Fractional-Order Control of a Micrometric Linear Axis

Table 3

𝜁-𝜓 combinations with dimensionless settling energy equivalent to the pure PD control with 𝜁=0.8.

Parameter set	𝜁	𝜓	Overshoot (%)	Dimensionless settling time	Dimensionless rise time
a0.8	0.8	0	17.78	5.07	0.81
b0.8	0.666	0.688	20.20	3.98	0.70
c0.8	0.5333	0.807	23.99	3.71	0.71
d0.8	0.4	0.7635	29.38	5.32	0.75
e0.8	0.2666	0.598	38.08	8.05	0.83
f0.8	0.2	0.4529	45.35	9.05	0.89
g0.8	0.15	0.251	55.23	15.08	0.97