control team welcome dr. spanos faculty advisors dr. helen boussalis dr. charles liu student...
Post on 21-Dec-2015
212 views
TRANSCRIPT
Control TeamControl TeamWelcome Dr. SpanosWelcome Dr. Spanos
Control TeamControl TeamWelcome Dr. SpanosWelcome Dr. Spanos
Faculty Advisors
Dr. Helen Boussalis
Dr. Charles Liu
Student Assistants
Jessica AlvarengaAllison Bretaña
04/18/23 NASA Grant URC NCC NNX08BA44A 1
State Estimation Methods:Observer and Kalman Filter
04/18/23 2NASA Grant URC NCC NNX08BA44A
Outline• Objective
• Project Background and Luenberger Observer
• Kalman Filter
• Single Panel Simulations
• Noise Modeling
• Future goals
• Timeline
• References
04/18/23 NASA Grant URC NCC NNX08BA44A 3
Fault Detection
• Component Failures cannot be allowed to cause a total malfunction
• Used to achieve a fault tolerant reconfigurable controller
04/18/23 NASA Grant URC NCC NNX08BA44A 4
Outline• Objective
• Project Background and Luenberger Observer
• Kalman Filter
• Single Panel Simulation
• Noise Modeling
• Future goals
• Timeline
• References
04/18/23 NASA Grant URC NCC NNX08BA44A 5
Fault Detection and Isolation
04/18/23 NASA Grant URC NCC NNX08BA44A 6
Fault Detection and Isolation
04/18/23 NASA Grant URC NCC NNX08BA44A 7
State Observer
Discrete System Model
Observer Design
04/18/23 8NASA Grant URC NCC NNX08BA44A
sfkCxky
kBukAxkx
)()(
)()()1(
)(ˆ)(ˆ
))(ˆ)(()()(ˆ)1(ˆ
kxCky
kykyLkBukxAkx
Residual ErrorErrorOutputkykykey :)(ˆ)()(
ErrorStatekxkxke :)(ˆ)()(
Dynamic State Error
State Observer
sLfkeLCAke )()()1(
PD KsKL ]1[
Dynamic Error Equation
PD Gains State Feedback (L)
04/18/23 9NASA Grant URC NCC NNX08BA44A
State Observer
)(ˆ)(ˆ
))(ˆ)(()()(ˆ)1(ˆ
kxCky
kykyLkBukxAkx
04/18/23 NASA Grant URC NCC NNX08BA44A 10
Simulink Observer Realization
State Observer
ErrorOutputkykykey :)(ˆ)()(
04/18/23 NASA Grant URC NCC NNX08BA44A 11
Simulink Simulation Results
State Observer
04/18/23 12NASA Grant URC NCC NNX08BA44A
Residual Error
Observer Simulated Output
Real System Output
Initatied Actuator Fault
Observer Discrepencies
Outline• Objective
• Project Background and Luenberg Observer
• Kalman Filter
• Single Panel Simulation
• Noise Modeling
• Future goals
• Timeline
• References
04/18/23 NASA Grant URC NCC NNX08BA44A 13
Kalman Filter Methodology
– Two Phases:– Predictions
• Previous Estimate Current Estimate
– Update
• Current Measurement Refines Current State estimate
PredictionPredictionPredictionPrediction UpdateUpdateUpdateUpdate
04/18/23 NASA Grant URC NCC NNX08BA44A 14
[1] http://www.nps.gov/gis/gps/glossary.htm
– “A numerical method used to track a
time-varying signal in the presence of noise.”[1]
– A method of estimating the internal states of a system
Kalman Equations
1111
kkk
kkkkk
vCxy
wBuxx
1111
111 ˆˆ
kkkkk
kkkk
QPP
Buxx
04/18/23 NASA Grant URC NCC NNX08BA44A 15
1][
]ˆ[ˆˆ
kkk
kkkkk
PCKIP
xCyKxx
RvvE
QwwE
kk
kk
),0(~
),0(~
Rv
Qw
k
k
System State Equations
Noise Distributions
Noise Variances
A Priori Equations
A Posteriori Equations
][ kkkk
kkk RCPC
CPK
Kalman Gain Equation
GainKalman :
CovarianceError
PosterioriA :
Covariance
Error PrioriA :
