is used to discretize a mass-spring-damper mechanical system (MSDMS), and thus the FPZeaD-type MSDMS model is obtained. For comparison purposes, Euler discretization (ED) formula with square model precision is also used to discretize the MSDMS, and thus the ED-type MSDMS model is obtained. Note that there is an important parameter called step length, which is closely related to the stability and the precision of the above two discrete-time models. In consideration of the effect of step length, the effective step-length domains of these two discrete-time MSDMS models are confirmed by theoretical analyses. Besides, numerical experimental results well verify the higher tracking precision of the FPZeaD-type MSDMS model as compared with the ED-type MSDMS model.