Hybrid Systems and Networked Control Systems Michael S. Branicky EECS Dept. Case Western Reserve...

Hybrid Systems and Networked Control Systems

Michael S. Branicky

EECS Dept.

Case Western Reserve University

NSF Planning Meeting on

Cyber-Physical Systems

27 July 2006

Networked ControlHardware

Diagnostics+Monitoring

Software Engineering

Security

Hybrid Dynamical System*• A set of dynamical

systems plus rules for jumping among them

[Raibert’s Hopper]

___________________* M.S. Branicky. Introduction to hybrid systems. In Handbook of Networked and Embedded Control Systems, Birkhauser, 2005.

Hybrid Dynamical System: Automata Viewpoint*

[Thermostat]

[Raibert’s Hopper]

[Bouncing Ball]


Adding Control: CHDS*

[Tiptronic Transmission]

• An HDS plus controlled switching and jumps


Networked Control Systems* (1)

• Numerous distributed agents• Physical and informational dependencies

___________________* M.S. Branicky, V. Liberatore, and S.M. Phillips. Networked control system co-simulation for co-design. Proc. ACC, 2003.

Networked Control Systems* (2)

• Control loops closed over heterogeneous networks


Mathematical Model:NCS Architecture*

An NCS Architecture is a 3-tuple: • Agent Dynamics: a set of stochastic hybrid systems

dXi(t)/dt = fi (Qi(t), Xi(t), QI[t], YI[t], R(t)) Yi(t) = gi (Qi(t), Xi(t), QI[t], YI[t], R(t))

• Network Information Flows: a directed graph GI = (V, EI), V = {1, 2, …, N}; e.g., e = (i, j)

• Network Topology: a colored, directed multigraph GN = (V, C, EN), V = {1, 2, …, N}; e.g., e = (c, i, j)


Fundamental Issues*• Time-Varying Transmission Period• Network Schedulability, Routing Protocols• Network-Induced Delays• Packet Loss

Plant

Controller

h(t)

Plant

Controller

h

DelayDelay

Plant

Controller

r

Plant

Plant

Controller

Controller

.

.

.N

etw

ork

h1(t)

hN(t)

___________________* M.S. Branicky, S.M. Phillips, W. Zhang (various): Proc. ACC, 2000; IEEE Cont. Systs. Mag., 2001; Proc. CDC, 2002.

Previous Work• Nilsson: Time-Stamp Packets, Gain Schedule on Delay• Walsh et al.: no delay+Max. Allowable Transfer Interval• Zhang, Branicky, Phillips: hsuff

• Hassibi, Boyd: Asynchronous dynamics systems• Elia, Mitter, others: Info theory: BW reqts. for CL stability• Teel/Nesic: Small gain theorem, composability

Control and Scheduling Co-Design*

• Control-theoretic characterization of stability and performance (bounds on transmission rate)

• Transmission scheduling satisfying network bandwidth constraints

Simultaneous optimization ofboth of these = Co-Design

Plant

Plant

Controller

Controller

.

.

.

Net

wor

k

h1(t)

hN(t)

___________________* M.S. Branicky, S.M. Phillips and W. Zhang. Scheduling and feedback co-design for networked control systems. Proc. CDC, 2002.

Co-Simulation*

Simulation languages

Bandwidthmonitoring

VisualizationNetwork dynamics

Plant output dynamics

Packet queueing and forwarding

Co-simulation of systems and networks

Plant agent(actuator, sensor, …)

Router

Controlleragent(SBC, PLC, …)


Co-Simulation Methodology*

• Simultaneously simulate both the dynamics of the control system and the network activity

• Vary parameters:– Number of plants, controllers, sensors– Sample scheduling– Network topology, routing algorithms– Cross-traffic– Etc.


