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Scenario Description

Scenario Description. Maggie Stringfellow Herring. 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 M&C must drop that antenna from signal combining

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Scenario Description

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  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 • M&C must drop that antenna from signal combining • M&C 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 (weight=0) [T0+.7 sec] • E. M&C directs signal processing to remove signal from antenna #5 from the correlation [T0+1 sec] • F. M&C issues a "shutdown" command to antenna #5 [T0+ 1sec] • G. M&C aborts the calibration activity for antenna #11,#12,#13 (has multiple steps) [T0+1 sec] • H. M&C directs antenna #11 to point at the spacecraft target [T0+1.2 sec] • I. antenna controller #11 reports that pointing errors are within tolerance [T0+6.2 sec] • J. M&C directs signal processing to add X-band, RCP signal from antenna #11 into the correlation [T0+6.4 sec] • K. signal processing correlator reports acceptable correlation using signal from antenna #11 [T0+7.4 sec] • L. M&C removes antenna #5 from the available resource pool (picked up by scheduling) [T0+10 sec] • M. M&C issues a service request for antenna #5 [T0+12 sec]

  4. A B C D E F G H I J K L M timeline Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C Ant 5 Mech Ant 5 Elec Ant 5 SP Array Signal Processing Antenna Control Building Cluster Control Building Receive Array & Scenario Timeline

  5. A. antenna controller #5 reports a high current load in the azimuth motor [T0] A Ant 5 Mech Ant 5 Elec Ant 5 SP Receive Array & Scenario Timeline B C D E F G H I J K L M timeline Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C 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] A B C D E F G H I J K L M timeline Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C Ant 5 Mech Ant 5 Elec Ant 5 SP Array Signal Processing Antenna Control Building Cluster Control Building

  7. Phased, conditioned, digitized A-1 IF W Correlator & Combiner Correlator & Combiner W Array Signal Processing Receive Array & Scenario Timeline C. signal processing correlator reports that it is unable to correlate signal from antenna #5 [T0+.6 sec] A B C D E F G H I J K L M timeline Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP Correlations ITI Arg Support Facility Power Combined Signal TR&C Ant 5 Mech Ant 5 Elec Ant 5 SP Ant 5 Elec Ant 5 SP Antenna Control Building Cluster Control Building

  8. W Receive Array & Scenario Timeline D. signal processing correlator removes signal #5 from the correlation (weight=0) [T0+.7 sec] A B C D E F G H I J K L M timeline Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI Arg Support Facility Correlator & Combiner Power Combined Signal TR&C Ant 5 Mech Ant 5 Elec Ant 5 SP Array Signal Processing Antenna Control Building Cluster Control Building

  9. Signal Inclusion Signal Inclusion Tracking Target {1-10, 14-20} Tracking Target {1-4, 6-10, 14-20} Tracking Calibration Target { 11 -13 } Tracking Calibration Target { 11 -13 } Receive Array & Scenario Timeline E. M&C directs signal processing to remove signal from antenna #5 from the correlation [T0+1 sec] A B C D E E F G H I J K L M timeline Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C Ant 5 Mech Ant 5 Elec Ant 5 SP Array Signal Processing Antenna Control Building Cluster Control Building

  10. Offline & ready Offline & ready Offline & ready Offline & not ready Offline & not ready Offline & not ready Signal Inclusion Tracking Tracking Tracking Shutdown Shutdown Shutdown Stowing Stowing Stowing Tracking Calibration Target { 11 -13 } Off-pnt Off-pnt Off-pnt Idle Idle Idle (5) (1-20) (1-4, 6-20) Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Tracking Target {1-4, 6-10, 14-20} Ant 1 Mech Ant 1 Elec Ant 1 SP W On-pnt On-pnt On-pnt Arg Support Facility Correlator & Combiner Power W Ant 5 Mech Ant 5 Elec Ant 5 SP Array Signal Processing Antenna Control Building Cluster Control Building Receive Array & Scenario Timeline F. M&C issues a "shutdown" command to antenna #5 [T0+ 1sec] A B C D E F G H I J K L M timeline Correlations ITI Combined Signal TR&C

