Page 92 - IJOCTA-15-2

Comparison of fractional order sliding mode controllers on robot manipulator
only. So, approach 2 performance with small de-
rivative values is worse compared to other control
structures. For α = 1, the SMC and approach 2
have the same sliding surfaces. So, both of them
must have similar results. It is seen from the Fig-
ures (2, 3), that for α = 0.9, the approach 2 and
SMC have close results. As the α gets closer to 1,
the difference in results will also get smaller. The
same situations can be seen in error Figures (4, 5)
that for α = 0.9 the approach 2 and SMC errors
are less compared to other α values. As the α
value increases, the differences in errors will also
get smaller. Also, it is seen in Table (2) that ap-
proach 2 RMSE values decrease for increasing α
values and come close to SMC. The main reason
for the positive effect of α is that the derivative
effect increases as α increases as stated before for
approach 1.
Figure 5. Θ 2 error under SMC and FOSMC
controllers

Figure 4. Θ 1 error under SMC and FOSMC
controllers Figure 6. Θ 1 control signals under SMC and FOSMC
controllers

According to Eq. (31), approach 3 has a close
sliding surface to SMC for α = 0. Approach 3
derivative value is the same as SMC derivative
value for α = 0 but approach 3 error coefficients’
(µ, β) total value is twice bigger than the SMC
error coefficient’s value for the given constants
µ = 1, β = 1, c = 1. So, as seen from the Figures
(2, 3), approach 3 and SMC have close results
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