Scenario Description

1
Scenario Description

• Maggie Stringfellow Herring

2
Antenna Tracking Scenario

• Summarized from an Oct. 11 e-mail from Scott
  Morgan
• Group of 20 antennas tracking a target
• Working fine for 4 hours
• One antenna fails to maintain pointing
• MC must drop that antenna from signal combining
• MC allocates a spare antenna and brings it into
  the group

3
Sample Operational Scenario
We are using this operational scenario from Scott
Morgan to focus our initial analysis and design
efforts.

• Initial conditions
• 20 antennas (1-20) involved in a spacecraft
  tracking pass
• one target in the beam (not a multiple
  spacecraft support)
• 5 hours remain in the activity
• the activity has been going for 4 hours
• 15 antennas are required to provide the
  requested snr
• 3 antennas (11,12,13) are currently being
  calibrated (they are not pointing at the
  spacecraft)
• X-band, RCP downlink
• no uplink
• Scenario
• A. antenna controller 5 reports a high current
  load in the azimuth motor T0
• B. antenna controller 5 reports that pointing
  error exceeds the maximum tolerance T0.5 sec
• C. signal processing correlator reports that it
  is unable to correlate signal from antenna 5
  T0.6 sec
• D. signal processing correlator removes signal 5
  from the correlation (weight0) T0.7 sec
• E. MC directs signal processing to remove signal
  from antenna 5 from the correlation T01 sec
• F. MC issues a "shutdown" command to antenna 5
  T0 1sec
• G. MC aborts the calibration activity for
  antenna 11,12,13 (has multiple steps) T01
  sec
• H. MC directs antenna 11 to point at the
  spacecraft target T01.2 sec