  11. (1-4, 6-20) (1-4, 6-10, 14-20) (5) (5) Offline & ready Offline & ready Offline & ready Offline & not ready Offline & not ready Offline & not ready (11-13) Signal Inclusion Signal Inclusion Tracking Tracking Tracking Tracking Target {1-4, 6-10, 14-20} Tracking Target {1-4, 6-10, 14-20} Shutdown Shutdown Shutdown (1-4, 6-10, 14-20) Stowing Stowing Stowing Tracking Calibration Target { } Tracking Calibration Target { 11 -13 } Off-pnt Off-pnt Off-pnt Idle Idle Idle Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec On-pnt On-pnt On-pnt (5) Arg Support Facility Power Ant 11 Mech Ant 11 Elec (11-13) Antenna Control Building Receive Array & Scenario Timeline G. M&C aborts the calibration activity for antenna #11,#12,#13 (has multiple steps) [T0+1 sec] A B C D E F G H I J K L M timeline Phased, conditioned, digitized A-1 IF Ant 1 SP W Correlations ITI Correlator & Combiner Combined Signal W TR&C Ant 11 SP Array Signal Processing Cluster Control Building

  12. Offline & ready Offline & ready Offline & not ready Offline & not ready Signal Inclusion Tracking Tracking Tracking Target {1-4, 6-10, 14-20} Shutdown Shutdown Stowing Stowing Tracking Calibration Target { } Off-pnt Off-pnt Idle Idle (11) Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec (11) Ant 1 SP W Correlations ITI On-pnt On-pnt Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C Ant 11 Mech Ant 11 Elec Ant 11 SP Array Signal Processing Antenna Control Building Cluster Control Building Receive Array & Scenario Timeline H. M&C directs antenna #11 to point at the spacecraft target [T0+1.2 sec] A B C D E F G H I J K L M timeline

  13. Offline & ready Offline & ready Offline & not ready Offline & not ready Signal Inclusion (11) Tracking Tracking Tracking Target {1-4, 6-10, 14-20} Shutdown Shutdown Stowing Stowing Tracking Calibration Target { } Off-pnt Off-pnt Idle Idle (11) Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI On-pnt On-pnt Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C Ant 11 Mech Ant 11 Elec Ant 11 SP Array Signal Processing Antenna Control Building Cluster Control Building Receive Array & Scenario Timeline I. antenna controller #11 reports that pointing errors are within tolerance [T0+6.2 sec] A B C D E F G H I J K L M timeline

  14. Signal Inclusion Signal Inclusion Tracking Target {1-4, 6-10, 14-20} Tracking Calibration Target { } Tracking Calibration Target { } Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Tracking Target {1-4, 6-11, 14-20} Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C Ant 11 Mech Ant 11 Elec Ant 11 SP Array Signal Processing Antenna Control Building Cluster Control Building Receive Array & Scenario Timeline J. M&C directs signal processing to add X-band, RCP signal from antenna #11 into the correlation [T0+6.4 sec] A B C D E F G H I J K L M timeline

  15. Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI Arg Support Facility Correlator & Combiner Correlator & Combiner Power Combined Signal W TR&C Ant 11 Mech Ant 11 Elec Ant 11 SP Array Signal Processing Antenna Control Building Cluster Control Building Receive Array & Scenario Timeline K. signal processing correlator reports acceptable correlation using signal from antenna #11 [T0+7.4 sec]. A B C D E F G H I J K L M timeline RF from SRC Analog

  16. Offline & ready Offline & ready Offline & not ready Offline & not ready (5) Tracking Tracking Shutdown Shutdown Off-pnt Off-pnt Stowing Stowing (5) Phased, conditioned, digitized A-1 IF Idle Idle Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI On-pnt On-pnt Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C Ant 5 Mech Ant 5 Elec Ant 5 SP Array Signal Processing Antenna Control Building Cluster Control Building Receive Array & Scenario Timeline L. M&C removes antenna #5 from the available resource pool (picked up by scheduling) [T0+10 sec] A B C D E F G H I J K L M timeline

  17. Service Request Issued Phased, conditioned, digitized A-1 IF Focused A-1 Analog A-1 IF Analog RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C Ant 5 Mech Ant 5 Elec Ant 5 SP Array Signal Processing Antenna Control Building Cluster Control Building Receive Array & Scenario Timeline M. M&C issues a service request for antenna #5 [T0+12 sec] A B C D E F G H I J K L M timeline