Estimate PosterioriA :ˆ
Estimate PrioriA :ˆ
Noiset Measuremen:
Noise Process:
MatricesState:,
MatrixTransition State:
Output:
Control:
States:
k
k
k
k
k
k
k
k
k
k
k
K
P
P
x
x
v
w
CB
y
u
x
∑∑ ∑∑
DelayDelay
+
-
+
+
∑∑
DelayDelay
∑∑
+
++
+
+
Kalman Filter Realization
04/18/23 NASA Grant URC NCC NNX08BA44A 16
Outline• Objective
• Project Background and Luenberg Observer
• Kalman Filter
• Single Panel Simulations
• Noise Modeling
• Future goals
• Timeline
• References
04/18/23 NASA Grant URC NCC NNX08BA44A 17
Single Panel Model
04/18/23 18NASA Grant URC NCC NNX08BA44A
trans1* u
Transformation
Input Z
System Model with Noise
Output Scopes
Sensors w/ PID & Faults1
Output Scopes
Sensors w/ PID & Faults
Scope
Primary ReferenceInputs
PIDController
u
y
Kalman Output: Residual
Kalman Output Estimate
Kalman Filter Model
Addetive Faults
Output Scopes
Actuators w/ PID & Faults
Single Panel Model
04/18/23 19NASA Grant URC NCC NNX08BA44A
1
Z
System Output Z
c1* u
C1
Band-LimitedWhite Noise, w Band-Limited
White Noise, v
b1* u
B1
a1* u
A1
1
Input
Single Panel Kalman Filter
04/18/23 20NASA Grant URC NCC NNX08BA44A
y - y ^ = y - H x-^
xk-^
xk^x
k-1^
Residual
y ^
y ^
2
Kalman Output Estimate
1
Kalman Output: Residual
z
1
Unit Delay
System Output Z
y - y ^K ( z - H x _̂ )
Kalman Gain
c1* u
C1
b1* u
B1
a1* u
A1
2
y
1
u
Single Panel Kalman Gain
04/18/23 21NASA Grant URC NCC NNX08BA44A
P
PC'
CPC'
K
CP
Kk = ( P
k * CT ) / (C * P
k * CT + R)
Pk- = ( A * P
k-1 * AT ) + Q
Pk = ( I - K
k * C ) * P
k-
1
K ( z - H x^_ )
z
1
MatrixMultiply
MatrixMultiply
Inv
Divide
R
Constant1
Q
Constant
c1* u
C1
u*K
C'
c1* u
C
a1* u
A1
u*K
A'
1
y - y ^
No Noise, No Fault
04/18/23 NASA Grant URC NCC NNX08BA44A 22
System Simulation Edge Sensor Estimates
KF Edge Sensor Estimates
KF Edge Sensor Residuals
Magnified View of KF Edge Sensor Residuals
No Noise, Additive Sensor Fault
04/18/23 NASA Grant URC NCC NNX08BA44A 23
System Simulation Edge Sensor Estimates
KF Edge Sensor Estimates
KF Edge Sensor Residuals
Simulated Noise and Additive Sensor Fault
04/18/23 NASA Grant URC NCC NNX08BA44A 24
System Simulation Edge Sensor Estimates
KF Edge Sensor Estimates
KF Edge Sensor Residuals
Issues with Simulation
• Long run times (10 sec took ~10 minutes)
• Faulty residuals
• Difficult to tune noise
04/18/23 NASA Grant URC NCC NNX08BA44A 25
Solution
• Develop a new and efficient simulation code
• Create accurate process and measurement noise models
• Simulation of an open-loop system
04/18/23 NASA Grant URC NCC NNX08BA44A 26
Outline• Objective
• Project Background and Luenberg Observer
• Kalman Filter
• Single Panel Simulation
• Noise Modeling
• Future goals
• Timeline
• References
04/18/23 NASA Grant URC NCC NNX08BA44A 27
• Case 1: Assume no process noise– All noise attributed to sensors
• Case 2: Assume no sensors noise– All noise attributed to process
• Case 3: Combination of process and sensor noise (Real Scenario)
2/18/2010 NASA Grant URC NCC NNX08BA44A 28
Noise Scenarios
Case 1: No process noise
04/18/23 NASA Grant URC NCC NNX08BA44A 29
w=0, v~N(0,R)
Sensor noise is attributed to the measurements.
