Tracking control of ship course system using new six-step zead (Zhang et al discretization) formula with high precision

Abstract

In this paper, firstly, a new six-step Zhang et al discretization (SSZeaD) formula is proposed, which is with the truncation error proportional to the fourth power of sampling period. Then, the SSZeaD formula is used to discretize a ship course system (SCS) for tracking control, and thus the SSZeaD-type SCS model is developed. For comparison purposes, the classical Euler forward formula (EFF) with the truncation error proportional to the first power of sampling period is also used to discretize the SCS, and thus the EFF-type SCS model is obtained. Besides, there is an important parameter called stepsize, which is closely related to the stability and the precision of the above two discrete-time models. In view of the importance of the stepsize, the effective stepsize domains of these two discrete-time models are confirmed by theoretical analyses. Finally, numerical experimental results well verify the higher tracking precision of the SSZeaD-type SCS model as compared with the EFF-type SCS model.