4
Receive Array Scenario Timeline
5
Receive Array Scenario Timeline
B
C
D
E
F
G
H
I
J
K
L
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timeline
Phased, conditioned, digitized A-1
IF
A-1 IF Analog
Focused A-1 Analog
Ant 1 SP
Ant 1 Elec
Ant 1 Mech
RF from SRC Analog
Ant 1 SP
Ant 1 Mech
Ant 1 Elec
Correlations
ITI
W
Arg Support Facility
Correlator Combiner
Power
Combined Signal
W
TRC
Array Signal Processing
Antenna Control Building
Cluster Control Building
6
Receive Array Scenario Timeline
B. antenna controller 5 reports that pointing
error exceeds the maximum tolerance T0.5 sec
B
A
C
D
E
F
G
H
I
J
K
L
M
timeline
Phased, conditioned, digitized A-1
IF
A-1 IF Analog
Focused A-1 Analog
Ant 1 SP
Ant 1 Elec
Ant 1 Mech
RF from SRC Analog
Ant 1 SP
Ant 1 Mech
Ant 1 Elec
Correlations
ITI
W
Arg Support Facility
Correlator Combiner
Power
Combined Signal
W
TRC
Ant 5 Elec
Ant 5 Mech
Ant 5 SP
Array Signal Processing
Antenna Control Building
Cluster Control Building
7
Receive Array Scenario Timeline
C. signal processing correlator reports that it
is unable to correlate signal from antenna 5
T0.6 sec
C
A
B
D
E
F
G
H
I
J
K
L
M
timeline
A-1 IF Analog
Focused A-1 Analog
Ant 1 SP
Ant 1 Elec
Ant 1 Mech
RF from SRC Analog
Ant 1 SP
Ant 1 Mech
Ant 1 Elec
Correlations
ITI
Arg Support Facility
Power
Combined Signal
TRC
Ant 5 Elec
Ant 5 Mech
Ant 5 SP
Ant 5 Elec
Ant 5 SP
Antenna Control Building
Cluster Control Building
8
Receive Array Scenario Timeline
D. signal processing correlator removes signal 5
from the correlation (weight0) T0.7 sec
D
A
B
C
E
F
G
H
I
J
K
L
M
timeline
Phased, conditioned, digitized A-1
IF
A-1 IF Analog
Focused A-1 Analog
Ant 1 SP
Ant 1 Elec
Ant 1 Mech
RF from SRC Analog
Ant 1 SP
Ant 1 Mech
Ant 1 Elec
Correlations
ITI
W
Arg Support Facility
Correlator Combiner
Power
Combined Signal
TRC
Ant 5 Mech
Ant 5 Elec
Ant 5 SP
Array Signal Processing
Antenna Control Building
Cluster Control Building
9
Receive Array Scenario Timeline
E. MC directs signal processing to remove signal
from antenna 5 from the correlation T01 sec
E
E
A
B
C
D
F
G
H
I
J
K
L
M
timeline
Phased, conditioned, digitized A-1
IF
A-1 IF Analog
Focused A-1 Analog
Ant 1 SP
Ant 1 Elec
Ant 1 Mech
RF from SRC Analog
Ant 1 SP
Ant 1 Mech
Ant 1 Elec
Correlations
ITI
W
Arg Support Facility
Correlator Combiner
Power
Combined Signal
W
TRC
Ant 5 Mech
Ant 5 Elec
Ant 5 SP
Array Signal Processing
Antenna Control Building
Cluster Control Building
10
Receive Array Scenario Timeline
F. MC issues a "shutdown" command to antenna 5
T0 1sec
F
A
B
C
D
E
G
H
I
J
K
L
M
timeline
Correlations
ITI
Combined Signal
TRC
11
Receive Array Scenario Timeline
G. MC aborts the calibration activity for
antenna 11,12,13 (has multiple steps) T01
sec
G
A
B
C
D
E
F
H
I
J
K
L
M
timeline
Phased, conditioned, digitized A-1
IF
Ant 1 SP
Correlations
ITI
W
Correlator Combiner
Combined Signal
W
TRC
Ant 11 SP
Array Signal Processing
Cluster Control Building
12
Receive Array Scenario Timeline
H. MC directs antenna 11 to point at the
spacecraft target T01.2 sec
H
A
B
C
D
E
F
G
I
J
K
L
M
timeline
13
Receive Array Scenario Timeline
I. antenna controller 11 reports that pointing
errors are within tolerance T06.2 sec
I
A
B
C
D
E
F
G
H
J
K
L
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timeline
14
Receive Array Scenario Timeline
J. MC directs signal processing to add X-band,
RCP signal from antenna 11 into the correlation
T06.4 sec
J
A
B
C
D
E
F
G
H
I
K
L
M
timeline
15
Receive Array Scenario Timeline
K. signal processing correlator reports
acceptable correlation using signal from antenna
11 T07.4 sec.
K
A
B
C
D
E
F
G
H
I
J
L
M
timeline
RF from SRC Analog
16
Receive Array Scenario Timeline
L. MC removes antenna 5 from the available
resource pool (picked up by scheduling) T010
sec
L
A
B
C
D
E
F
G
H
I
J
K
M
timeline
17
Receive Array Scenario Timeline
M. MC issues a service request for antenna 5
T012 sec
M
A
B
C
D
E
F
G
H
I
J
K
L
timeline
18
Analysis of System Under Control
19
General Approach
DSAN operations scenario
1
You are here
guides
Analysis of system under control
2
produces
Physics model of system under control
3
informs
informs
MC software design
Goal/macro-based DSAN operations
4
5
20
Complete State Effects DiagramPhysics Model
Screendump from database tool.
21
Notation of State Effects Diagram
Notation
Meaning
Ant N Elect Power
A physical state variable of the system under
control, identified because of its relevance to
how things work.
Msmt Ant N Elect Power
A measurement from the system under control. It
provides evidence about the values of state
variable(s) that affect it.
Cmd Signal Inclusion
A command that affects the system under control.
A command affects the values of one or more
state variables.
A affects B, based on physics and design. A
state variable can affect other state variables
and measurements. A command can affect one or
more state variables.
A
B
22
Assumptions

• Approach
• Scenario Driven
• Models inferred from DSAN documents
• Incremental Small Deltas in Scope
• Qualitative Models
• One Subarray
• Treat each subsystem as a black box.
• Antenna Mechanical Subsystem model based on modes
  of the antenna rather than, e.g., az/el pointing
• Omitted measurements that provide redundant
  information
• Correlator Signal Weights