111
kkk
kkkk
vCxy
Buxx
DIRECTDIRECTMeasurement NoiseMeasurement Noise
04/18/23 30NASA Grant URC NCC
NNX08BA44A
Edge Sensor Data Edge Sensor Data (System at rest)(System at rest)
04/18/23NASA Grant URC NCC NNX08BA44A
31
Single Panel Edge Sensor Single Panel Edge Sensor Data (System at rest)Data (System at rest)
04/18/23 NASA Grant URC NCC NNX08BA44A 32
Case 2: No Sensor Noise
w~N(0,Q), v=0
Sensor noise is attributed to noise in the process.
Are not directly observing states.
04/18/23 NASA Grant URC NCC NNX08BA44A 33
kk
kkkkk
Cxy
wBuxx
111
Inversion of State Space
A: n x n B: n x m C: p x n
However, C may not be square, as in our case, and is not invertible.
04/18/23 NASA Grant URC NCC NNX08BA44A 34
111
11
111
1
111
111
)(
kkkkk
kk
kk
kk
kkkkk
kkkkk
BuyCyCw
xyC
similarlyxyC
Cxy
Buxxw
wBuxx
Moore-Penrose Pseudo Inverse
• Use the Moore-Penrose Pseudo Inverse to invert the state space model and allow us to make process noise calculations using sensor measurements.
04/18/23 NASA Grant URC NCC NNX08BA44A 35
. transposeconjugateor TransposeHermetian theIs and
,)(
satisfies which Inverse Pseudo Penrose-Moore theis
, where
,
:gives This
*
*
1
111
C
CCCC
C
CCC
Buyyw
C
kkCkkCk
• Use mathematical equation to determine process noise
where
• Calculate mean, standard deviation and variance of process noise using MATLAB
2/18/2010 NASA Grant URC NCC NNX08BA44A 36
Noise Modeling
2/18/2010 NASA Grant URC NCC NNX08BA44A 37
PANEL 1 PANEL 2 PANEL 3 PANEL 4 PANEL 5 PANEL 6STATE mean std. dev. variance mean std. dev. variance mean std. dev. variance mean std. dev. variance mean std. dev. variance mean std. dev. variance
1 -6.16338 0.151601 0.022983 7.549682 0.094799 0.008987 -0.50693 0.541283 0.292988 3.442127 0.763661 0.583179 1.613433 0.845681 0.715177 -1.66758 0.306442 0.0939072 -0.02756 0.131574 0.017312 -1.23316 0.060106 0.003613 -1.29316 0.789476 0.623273 10.80916 0.639489 0.408947 6.087263 0.650141 0.422684 2.313367 1.290944 1.6665363 -6.56202 0.345914 0.119657 4.736639 0.121153 0.014678 3.138532 0.540469 0.292107 1.797797 0.353535 0.124987 2.394228 1.01984 1.040073 -1.25442 0.310149 0.0961924 -4.60967 0.087644 0.007682 3.2591 0.080688 0.006511 1.316403 0.065577 0.0043 3.96695 0.106595 0.011362 2.08668 0.215191 0.046307 1.43054 0.438764 0.1925145 14.10429 3.075365 9.457871 13.38073 0.824995 0.680617 -32.906 0.683676 0.467413 14.57379 2.741044 7.513324 -3.37381 2.541154 6.457463 -7.31638 1.792657 3.213626 -1.01944 0.947898 0.898511 9.360859 0.250873 0.062937 -7.39944 0.806468 0.650391 -1.14779 1.516844 2.300817 -3.83095 0.662759 0.439249 -4.07433 1.240767 1.5395037 6.732807 0.682667 0.466034 -0.90668 0.187941 0.035322 -8.55227 0.610493 0.372702 6.071319 0.306403 0.093883 0.866875 1.14848 1.319007 -0.56379 0.5888 0.3466868 -31.4423 4.464805 19.93448 1.021753 1.226868 1.505206 33.65548 1.319123 1.740087 20.05731 2.236104 5.000161 