In this paper, a relative degree two (RD2) sliding variable based discrete time sliding mode control (DTSMC) is designed for a linear time invariant system when output sampling is done faster than control input computation. The RD2 framework has been established for better performance and improved robustness of the discrete time sliding mode control system. The paradigm of fast output sampling (FOS) is utilized since it allows control computation using only the sampled output information, which is important from the implementation perspective making the design practical. A formal analysis is presented to establish the range of the controller parameters for this novel combination of DTSMC with RD2 sliding variable in the FOS framework. Also, a quantitative analysis of robustness in terms of ultimate band for the RD2 approach is done and compared with that of the RD1 approach. The theory is validated in a test bench application of a buck converter for tracking voltage references utilizing the FOS paradigm. The FOS paradigm had previously not been tested in any practical system with DTSMC, and this is the first time it is presented for the dc–dc buck converter system.

在本文中，当输出采样速度快于控制输入计算速度时，针对线性时不变系统设计了基于相对度二 (RD2) 滑动变量的离散时间滑动模式控制 (DTSMC)。RD2框架的建立是为了提高离散时间滑模控制系统的性能和鲁棒性。使用快速输出采样 (FOS) 的范例是因为它允许仅使用采样输出信息进行控制计算，这从使设计实用的实现角度来看很重要。提出了一种正式的分析，以确定 FOS 框架中 DTSMC 与 RD2 滑动变量的这种新颖组合的控制器参数范围。还，对 RD2 方法的最终频带稳健性进行了定量分析，并与 RD1 方法进行了比较。该理论在降压转换器的测试台应用中得到验证，用于使用 FOS 范例跟踪电压参考。FOS 范例以前没有在任何带有 DTSMC 的实际系统中进行过测试，这是第一次针对 dc-dc 降压转换器系统提出。