23
Simplification

• Simplification of the Signal Flow Path
• Omitted Antenna Signal Processing
• Omitted Antenna Electronics
• Omitted Signal Delays
• States not mentioned in the scenario were
  eliminated.
• Health Power
• Array Support Facility
• Ant. Electronics, Ant. Signal Processing
• Combined state variables
• Correlator Combiner states
• Analog Signal Analog IF Digital IF
• Background Signal Noise states

24
Signal Flow Diagram Physics Model
A-1 IF Analog
Focused A-1 Analog
Phased, conditioned, digitized A-1
IF
Ant 1 SP
Ant 1 Elec
Ant 1 Mech
RF from SRC Analog
Ant 1 Elec
Ant 1 Mech
Ant 1 SP
Correlations
ITI
W
Correlator Combiner
Arg Support Facility
Power
Combined Signal
W
TRC
Ant 11 SP
Ant 11 Elec
Ant 11 Mech
Array Signal Processing
Antenna Control Building
Cluster Control Building
25
Scoped out Physics Model
26
Complete State Effects DiagramPhysics Model
Screen dump from database tool.
27
Signal Flow Diagram Physics Model
A-1 IF Analog
Focused A-1 Analog
Phased, conditioned, digitized A-1
IF
Ant 1 SP
Ant 1 Elec
Ant 1 Mech
RF from SRC Analog
Ant 1 Elec
Ant 1 Mech
Ant 1 SP
Correlations
ITI
W
Correlator Combiner
Arg Support Facility
Power
Combined Signal
W
TRC
Ant 11 SP
Ant 11 Elec
Ant 11 Mech
Array Signal Processing
Antenna Control Building
Cluster Control Building
28
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29
Antenna_N Received Signal Model

• If Ant_N Mechanical Pointing, Power, OpMode
  Health is Tracking Healthy, and Target Signal
  State is Present
• then Received Signal has a Target Content
  Factor (TCF) value of One.
• else Received Signal has a TCF value of Zero.

30
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31
Antenna_N Mechanical Pointing, Power, OpMode and
Heath
Repaired msmt
Go offline cmd
Come online cmd
Power off
Power off
Begin Tracking
Power on
End-of-profile or go-idle
For now, only one fault mode
32
Physics Models, 2

• Ant_N Received Signal
• If Ant_N Mech OpMode Health not shutdown or
  offline
• if Target Signal State present
• and Ant_N Mech OpMode Health on-point
• then Target Noise Background
• else Noise Background
• Background Noise Signal State
• Always present
• Target Signal State
• Present or Not Present

33
Physics Models, 3

• Array SP Correlator Combiner State
• Signal Inclusion A list of all the contributing
  signals to a subarray. These signals include
  signals that are weighted low and signals from
  calibrating antennas.
• Signal Inclusion Command Model
• Command models represent how states are affected
  by commands
• A Signal Inclusion Command can add or remove
  signals to the correlator combiner.
• example
• before Signal Inclusion of antennas tracking
  target 1 - 10
• Signal Inclusion of antennas tracking
  calibration target 11 - 13
• cmd Cmd Signal Inclusion Remove signal 5
• after Target Signal Inclusion 1 4, 6
  10
• Calibration Signal Inclusion 11-13

34
Physics Models, 4

• Combined Signal State
• After the individual signals have been weighted,
  the Combined Signal State is their scaled content
  factors.
• (Content factor is the number of target
  signals and background signals noise signals
  received from an antenna.)
• example
• Ant 1 receives Target Background Noise
• Ant 2 receives Target Background
  Noise
• Ant 3 receives Background Noise
• Assuming all signals are weighted 1
• Target content factor is 2 and background
  noise content factor is 3.
• Assuming signal 3 is weighted 0
• Target content factor is 2 and background
  noise content factor is 2.

35
Measurement Model

• Measurement Models
• Represent how measurements are affected by states
  
• Correlation Matrix Measurement
• Correlation matrix measurement equals
  Correlations(signal from antenna 1, signal from
  antenna 2, ..., signal from antenna N) where each
  correlation ij in the matrix will be above
  correlation threshold or below threshold.
• Each ij in the matrix is above threshold if its
  target content factor is greater than or equal to
  their noise content factor. Otherwise ij is below
  threshold.