28.00057 4.670018 21.80907 1.590931 3.430741 11.769989 5.057215 1.492933 2.22885 6.763659 0.397679 0.158149 -14.2327 0.376554 0.141793 6.644327 1.218853 1.485602 -1.99029 1.239344 1.535973 -1.91605 0.769243 0.59173410 -4.88285 0.942825 0.888919 -6.33453 0.267585 0.071602 10.81644 0.829386 0.68788 2.651626 1.521532 2.315058 4.531653 0.529614 0.280491 6.856123 1.650637 2.72460311 -9.0353 0.658259 0.433305 7.20533 0.262258 0.068779 9.54112 1.843249 3.397568 -29.2856 1.746427 3.050008 -17.9683 1.686115 2.842985 1.018385 2.692463 7.24935512 -3.93729 0.955842 0.913635 -2.01874 0.263814 0.069598 3.48422 0.779793 0.608077 15.70021 1.06811 1.140858 12.03615 0.386468 0.149357 1.737163 1.813873 3.29013413 -5.04278 1.251015 1.565039 11.92345 0.361935 0.130997 -8.27734 0.296692 0.088026 10.17356 1.220009 1.488422 0.679103 0.724412 0.524773 1.262926 0.684781 0.46892514 13.17072 0.750368 0.563052 -5.27878 0.323097 0.104391 -2.8995 1.568924 2.461523 -33.4333 1.368429 1.872599 -20.2629 0.555023 0.308051 -7.14973 3.737233 13.9669115 -32.1695 2.646428 7.003581 -0.13942 0.91032 0.828682 25.35087 3.526859 12.43873 51.91797 4.149316 17.21682 36.17415 1.256982 1.580005 23.82574 8.265156 68.312816 -0.49436 0.710994 0.505513 -6.87684 0.183327 0.033609 8.663878 0.211037 0.044536 -7.68765 1.014574 1.029359 -1.80446 0.446535 0.199393 3.207253 0.42487 0.18051517 -1.36616 0.820784 0.673687 5.465606 0.230778 0.053258 -3.24015 0.362225 0.131207 -3.67876 0.831127 0.690772 -5.14577 0.34753 0.120777 0.334765 0.674779 0.45532718 1.259203 0.493048 0.243096 5.784451 0.143753 0.020665 -10.5391 0.417255 0.174102 17.60379 0.852202 0.726249 7.960239 0.62766 0.393957 -2.94512 0.83618 0.69919719 -41.9464 2.137926 4.570727 24.3815 0.777469 0.604458 23.29307 1.969631 3.879448 17.17468 0.947347 0.897466 17.27459 4.913287 24.14039 1.419739 1.993257 3.97307220 20.56158 1.339986 1.795562 -6.74163 0.453423 0.205592 -28.9581 3.748309 14.04982 49.38333 2.301965 5.299044 21.75745 4.7632 22.68807 2.183285 4.657003 21.6876721 -43.843 2.299461 5.287521 61.1673 0.871758 0.759962 -6.3887 7.941124 63.06145 29.76193 7.608398 57.88773 28.44375 11.83002 139.9495 -45.226 6.180394 38.1972722 -13.9888 0.883045 0.779769 3.86685 0.294509 0.086736 17.33633 1.611491 2.596903 -20.7948 1.023012 1.046554 -8.17725 2.399821 5.75914 1.426667 1.756177 3.08415623 11.83478 1.848239 3.415989 7.652212 0.50636 0.256401 -23.9567 0.426612 0.181998 13.36027 1.825611 3.332854 0.774112 1.647124 2.713019 -7.29733 1.191057 1.41861624 4.693166 1.262302 1.593405 1.144195 0.351107 0.123276 -3.04765 0.713218 0.50868 -20.0107 1.134723 1.287596 -15.7416 0.672405 0.452129 0.470809 1.909501 3.64619325 13.56646 0.923029 0.851983 -12.3327 0.410051 0.168142 -18.6624 4.630475 21.4413 67.34064 3.800936 14.44711 38.4976 4.280382 18.32167 5.051207 6.912096 47.7770726 56.90523 2.252087 5.071897 -21.8818 