Lecture 4. Applications

Transcription

1 Lecture 4. Applications

2 Summary Tools such as HyTech, CheckMate, Uppaal, Kronos have been used in many contexts typically to verify safety of a control design or to get tight bounds on parameters (e.g. steam boiler, audio control) This lecture shows where hybrid systems theory can fit in some application domains

3 Applications Outline! Embedded Control Systems " Autonomous Mobile Robots " Biological Systems

4 Embedded Controller Development Process For Automobile Transmissions Former Practice redesign feature specification describe control logic using relay-ladder diagrams fix bugs code write assembly code for the control microprocessor test on engine/ vehicle drive the car around the test track production hope for the best

5 Automotive Embedded Controller Design: State of the Practice Computer-Aided Control System Design feature specification executable spec. code simulation test on engine/ vehicle code generation production hardware in the loop

6 Executable Specifications Using MATLAB/Simulink/Stateflow

7 Transmission Control Logic

8 Opportunity to Apply Formal Verification Techniques Computer-Aided Control System Design feature specification executable spec. code test on engine/ vehicle simulation code generation model checking Objective: Verify feature behavior for the entire range of operating conditions. production hardware in the loop

9 Automotive Engine Control in Cut-off Mode Control law: Decide when to inject air/fuel for torque to minimize acceleration peaks during the cut-off operation. Problem: Verify the event-driven implementation of a control law designed in continuous time. Application of CheckMate due to Krogh et al

10 Automotive Powertrain Model Model from Magneti Marelli Engine Control Division Four-stroke, four cylinder engine Continuous-time powertrain model Hybrid model for cylinder cycles

11 CheckMate Model h000 h001 h010 h011 h100 predictor h000 h001 h010 h011 h100 power train h101 h110 h111 dynamics q h101 angle driveline h110 Mux M3 q h111 NOT NOT finish_line angle_trigger XOR M4 reach_180 NOT not1 start u torque NOT x1 reach_zero not2 M2 m x2 u simula simula M1 Mux Demux angle (degrees) x1 v x2

12 Continuous Dynamics x = Ax + Bu u = 0 (no air-fuel) or 10 x 1 = engine block angle x 2 = wheel revolution speed (radians) x 3 = axle torsion angle (in radians) x 4 = crankshaft revolution speed (rpm) x 5 = crankshaft angle (degrees)

13 Controller Specification Sliding mode control law derived in continuous time Hybrid implementation due to discrete torque decisions Remain within acceleration limits while tracking a sliding mode.

14 Cylinder Cycle Exhaust Phase_change Intake Phase_change Phase_change Combustion Phase_change Compression Control decision to apply torque on the power stroke must be made before the intake stroke three step lookahead.

15 Crankshaft Angle Rate Logic h000 h001 h010 h011 predictor Cylinder state transitions occur every h o. Crankshaft angle switches h001 h010 between 0 o and 180 o, angle rate h011 switches between +rate q and -rate. h100 h101 h110 h111 h100 h101 angle driveline h110 Mux M3 q h111 NOT NOT finish_line angle_trigger XOR M4 reach_180 NOT not1 start u torque NOT x1 reach_zero not2 M2 m x2 u simula si mula M1 Mux Demux angle (degrees) x1 v x2

16 Predictive Control Logic The discrete state indicates the torque decisions for the current and next two power strokes (i.e., for three of the four cylinders). Transitions from each state depend on whether predicted state for the next power stroke is closer to the sliding mode with or without torque. The 9th state (not shown) is the end simulation state--reachable from any of the other 8 states.

17 Flowpipe for One Discrete Sequence

18 Applications Outline # Embedded Control Systems! Autonomous Mobile Robots " Biological Systems

19 Programming Interacting Autonomous Robots Many modes Individual modes are well understood, but not their interaction. Software design Modes designed bottom-up Protocols top-down Modular design to ensure reusability Tasks: Formation control, cooperative control

20 Software Design Methodology CHARON Code (High level language) CHARON CHARONto to Java Translator Drivers Java Libraries Java Code Control Code Generator Simulator Code Generator Human Interface

21 Vision-Based Control: Mode Switching

22 Reactive Vision Based Controllers Control Wall- Following Avoid Obstacle Collision Recovery Motion Controller Range Mapper Robot Position Estimator Target Detector Edge Detector Collision Detector Color Blob Finder Frame Grabber Actuators