A represents above threshold and B represents
below threshold.
The signals from antennas one and two are Target
Background Noise and the signal from antenna
three is just Background Noise.
36
Analysis of System Under Control Summary

• Models captures in the State Database tool
• Central repository for both Systems and Software
  engineers
• Models directly used in simulations
• Models can be easily changed from low fidelity to
  high fidelity.
• We have already worked up higher fidelity models
  for increment 2
• Models are used to inform the design of the
  control system.
• Systems Software Design Unification

37
Establishinga Control Point of View
38
Where to Begin

• Control is about changing things to meet your
  objectives
• There is an intrinsic notion of one thing being
  responsible for another
• To think in terms of control, it is important to
  separate
• We do not assume a priori that interactions
  adhere to any particular hierarchy
• Therefore, we adopt the notion of a system of
  cooperating controllers a Control System
• What is the Control System?

39
Decomposition for ControlThe Central Role of
Models

• Control System
• The functionality of control is separate from the
  rest of the system
• A model of the system under control can be used
  to inform the design and operation of the control
  system
• This avoids self-reference, which simplifies the
  description of control functions
• System Under Control
• The vehicle and its environment are considered
  together as an integrated entity
• Certain key software elements, such as hardware
  I/O and data management and transport functions,
  are included in the system under control
• This partitioning presents an abstract interface
  that can be tailored to be modeled more easily
  than arbitrary functional interfaces
• It may have control functions embedded within it
  (usually localized and comparatively simple), but
  these are just more behavior to be modeled

40
The Fundamental Message

• To understand the control system
• what it needs to do, what it needs to be
• you need to carefully delineate it from the
  system under control
• and exploit your understanding of it in terms of
  models of the system under control

41
Facts of Life

• Somehow, the models systems engineers understand
  must inform what software designers build
• Whether overt and explicit, or hidden quietly in
  the minds of the engineers, models have always
  existed
• Understanding and modeling are essentially the
  same thing
• Software design is ultimately a reflection of
  this understanding, and therefore a reflection of
  these models
• To the extent the software design reflects the
  systems engineers understanding, the software
  will perform as the systems engineers desire
• That is,

42
System Software is a Surrogate for Systems
Engineers
and Software Engineers perform the transformation
43
This Is WhereState Analysis Steps In

• State analysis asserts these basic principles

Control, which subsumes all aspects of system
operation,can be understood and exercised only
through models Models ought to be explicitly
identified and used in a waythat assures
consensus among systems engineers The manner in
which models inform software design and operation
ought to be direct, requiring minimal translation
44
Simple ExampleA Camera on a Scan Platform

• The camera turns on the gimbaled platform to
  point at a target
• Picture data from the camera is stored separately
• A heater can keep it warm when the camera is OFF

• Since control is about change, we need a way to
  talk about change
• This is accomplishedwith the notion of

Example System
State
45
Modeling the System Under Control

• Six State Variables are defined
• Camera Temperature real number in C
• Camera Heater ON or OFF
• and so on
• They are related as shown in a State Effects
  Diagram diagram
• Models describe these effects in detail
• A thermal modeldescribes temperatureversus
  camera andheater power
• The camera powers ONin idle mode it canttake
  pictures when OFF
• Whats in a picturedepends on where thecamera
  is pointed andhow the camera isoperated
• and so on

46
A Simple Sequence

• The sequence used to take a picture of some
  target might look something like this

47
Modeling the System Under Control

• Identifies the important state variables in the
  system
• Describes the causal effects among the state
  variables, commands and measurements (under both
  nominal and off-nominal situations)
• Uses any appropriate representation, e.g.,
  differential equations, tables, state charts,
  pseudo-code, plain text, etc.
• Behavioral models of this type are invaluable, in
  that they can be used for multiple purposes,
  including
• Informing the design of flight and ground
  software (e.g., estimation and control
  algorithms)
• Using them directly in model-based estimation
  control software (e.g., Kalman filters)
• Informing the design of fault protection
  mechanisms (models of nominal and off-nominal
  behavior can feed into Fault Tree and FMECA
  analyses, risk analyses, and fault
  monitor/response design)
• Feeding directly into simulations and
• Using them for planning and scheduling purposes
  (including automated approaches, either on the
  ground or onboard the spacecraft).

