Lecture
1.What methods of model construction (analytical, experimental, and experimental-analytical) are used at the stage of designing the elements and subsystems of an aircraft engine control system (ECS)?
2.How should experimental data be collected, and how should this data, gathered under real conditions of hardware-in-the-loop and full-scale modeling of an aircraft ECS, be used?
3.Justify the choice of the implementation scheme for identifying subsystems of an aircraft ECS in hardware-in-the-loop and full-scale modeling.
4.Which description is preferable for the subsystems of an aircraft ECS?
5.Is an unobservable control system always uncontrollable?
6.Give an example of the non-identifiability of a 3rd-order object with unknown parameters.
7.Under what conditions will the matrix UU T be ill-conditioned? How will this affect the estimation of parameters in a single-variable and multivariable linear regression model?
8. Examine the controllability of the system defined by the equation
dX (t)
= AX (t) + BU (t),
where A =
1
−1
,
B =
2
dt
Y (t) = CX (t) + DU (t),
−1
1
2
9. Examine the
observability
of the system defined by the
equation
dX (t)
= AX (t) + BU (t),
where A =
1
−1
,
B =
2 , C = 1
2 .
dt
[
]
Y (t) = CX (t) + DU (t),
−1
1
2
10. Construct a discrete state-space transfer model for
the system with the transfer
for
function of the system with the transfer
with
function
function
W (z) =
0.6z
.
z3 −2.5z2 +1.4z −0.9
11. Identify the discrete
first-order
system
order
y(k +1) = ay(k) +bu(k),
using
linear regression, based on
the following input-output data:
k
0
1
2
3
4
5
6
7
8
9
10
u
0
0
1
1
1
1
0
0
1
1
1
y
–5
–4
–4
–2
–2
–2
0
1
1
0
1
65
12. Identify the
parameter
matrices
A = a11
a12
,
a21
a22
B =
b1
dX (t)
= AX (t) + BU (t) of the system by means of regression from the following
system
dt
b2
measurement results:
t
0
1
2
3
4
5
6
7
x1
1.00
0.99
0.97
0.96
0.95
0.94
0.93
0.92
x2
0.00
–0.10
–0.19
–0.23
–0.28
–0.25
–0.22
–0.18
u
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
13. Determine the parameters of the nonlinear model y = aebx +c
based
on a regression model using the following data:
x
1.84
1.92
2.00
2.08
2.16
2.24
2.32
2.40
2.48
y
61.70
62.50
63.00
63.55
64.50
65.00
65.40
66.40
67.10
14. Determine the algorithm for estimating the parameters of a system with measurement constraints (unmeasured variable x2), if the structure of the coefficient matrix has the form
1
0
0
a11
0
A = b1
.
0
a21
a22
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