23 Controllers for Maintaining Formation Y ψ 1 2 v 1, ω 1 Y v 1, ω 1 d (x 2,y 2,θ 2 ) l 12 v 2, ω 2 (x 1,y 1,θ 1 ) d (x 3,y 3,θ 3 ) l 12 (x 1,y 1,θ 1 ) v 3, ω 3 v 2, ω 2 l 23 (x 2,y 2,θ 2 ) v j = cos γ sin X ( b + ωˆ cos(ˆ θ Estimate of relative position, orientation, 1 linear ω = and [ s sin angular γ + l cos velocities γ ( b + ωˆ ) + required! v sin(ˆ θ θ )] j s ij d j ij ij l ij ij ij γ ij ij ij ij i ) + vˆ i i i i θ i j ) j X

24 Multirobot Coordination R 1 R 2 R 3 R 2 R 3 R 1

25 Rules for Mode Switching l 13 l 13 = l 23 R 2 l 12 r 2 l 13 = l 23 + l 12 Autonomous Navigation l 23 R 3 l 13 R 1 l-ψ 23 l 13 = l 23 - l 12 r 2 r 1 l 12 l- l l-ψ 13 R r 1 l 12 = l 13 + l 23 l 12 l 23 r 1 r 2 Sensor constraints

26 Leader Follower and Obstacle Avoidance Leader is teleoperated Leader is autonomous (l R 12,,ψ 12 ) 2 R 1 l O2 Obs R 1 R 2 l 12

27 Mode Switching and Maintain Formation

28 Applications Outline # Embedded Control Systems # Autonomous Mobile Robots! Biological Systems

29 Cellular Networks "Networks of interacting biomolecules carry out many essential functions in living cells (gene regulation, protein production) "Both positive and negative feedback loops "Design principles poorly understood "Large amounts of data is becoming available "Beyond Human Genome: Behavioral models of cellular networks "Modeling becoming increasingly relevant as an aid to narrow the space of experiments

30 Regulatory Networks gene expression negative - START gene STOP regulation positive + transcription translation nascent protein cell-to-cell signaling chemical reaction

31 Hybrid Modeling of Biological Systems Traditionally, d ( LuxR ) biological systems LuxR = T are modeled using smooth functions. l luxr d [ x ] dt H sp = synthesis decay ± transform ± transport Φ( X, κ Xm, ν Xm ) dt b d r Ai LuxR + r Co k LuxR regulation LuxR / Ai CRP negative positive + - START LuxR / Ai luxr gene G transcription translation STOP X κ Xm sw ν Xm 2 X sw X Ai chemical reaction Ai protein LuxR d( luxr ) = Tc [ Φ( CRP, κ dt (1 Φ( LuxR Ai, κ luxr H RNA k G luxr CRP LuxR Ai, ν, ν CRP ) LuxR Ai )) + b )

32 Hybrid Modeling regulatory protein/complex Nonlinear dynamics (proteins involved in chemical reactions) Discrete jump (mrna) mode Linear dynamics (proteins not involved in chemical reactions) Essentially hybrid system high conc continuous model low conc stochastic model At low concentrations, a continuous approximation model might not be appropriate. Instead, a stochastic model should be used. In some cases, the biological description of a system is itself hybrid.

33 Luminescence / Quorum Sensing in Vibrio Fischeri

34 Luminescence Regulation O L + CRP camp - lux box O R luxr luxicdabeg CRP binding site - LuxR Ai + LuxI LuxA LuxR LuxB Ai Substrate luciferase

35 lum x & = Ax+ b 10 x8 x 8sw Reachability x 8 = x 8sw x = 8 x 8sw ( x 8 x & = Ax+ Co non-lum ) b 00 x8 x 8sw = Ax b i0 c0 = 0, c1 = 1 Under what conditions can the x4 bacterium switch H RNATlon Tc ( the ci + light? b ) = x 7 bi0 = 0 x 0 x & + x 8 lum dynamics x 8 sw switching surface nonlum dynamics ( x 7 Ai ) ( L I )

36 Simulation Results external A i (input) switch history luminesence (output) switch history concentrations for various entities

37 Summary $ Hybrid systems are necessary to model some biological regulatory networks. $ The simulation results of the luminescence control in Vibrio fischeri are in accordance with phenomena observed in experiments. $ Modeling concepts such as hierarchy, concurrency, reuse, are relevant for modular specifications $ Exploiting the structure of real biological systems will be essential to meet the challenge posed by the enormous complexity of biological regulatory networks.

38 Conclusions " A rich variety of domains match hybrid systems paradigm " Traditional benefits: safety verification, design of hybrid controllers " Formal models can be beneficial in more ways: modeling, understanding, programming, simulation " Emerging potential for integration with software engineering design tools