1.719363 2.956211 -12.3691 9.896664 97.94397 -118.894 5.991901 35.90288 -53.115 7.571164 57.32252 -66.0185 18.37947 337.80527 20.35218 1.917848 3.678142 -7.47378 0.973209 0.947135 3.304651 6.515976 42.45794 -70.1821 3.611628 13.04386 -28.2458 6.100969 37.22182 -37.6526 10.72388 115.001628 -7.45211 0.556038 0.309178 7.112312 0.179828 0.032338 1.928492 0.97547 0.951542 4.352816 0.711235 0.505856 4.924443 1.666709 2.777919 -4.8556 0.604823 0.3658129 12.43557 0.600764 0.360917 -11.6193 0.309096 0.095541 2.283272 0.925069 0.855753 -22.9529 0.574817 0.330415 -9.86732 0.60787 0.369506 -6.40242 2.341702 5.4835730 -2.48396 2.52386 6.369871 14.54849 0.718792 0.516662 -16.2446 1.207237 1.457422 16.30463 1.463358 2.141416 -1.3273 2.282925 5.211746 6.044186 1.718371 2.95279831 34.71309 1.118392 1.250801 -23.4768 0.841522 0.70816 -1.82415 3.439076 11.82725 -63.8923 1.670249 2.78973 -29.8742 1.959569 3.83991 -23.7484 7.785847 60.6194132 -8.95341 0.452141 0.204432 18.76359 0.366565 0.13437 5.434745 5.872934 34.49135 -46.0202 4.616042 21.30784 -21.5535 6.217607 38.65864 -24.1951 7.939902 63.0420433 -11.1308 1.916075 3.671345 -6.88849 0.536843 0.2882 15.59439 1.519765 2.309687 18.10864 2.478354 6.142238 16.39469 0.830282 0.689369 9.256328 3.499765 12.2483534 -18.0303 0.395919 0.156752 9.521829 0.338234 0.114402 8.673757 0.450529 0.202976 11.92681 0.304003 0.092418 6.427131 0.546304 0.298448 8.48887 1.977068 3.90879835 -20.3066 2.301924 5.298854 -12.6436 0.689615 0.475569 44.35304 1.040692 1.083039 -44.9621 3.07783 9.473035 -17.216 2.630995 6.922137 16.45427 1.835032 3.36734236 26.17034 3.823725 14.62088 -10.7961 1.069526 1.143886 -13.8137 1.441627 2.078288 -45.3406 1.583323 2.506911 -40.0176 4.525706 20.48201 8.817662 3.280777 10.763537 -3.3361 2.740591 7.510838 4.100992 0.868899 0.754986 10.02466 4.836579 23.39249 -25.9582 2.27757 5.187325 -1.44901 6.264672 39.24611 -27.2205 5.961346 35.5376538 -48.1625 4.848361 23.50661 32.89802 1.431249 2.048475 42.33865 9.91423 98.29195 -50.0319 5.238495 27.44183 -5.32283 14.17606 200.9606 -35.0797 10.08864 101.780739 0.469042 7.722104 59.63089 -36.5977 2.136976 4.566667 46.82179 3.508144 12.30707 -32.1143 4.081489 16.65855 13.7346 7.148948 51.10745 -18.4437 4.445823 19.7653440 150.4421 3.420579 11.70036 -140.167 2.922579 8.541469 20.50118 6.519705 42.50655 -280.586 7.923674 62.78462 -144.059 5.822045 33.89621 -36.5953 23.46778 550.736641 2.619508 1.54821 2.396954 7.612411 0.559561 0.313109 -12.8849 1.583765 2.508312 27.65688 1.808188 3.269543 22.26516 2.648602 7.015094 -21.1654 1.218967 1.48588142 -18.603 3.576372 12.79044 -11.5922 0.965438 0.932071 30.461 1.316825 1.734027 13.55685 3.494879 12.21418 20.22511 2.118491 4.488005 10.18664 3.980243 15.8423343 34.4221 15.02156 225.6471 224.1288 4.462938 19.91781 -269.087 20.4383 417.7242 157.9006 38.98844 1520.098 46.19118 20.35599 414.3663 -201.513 27.7892 772.239644 47.48899 3.650561 13.3266 5.847482 1.276171 1.628612 -55.1593 2.920337 8.528368 -15.3051 5.334263 28.45436 -18.3124 1.940334 3.764896 -37.6812 7.866977 61.8893245 -59.7554 2.674121 7.150921 33.57174 1.531525 2.345567 -9.02921 9.906136 98.13152 209.76 7.778674 60.50777 119.3493 4.942831 24.43158 35.61774 21.68449 470.217246 4.286548 8.015477 64.24787 17.51157 2.448981 5.997507 -64.6048 13.96711 195.0801 153.3645 5.453322 29.73872 47.67032 17.01947 289.6623 57.78278 19.53231 381.511347 33.25264 8.769659 76.90692 -100.74 2.500666 6.253331 69.40679 4.161419 17.31741 -52.0901 12.48055 155.7641 3.530202 5.279189 27.86984 19.03135 5.07586 25.7643648 -83.7287 2.317389 5.37029 19.49981 2.345878 5.503145 28.33433 15.5565 242.0048 187.9286 11.05429 122.1974 93.20885 11.03403 121.7498 98.7924 29.1192 847.9278
PANEL 1STATE mean std. dev. variance
1 -6.16338 0.151601 0.0229832 -0.02756 0.131574 0.0173123 -6.56202 0.345914 0.1196574 -4.60967 0.087644 0.0076825 14.10429 3.075365 9.4578716 -1.01944 0.947898 0.8985117 6.732807 0.682667 0.4660348 -31.4423 4.464805 19.934489 5.057215 1.492933 2.2288510 -4.88285 0.942825 0.88891911 -9.0353 0.658259 0.43330512 -3.93729 0.955842 0.91363513 -5.04278 1.251015 1.56503914 13.17072 0.750368 0.56305215 -32.1695 2.646428 7.00358116 -0.49436 0.710994 0.50551317 -1.36616 0.820784 0.67368718 1.259203 0.493048 0.24309619 -41.9464 2.137926 4.57072720 20.56158 1.339986 1.79556221 -43.843 2.299461 5.28752122 -13.9888 0.883045 0.77976923 11.83478 1.848239 3.41598924 4.693166 1.262302 1.59340525 13.56646 0.923029 0.85198326 56.90523 2.252087 5.07189727 20.35218 1.917848 3.67814228 -7.45211 0.556038 0.30917829 12.43557 0.600764 0.36091730 -2.48396 2.52386 6.36987131 34.71309 1.118392 1.25080132 -8.95341 0.452141 0.20443233 -11.1308 1.916075 3.67134534 -18.0303 0.395919 0.15675235 -20.3066 2.301924 5.29885436 26.17034 3.823725 14.6208837 -3.3361 2.740591 7.51083838 -48.1625 4.848361 23.5066139 0.469042 7.722104 59.6308940 150.4421 3.420579 11.7003641 2.619508 1.54821 2.39695442 -18.603 3.576372 12.7904443 34.4221 15.02156 225.647144 47.48899 3.650561 13.326645 -59.7554 2.674121 7.15092146 4.286548 8.015477 64.2478747 33.25264 8.769659 76.9069248 -83.7287 2.317389 5.37029
•Simulation focuses on Panel 1
•Apply the calculated variance to Gaussian White noise in simulation
2/18/2010NASA Grant URC NCC NNX08BA44A
38
Simulated Noise
Outline• Objective
• Project Background and Luenberg Observer
• Kalman Filter
• Implementation into a SISO System
• Initial simulations
• Noise Modeling
• Future goals
• Timeline
• References
04/18/23 NASA Grant URC NCC NNX08BA44A 40
Future Goals
• Improve the noise model for the homogenous case
• Noise analysis for non-homogenous cases– Step input– Impulse– Chirp– Sinusoid
• Develop algorithm for Testbed implementation
04/18/23 NASA Grant URC NCC NNX08BA44A 41