Co-Simulation Components (1):Network Topology, Parameters*

Capability like ns-2 to simulate network at packet level: • state-of-art, open-source software• follows packets over links• queuing and de-queuing at router buffers• GUI depicts packet flows• can capture delays, drop rates, inter-arrival times


Extensions of ns-2 release*:• plant “agents”: sample/send output at specific intervals• control “agents”: generate/send control back to plant• dynamics solved numerically using Ode utility, “in-line” (e.g., Euler), or through calls to Matlab

Co-Simulation Components (2):Plant and Controller Dynamics

Also: TrueTime [Lund] (Simulink plus network modules)Ptolemy, SHIFT [UCB] (+ other HS simu. langs.)

Need: comprehensive tools (ns-2 +SL/LV/Omola +Corba)various HIL integrations (HW, µprocs, emulators)


Analysis and Design Tools• Stability Regions* and Traffic Loci**

Both for an inverted pendulum on a cart (4-d), with feedback matrix designed for nominal delay of 50ms. Queue size = 25 (left), 120 (right)

___________________* W. Zhang, M.S. Branicky, and S.M. Phillips. Stability of networked control systems. IEEE Cont. Systs. Mag., Feb. 2001.** J.R. Hartman, M.S. Branicky, and V. Liberatore. Time-dependent dynamics in networked sensing and control. Proc. ACC, 2005.

Information Flow

• Flow– Sensor data– Remote controller– Control packets

• Timely delivery– Stability– Safety– Performance

Bandwidth Allocation for Control*

• Objectives:– Stability of control systems– Efficiency & fairness– Fully distributed, asynchronous, & scalable– Dynamic & self reconfigurable

___________________* A.T. Al-Hammouri, M.S. Branicky, V. Liberatore, and S.M. Phillips. Decentralized and dynamic bandwidth allocation in networked control systems. Proc. WPDRTS, 2006.

Queue Control: Results*

PI¤

P¤

___________________* A.T. Al-Hammouri, M.S. Branicky, V. Liberatore, and S.M. Phillips. Decentralized and dynamic bandwidth allocation in networked control systems. Proc. WPDRTS, 2006.

Synchronization: Ideas*

• Predictable application time– If control applied early, plant is not in the state

for which the control was meant – If control applied for too long, plant no longer

in desired state

• Keep plant simple– Low space requirements

• Integrate Playback, Sampling, and Control___________________* V. Liberatore. Integrated play-back, sensing, and networked control. Proc. INFOCOM, 2006.

Synchronization: Mechanics*• Send regular control

– Playback time• Late playback okay

– Expiration

• Piggyback contingency control

___________________* V. Liberatore. Integrated play-back, sensing, and networked control. Proc. INFOCOM, 2006.

Plant Output*

Open Loop Play-Back

___________________* V. Liberatore. Integrated play-back, sensing, and networked control. Proc. INFOCOM, 2006.

Cyber-Physical Systems Research

– Control theory:(stoch.) HS, non-uniform/stochastic samp., event- vs. time-basedhierarachical, composable (cf. Omola), multi-timescale (months to ms)

– Delays, Jitter, Loss Rates, BW• Characterization of networks (e.g., time-varying RTT, OWD delays)• Application and end-point adaptability to unpredictable delays

– Buffers– Control gains– Time synchronization

– Bandwidth allocation, queuing strategies, network partitioning• Control theoretical, blank-slate designs, Jack Stankovic’s *SP protocols

– Co-simulation, co-design– Application-oriented, end-to-end QoS (beyond stability to performance)– Distributed, real-time embedded middleware:

• Resource constraints vs. inter-operability and protocols• Sensors/transducers (cf. IEEE 1451, LXI Consortium), distributed timing services

(IEEE 1588, NTP; John Eidson: Time is a first-class object), data gathering (Lui Sha’s observability), resource management (discovery, “start up”), “certificates”

Thanks

• NSF CCR-0329910 on Networked Control

• Colleague: Vincenzo Liberatore, CWRU

Hybrid Systems and Networked Control Systems Michael S. Branicky EECS Dept. Case Western Reserve...

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