48
Modeling the System Under Control

• Iterative process for discovering state variables
  of the system under control and for incrementally
  constructing the model
• Identify needs define the high-level objectives
  for controlling the system.
• Identify state variables that capture what needs
  to be controlled to meet the objectives, and
  define their representation.
• Define state models for the identified state
  variables these may uncover additional state
  variables that affect the identified state
  variables.
• Identify measurements needed to estimate the
  state variables, and define their representation.
• Define measurement models for the identified
  measurements these may uncover additional state
  variables.
• Identify commands needed to control the state
  variables, and define their representation.
• Define command models for the identified commands
  these may uncover additional state variables.
• Repeat steps 2-7 on all newly discovered state
  variables, until all relevant variables and
  effects are accounted for.
• Return to step 1 to identify additional
  objectives, and proceed with additional
  iterations of the process until the scope of the
  mission has been covered.
• This modeling process can be used as part of a
  broader iterative incremental system and software
  development process, with cycles of modeling
  interwoven with cycles of software implementation

49
State Effects Diagrams and Models
50
State Effects Diagrams and Models
51
State Effects Diagrams and Models
Asynchronous to the execution cycle of the
antenna pointing, the antenna may be given a new
command. If the command is valid and the antenna
is healthy, powered and in tracking mode, the new
command will become the active command.
Specifically if antenna health HEALTHY, power
POWERED, opmode TRACKING and NEW_CMD is
valid CMD NEW_CMD TRACK_SEGMENT 0
TRAJ_IN_PROGRESS true else NEW_CMD is
ignored endif Every execution cycle, the
antenna pointing will exhibit the following
behavior set t t_next and t_next t delta_t
if antenna health HEALTHY, power POWERED,
and opmode TRACKING if TRAJ_IN_PROGRESS
true set TRACK_SEGMENT_COMPLETE ((az(t)
CMDTRACK_SEGMENT.az) AND (el(t)
CMDTRACK_SEGMENT.el)) set TRACK_COMPLETE
(TRACK_SEGMENT length(CMD) - 1) AND
TRACK_SEGMENT_COMPLETE if (TRACK_COMPLETE)
then hold position (done with track)
el_rate 0 az_rate 0
el_angle(t_next)el_angle(t)
az_angle(t_next)az_angle(t) set
TRAJ_IN_PROGRESS false else if
TRACK_SEGMENT_COMPLETE then increment
TRACK_SEGMENT endif // compute az_rate and
el_rate for segment TRACK_SEGMENT el_rate
(CMDTRACK_SEGMENT.el - el(t)) /
(CMDTRACK_SEGMENT.t - t) az_rate
(CMDTRACK_SEGMENT.az - az(t)) /
(CMDTRACK_SEGMENT.t - t) // apply az_rate
and el_rate for first delta_t in segment
TRACK_SEGMENT az(t_next) az(t) az_rate
delta_t, same for el else hold position (no
command to follow) el_rate 0 az_rate
0 el_angle(t_next)el_angle(t)
az_angle(t_next)az_angle(t) endif
52
Model Informs Software Design
IMU Power SwitchCmd
IMU OpMode Cmd
IMU Power Switch State Health
IMU Power, OpMode Health
IMU Power Switch Msmnt
IMU Msmnt
53
State Discovery is About Physical States
Control System

• A state is a property of a thing
• Mass of a spacecraft
• Pointing of a camera
• Etc.
• Physical States
• Exist in System Under Control
• Includes hardware states, environment states, and
  even software states

Elaboration, projection, scheduling
State variables
State variables
State variables
Intent
Knowledge
Execution
Estimation
Control
measurements
commands
System Under Control
Physical states identified during analysis will
later be implemented as state variables in the
control system software
54
State Discovery

• Quiz Identify physical states relevant to the
  control problem.

cameratemperature
actuatorhealth
switchposition
sensorhealth
meas
sensorscalefactor
batteryvoltage
Switch Sensor
sensorbias
heat flow
heaterresistance
heater health
ambient temperature
55
State DiscoveryStart with What You Need to
Control

• Identify a state variable that the control system
  needs to control

Camera Temperature
Legend
state variable
measurement
command
56
State DiscoveryIdentify Affecting States (1)

• Work your way out from objective state variables
  to state variables that affect them

Camera Temperature
Heater Heat Flow
Ambient Temperature
Camera Thermal Mass
Thermal Resistance
Camera Op Mode
Legend
state variable
measurement
command
57
State DiscoveryIdentify Affecting States (2)

• Work your way out to other affecting state
  variables

Switch Position
Camera Temperature
Heater Heat Flow
Heater Health Resistance
Battery Voltage
Ambient Temperature
Camera Thermal Mass
Thermal Resistance
Camera Op Mode
Legend
state variable
measurement
command
58
State DiscoveryAdd Measurements (1)

• What measurements provide evidence about states
  weve identified?

