Page 62 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

Adaptive Dynamic Surface Control of Two-Inertia Systems With LuGre Friction Model 53

Table 3.1 Nominal parameters of the test-rig
Parameter Value Unit
Power 1.5 kW
Nominal motor voltage 230 V
Shaft length 40 cm
Nominal speed 3600 r/min
Motor inertia J m 0.0062 kg m
Load inertia J l 0.004106 kg m
Stiffness coefficient k f 65 N m

Figure 3.8 Tracking performance for sinusoid wave (A) PID, (B) ECDSC, and (C) tracking
error.

The controller parameters are given as set as ρ 1,i = ρ 2,i = 1(i = 1,2,3),
H = 100, α = 1/2, β = 2/3, 1 = 2 = 0.1, k 1 = 2,k 2 = 10,k 3 = 15. The
prescribed performance function parameters are μ i0 = 4, μ i∞ = 1, κ i = 3,
and δ = 1.5, δ i = 2, i = 1,2,3. The ESN parameters are the same as those
i
used in the simulation. For comparison, a PID control is also tested with
parameters K p = 4, K i = 0.25, and K d = 0.03.
In the experiments, a sinusoid signal x d = 5sin(0.4πt) is adopted as ref-
erence signal. The experiment results are shown in Fig. 3.8. We can find