Chattering-Free Reference Sliding Variable-Based SMC

Table 1

Comparison of the obtained quasi-sliding mode band widths and maximum state errors.

Discretization period	Proposed new strategy	Original strategy
Ultimate band width
T = 0.1 s	2·6.13·10^−2 = 2·6.13·T^2	2·0.65
T = 0.05 s	2·1.55·10^−2 = 2·6.2·T^2
T = 0.01 s	2·6.2·10^−4 = 2·6.2·T^2
Maximum error of η1
T = 0.1 s	0.003 = 0.3·T^2	0.0321
T = 0.05 s	0.0004 = 0.16·T^2
T = 0.01 s	0.000031 = 0.31·T^2
Maximum error of η2
T = 0.1 s	0.0605 = 6.05·T^2	0.6419
T = 0.05 s	0.01538 = 6.15·T^2
T = 0.01 s	0.00062 = 6.2·T^2