  18. Analysis of System Under Control

  19. General Approach 1 DSAN operations scenario You are here guides Analysis of system under control 2 produces Physics model of system under control 3 informs informs M&C 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. Ant_N Received Signal State Msmt: Correlation Matrix Target & Background State Ant_N Mech & OpMode State Correlator & Combiner State Combined Signal State Signal Flow Diagram & Physics Model Focused A-1 Analog A-1 IF Analog Phased, conditioned, digitized A-1 IF RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C Ant 11 Mech Ant 11 Elec Ant 11 SP 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. Ant_N Received Signal State Msmt: Correlation Matrix Target & Background State Ant_N Mech & OpMode State Correlator & Combiner State Combined Signal State Signal Flow Diagram & Physics Model Focused A-1 Analog A-1 IF Analog Phased, conditioned, digitized A-1 IF RF from SRC Analog Ant 1 Mech Ant 1 Elec Ant 1 SP Ant 1 Mech Ant 1 Elec Ant 1 SP W Correlations ITI Arg Support Facility Correlator & Combiner Power Combined Signal W TR&C Ant 11 Mech Ant 11 Elec Ant 11 SP Array Signal Processing Antenna Control Building Cluster Control Building

  28. 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.

  29. Shutdown Offline & not ready Tracking On-pnt msmst Off-pnt msmt Offline & ready Off-pnt Idle On-pnt Unhealthy Motor current goes high Motor flagged as “repaired” Healthy 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

  30. 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

  31. 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 }

  32. 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 receivesTarget + Background & Noise Ant 3 receivesBackground & 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.

  33. Antennas 1 2 3 1 A A B 2 A A B 3 B B A 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. Eachijin the matrix is above threshold if its target content factor is greater than or equal to their noise content factor. Otherwise ijis below threshold. Arepresents above threshold and Brepresents below threshold. The signals from antennas one and two are Target + Background & Noise and the signal from antenna three is just Background & Noise.

  34. 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

  35. Establishinga Control Point of View

  36. …what is doing the controlling from what is being controlled 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?

  37. The Control System has cognizance over the System Under Control Model of the… System Under Control Control System ControlS/W measurements commands System Under Control OtherS/W Hardware Environment 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 abstractinterface 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

  38. Model of the… System Under Control Control System measurements commands System Under Control 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

  39. 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 engineer’s understanding, the software will perform as the systems engineers desire That is, …

  40. Blah blah SHALL not do (TBD) or whatever … blah blah blah ERROR . . . ERROR . . . ERR OR . . . ERROR . . . ERROR . . . ERROR . . . ERROR . . . ER ROR . . . ERROR . . . ERROR . . . ERROR . . . ERROR . . . E RROR . . . ERROR . . . ERRO R . . . ERROR . . . ER Bezillions of lines of pure gobbledy gook full of arcane jargon that no one understands, but it sure looks impressive                   2       E = m c doesn't it? System Software is a Surrogate for SystemsEngineers… and Software Engineers perform the transformation

  41. 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

  42. Heater Camera Data Platform Simple Example:A 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

  43. State Effects Diagram Camera Temp’ State VARIABLE A affects state variable B A B Camera Data Status Camera Mode Camera Heater Platform Pointing Camera Power Modeling the System Under Control • Six StateVariables 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 can’ttake pictures when OFF • What’s in a picturedepends on where thecamera is pointed andhow the camera isoperated and so on…

  44. Taking a Picture Operator’s View: 1:00 PM Camera Heater OFF + 2m Camera ON + 8m Turn platform to target Turn done Take picture + 1m Camera OFF + 2m Camera Heater ON State Effects Diagram Camera Temp’ State VARIABLE A affects state variable B • This sequence affects the states we have defined A B Camera Data Status Camera Mode Camera Heater Platform Pointing Camera Power A Simple Sequence • The sequence used to take a picture of some target might look something like this

  45. 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).

  46. 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

  47. State Effects Diagrams and Models

  48. State Effects Diagrams and Models

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