Switch Pos. Measurement
Temperature Measurement
Switch Position
Camera Temperature
Heater Heat Flow
Heater Health Resistance
Battery Voltage
Ambient Temperature
Camera Thermal Mass
Thermal Resistance
Camera Op Mode
Legend
state variable
measurement
command
59
State DiscoveryAdd Measurements (2)

• How are these measurements affected by other
  states?

Switch Pos. Measurement
Temperature Measurement
Switch Position
Switch Sensor Health
Camera Temperature
Heater Heat Flow
Heater Health Resistance
Temperature Sensor Health
Sensor Scale Factor
Sensor Bias
Battery Voltage
Ambient Temperature
Camera Thermal Mass
Thermal Resistance
Camera Op Mode
Legend
state variable
measurement
command
60
State DiscoveryAdd Commands (1)

• What commands do we have to influence the
  controlled state?

Switch Pos. Measurement
Switch Command
Temperature Measurement
Switch Position
Switch Sensor Health
Camera Temperature
Heater Heat Flow
Heater Health Resistance
Temperature Sensor Health
Sensor Scale Factor
Sensor Bias
Battery Voltage
Ambient Temperature
Camera Thermal Mass
Thermal Resistance
Camera Op Mode
Legend
state variable
measurement
command
61
State DiscoveryAdd Commands (2)

• What other states contribute to the effect of the
  command?

Switch Pos. Measurement
Switch Command
Temperature Measurement
Switch Position
Switch Actuator Health
Switch Sensor Health
Camera Temperature
Heater Heat Flow
Heater Health Resistance
Temperature Sensor Health
Sensor Scale Factor
Sensor Bias
Battery Voltage
Ambient Temperature
Camera Thermal Mass
Thermal Resistance
Camera Op Mode
Legend
state variable
measurement
command
62
State DiscoveryAm I Done Yet, Have I Gone Too
Far?

• Youre done when everything you care about is
  accounted for as states or effects
• Make models only as complex as needed apply good
  engineering judgment
• If a state doesnt affect any state you care
  about, and you dont care about the state, then
  you dont need to model it (e.g. location of
  Venus for a Mars Lander)
• If a state, command, measurement, or effect is
  purposely omitted because it is deemed
  insignificant, the reason should be documented
• Youve gone too far if the same state is
  represented in more than one state variable
• Unique state representation ensures consistency
  and simplifies implementation

63
State Analysis Checklist

• Start with an objective
• a state that the control system needs to control
• Add affecting states
• Decide what states to combine or separate
• Consider time derivatives, mathematical
  convenience, co-estimation, co-control, and
  combined telemetry
• Add measurements
• Identify measurements that are informative about
  those states
• Identify other states that affect the
  measurements
• Be sure to include sensor health state and
  calibration state
• Add commands
• Identify any commands that affect the states
• Identify other states that affect what the
  commands do
• Be sure to include actuator health state and
  calibration state

64
State AnalysisContinues with Modeling of Effects

• State Effects Model
• Measurement Model
• Command Model

65
State Effects Model

• A state effects model describes the behavior of a
  physical state variable, including how other
  state variables (if any) affect it
• Its a function of true state
• Its a predictive model, based on physics
• The model serves multiple purposes simulation,
  estimation, control, goal elaboration, etc.