Outline• Objective
• Project Background and Luenberg Observer
• Kalman Filter
• Implementation into a SISO System
• Initial simulations
• Noise Modeling
• Future goals
• Timeline
• References
04/18/23 NASA Grant URC NCC NNX08BA44A 42
Timeline
04/18/23 NASA Grant URC NCC NNX08BA44A 43
2009 MAR APR MAY JUN JUL
Jessica
Alvarenga
Introduction to SPACE Laboratory and Testbed Kalman Filter Familiarization and Paper Surveying.D
O
C
U
M
E
N
T
A
T
I
O
N
Learn Matlab, LabVIEW and C
Chris
TorresObserver
Timeline
04/18/23 NASA Grant URC NCC NNX08BA44A 44
2009 AUG SEP OCT NOV DEC
Jessica
Alvarenga
Kalman Filter Simulation in Matlab.
Initial Simulation of Testbed NoiseFinalize Matlab Simulation.
D
O
C
U
M
E
N
T
A
T
I
O
N
NSF GK-12 IMPACT LA
Allison
Bretaña
Introduction to Testbed
Initial Training
Chris
Torres
Kalman Filter Design
Testbed Noise Analysis Kalman Filter Simulation
Timeline
04/18/23 NASA Grant URC NCC NNX08BA44A 45
DEC JAN FEB MAR APR MAY JUN JUL
Jessica
Alvarenga
Noise Modeling and Investigation of Plant Model Coding Implementation of KF in C codeD
O
C
U
M
E
N
T
A
T
I
O
N
NSF GK-12 IMPACT LA
Allison
Bretaña
Familiarization with Testbed Simulink Modeling of KF FDI SchemaIntegration of sensor noise statistics
into KF FDI Schema
Initial training period Sensor Noise Modeling Integration of Noise Model into C code
Outline• Objective
• Project Background
• Lyapunov Observer
• Kalman Filter
• Implementation into a SISO System
• Initial simulations
• Noise Modeling
• Future goals
• Timeline
• References
04/18/23 NASA Grant URC NCC NNX08BA44A 46
ReferencesAndrews, A. and Grewal, M. (2001). Kalman Filtering: theory and practice using MATLAB. New
York, NY: John Wiley and Sons Inc.
Boussalis, H., “Stability of Large Scale Systems”, New Mexico, USA, November, 1979.
Boussalis, H., Guillaume, D., Wu, C., Liu, C. (2009). Space URC Annual Report. NASA, 139.
Boussalis, H., Mirmirani, M., Chassiako, A., Rad, K., “The Use of Decentralized Control in Design of a Large Segmented Space Reflector”, Control and Structures Research Laboratory, California.
Cao, Yi (February 5, 2010 information retrieved). MATLAB Central. http://www.mathworks.com/matlabcentral/fileexchange/18465
Clark, B., Larson, E., Parker,E. Model-Based Sensor and Actuator Fault Detection and Isolation. NASA Langley Research Center,5.
Greg, W. & Bishop, G. (2006). An Introduction to the Kalman Filter. University of North Carolina at Chapel Hill, NC 27599-3175.
NASA. (November 30, 2009 revision). James Webb Space Telescope. Retrieved from www.jswt.nasa.gov/
Simon, D. (2001). Kalman Filtering. Embedded Systems Programming, 73-79.
Simon, D. (2006). Optimal State Estimation: Kalman, H Infinity and Nonlinear Approaches. Hoboken, NJ. John Wiley and Sons Inc.
04/18/23 NASA Grant URC NCC NNX08BA44A 47
Questions?
Thank You
04/18/23 48NASA Grant URC NCC NNX08BA44A