department of mechanical engineering the university of strathclyde, glasgow hybrid systems:...
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Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Hybrid Systems: Modelling, Analysis and Control
Yan Pang Department of Mechanical Engineering
The University of Strathclyde
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Outline
• Why Hybrid Systems?
• What Are Hybrid Systems?
• A Thermostat Example
• Hybrid Models : Hybrid Automata
• Current Research Areas
• Applications: The Batch Evaporator and Air Traffic Control System
• Conclusions
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Motivation•Computer Electronics
•Office Automation
•Automobiles
•Industry Process Plants
•Air Traffic Management Systems
•...
Hybrid models describe systems composed of both continuous and discrete components, the former typically associated with dynamical laws (e.g., physical systems), the latter with logic devices, such as switches, digital circuitry, software code.
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Hybrid Systems
• FA=(Q, Σ, δ)
• Q={1,2,3,4,5}
• Σ={a,b,c}
• δ=Q ΣQ
Computer ScienceFinite state machines
Computer ScienceFinite state machines
Control theoryContinuous dynamical systems
Control theoryContinuous dynamical systems
Hybrid Systems
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Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Simple Example
• Model of room, heater and thermostat• x : room temperature• Thermostat switches heater on between 68 & 70• Thermostat switches heater off between 80 & 82• Room warms and cools exponentially
Discrete states :{on,off} Continuous variable : x
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Hybrid Automata
Hybrid Automaton
State space Input space Vector fieldGuard setInvariant set
Remarks: and countable,
Can add outputs, etc. (not needed here)
),,,,( InvGfVSH XQS
DC VVV
XQVQG D :
nRVXf :
XQInv :
Q DV nRX mC RV
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Model of Thermostat
Hybrid automaton Model A possible trajectory
guard
Invariant
Vector fieldguard
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Current Research Directions
1. Modelling & Simulation
2. Analysis & Verification
3. Controller Synthesis
4. Applications
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
The Batch Evaporator
The Evaporation Process
1. The solution is filled into tank T1 and the solvent is evaporated until the desired concentration is reached. During evaporation the condenser collects the steam.
2. When the desired concentration is reached, the material is drained from T1 to T2 as soon as T2 is available, i.e. emptied from the previous batch.
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
The Batch Evaporator SimulationInitial set: I = q1×X1, where X1 = {0.2m x1 0.22m 0.28m x2 0.3 m x3=373K} Target set: F = q3×X3, where X3 = {0.01m x1 0.04m 0.08m x2 0.18 m 338K x3 373K} Invariant sets: INV(qi) = {0 x1 0.04m 0 x2 0.4 m 338K x3 400K }
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Air Traffic Management Systems
Two aircraft joining and
collision avoidance scheme
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Optimal Control
Control Objectives: Aircraft 2 is joining the path of Aircraft 1, in approach to the airport,
and it is up to the controller to ensure that a minimum separation between the two aircraft is maintained and also minimize all the cost during this procedure.
Optimal trajectory : By linear programming and quantifier elimination techniques
Department of Mechanical EngineeringThe University of Strathclyde, Glasgow
Conclusions
The interest in hybrid systems has grown over in last few years
• Theoretical Challenges : computer science + control theory
• Impact on Application: automotive power train control, batch system, bioengineering process, mixed integer process control, embedded software verification.
Current and Further Research
• Control Synthesis : Reachability Analysis, Under approximation reachable sets. (linear, non-linear)
• Optimal Control: Linear Programming(LP), Quantifier Elimination(QE) techniques
• Model Predictive Control (MPC) : Mixed Integer Programming (MIP)