State Effects Diagram
A Model of the Effects If switch is closed and
heater is healthy then heat flow k ? V2 /
R else heat flow 0
Switch Position
Heater Heat Flow
Heater Health Resistance R
Battery Voltage V
66
Measurement Model for a Switch Sensor

• A measurement model describes how one or more
  states affect a sensors measurement values
• Its a function of all affecting states
• Its a predictive model of what the sensor will
  produce
• The model is a requirement on the hardware
• Sensors often measure more than a single state
  variable

Measurement Model Table entries specifies
measurement.
State Effects Diagram
Sensor Health
Sensor Healthy Sensor Unhealthy
Opened Opened-meas anything
Closed Closed-meas anything
Tripped Tripped-meas anything
Switch Pos. Measurement
Switch Position
Switch Position
Switch Sensor Health
67
Measurement Model for a Temp Sensor

• This model shows effects of continuous and
  discrete states
• Its a predictive model of what the sensor will
  produce
• Predicted values are in DN (data numbers), not
  engineering units
• A measurement is meaningless without a
  measurement model
• A measurement model holds information that an
  estimator uses to interpret measurements

State Effects Diagram
Measurement Model if temperature sensor healthy
then measurement scale factor ?
(temperature sensor bias) else measurement
255
Camera Temperature
Temperature Sensor Health
Sensor Scale Factor
Sensor Bias
68
Direction of a Measurement Model

• A measurement model takes state values as input
  and predicts measurements
• It describes the sensors transfer function
• It is EU to DN
• Cant do this with DN to EU model
• Also show fault case sensor failed 255 DN, same
  model
• However, an estimator needs to do the opposite
• Given a measurement, estimate the states
• Can invert previous measurement model to convert
  DN to EU
• Is this inverted model OK?

If measurement 255 then sensor is
unhealthy temperature unknown else
sensor is healthy temperature (measurement /
scale factor) - bias
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Direction of a Measurement Model (2)
If measurement 255 then sensor is
unhealthy temperature unknown else
sensor is healthy temperature (measurement /
scale factor) - bias

• BugIf temperature slowly rises to produce
  measurement of 255 then
• temperature suddenly unknown
• healthy sensor is marked unhealthy
• In general, measurement models are not invertible
• Estimators often employ predictor-corrector
  algorithms (e.g. Kalman filters) or
  hypothesize-and-test algorithms (esp. for
  diagnosis)
• State Analysis documents the forward model and
  discourages inversion

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Measurements Key Properties

• Measurements are not States
• A measurement provides evidence about states
• A measurement represents a moment in time
• State is continuous in time and includes
  uncertainty
• A measurement is a function of state (true
  state, not estimated state)
• This function is the Measurement Model
• Includes EU to DN conversion
• Includes measurement noise, latency
• Can be used to compare predict with actual
  measurement (compute residual)
• Sensors always measure more than the intended
  state
• Sensor health, bias, scale factor, and other
  side effects

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Command Model

• A command model describes effects of commands
  sent to an actuator
• The effects depend on state when command issued
• The model describes instantaneous effects
• A command model informs
• Estimator design
• Controller design

Command Model
close-cmd actuator healthy
State Effects Diagram
Opened
Closed
Switch Command
open-cmd actuator healthy
open-cmd actuator healthy
Switch Position
Switch Actuator Health
over current
Tripped
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Command Model An Alternate Form

• Command models can be described in more than one
  way
• This equivalent model captures the same command
  effects
• Whats important is that the model be reviewable

Command Model If switch actuator is healthy,
then look up new state in table, else no change
in state
Switch command
Open Close
Opened Opened (no change) Closed
Closed Opened Closed (no change)
Tripped Opened (reset) Tripped (unchanged)
State Effects Diagram
Switch Command
Switch position
Switch Position
Switch Actuator Health
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The Model

• When we say The Model, it means

State Variables
State Effects Models
State Effects Models
State Effects Models
Command Models
Measurement Models
Command Models
Measurement Models
Command Models
Measurement Models
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The ModelMore Than Just a Diagram

• Captures physics of how state evolves over time,
  and under the influence of other states, e.g.
• Increasing temperature when heater is on
• Relation between heat flow and heater switch
• How a sensor behaves in a fault mode
• Physical assumptions must be explicitly
  specified, e.g.
• Flexibility of rover mast is assumed negligible
• Information in the model is used in
• Estimators ? Controllers ? Goal elaborations
• Scheduling ? Resource management ? etc
• Traditional systems engineering approaches
  capture most of this information in multiple
  disparate artifacts, allowing for inconsistencies