Adaptative high-gain extended Kalman filter and applications

tel-00559107, version 1 - 24 Jan 2011
Parameter Value Role
Q diag(1, 10 −1 , 10 −2 ) Filtering
R 1 Filtering
θ1 4 High-gain
β 1664 π
e Adaptation*
m1 0.005 Adaptation*
m2 4 Adaptation
λ 5 Adaptation*
∆T 0.1 Adaptation*
d 1 Innovation
δ 0.1 Innovation*
Table 4.1: Final choice of parameters (*: Application-free parameters).
4.2.4 Simulation Results
The performance of the observer is accounted for via two scenarios:
− scenario 2: a single change in the load torque is performed at time 30,
4.2 Simulation
− scenario 3: a series of changes are implemented every 20 units of time. The sequence
of the values taken by Tl is [0.55, 2.5, 1.2, 1.5, 3.0.8, 0.55].
The output of the system for each scenario is displayed in Figure 4.12. The estimation
results are displayed in
− Figures 4.13 and 4.14, for scenario 2,
− Figures 4.15 and 4.16, for scenario 3.
In all the figures, the thick black line corresponds to the real values of the state variables. In
each case the behaviors of several observers are shown:
− dark blue plot: estimation rendered by an extended Kalman filter, with Q and R
matrices as given in Table 4.1,
Scenario 1 u(t) = 120 + 12 sin(t), Tl(t) = 0.55 ∀t ≥ 0
Scenario 2 u(t) = 120, Tl(t) =0.55 ∀t ∈ [0; 30[ then Tl(t) =
2.55 ∀t ∈ [30; 100[
Scenario 3 u(t) = 120, Tl(0) = 0.55, Tl(k20),
k > 0 changes according to the sequence
[0.55, 2.5, 1.2, 1.5, 3.0.8, 0.55]
Figure 4.11: The several simulation scenarios.
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