passivity-based control design for cyber-physical systemspantsakl/publications/381-cps-ca08.pdf ·...

Passivity-Based Control Design for Cyber-PhysicalSystems

Xenofon Koutsoukos∗, Nicholas Kottenstette†, Joe Hall∗, Panos Antsaklis†, Janos Sztipanovits∗

∗ISIS/Vanderbilt University †University of Notre Dame

Abstract—Real-life Cyber-Physical Systems (CPSs), such asautomotive vehicles, building automation systems, and groupsof unmanned air vehicles are monitored and controlled bynetworked control systems. The overall system dynamics emergesfrom the interaction among physical dynamics, computationaldynamics, and communication networks. Network uncertaintiessuch as time-varying delay and packet loss cause significantchallenges that probihit the application of traditional component-based design methods. This paper proposes a passive controlarchitecture for designing CPSs that are insensitive to net-work uncertainties. The proposed method improves orthogonalityacross the controller design and implementation design layerswith respect to network uncertainties, thus empowering model-driven development. The paper presents the architecture for asimplified system consisting of a robotic manipulator controlledby a digital controller over a wireless network and simulationresults that show that the system is insensitive to time-varyingnetwork delays.

I. I NTRODUCTION

The heterogeneous composition of computing, sensing, ac-tuation, and communication components has enabled a moderngrand vision for real-world Cyber Physical Systems (CPSs).Real-world CPSs, such as automotive vehicles, building au-tomation systems, and groups of unmanned air vehicles aremonitored and controlled by networked control systems andthe overall system dynamics emerges from the interactionamong physical dynamics, computational dynamics, and com-munication networks. Design of CPSs requires controllingreal-world system behavior and interactions in dynamic anduncertain conditions. This paper, in particular, aims at appli-cations that integrate computational and physical devices usingwireless networks such as medical device networks, groups ofunmanned vehicles, and transportation networks.

This work is motivated by the rapidly increasing use of net-work control system architectures in constructing real-worldCPSs and aims at addressing fundamental problems caused bynetworks effects, such as time-varying delay, jitter, data ratelimitations, and packet loss. To deal with these implementationuncertainties, we propose a model-design flow on top ofpassivity, a very significant concept from system theory [1].A precise mathematical definition requires many technicaldetails, but the main idea is that a passive system cannot applyan infinite amount of energy to its environment. The inherentsafety that passive systems provide is fundamental in buildingsystems that are insensitive to implementation uncertainties.Passive systems have been exploited for the design of diverse

systems such as smart exercise machines [2], teleoperators [3],digital filters [4], and networked control systems [5]–[7].

The main idea of our approach is that by imposing passivityconstraints on the component dynamics, the design becomesinsensitive to network effects, thus establishing orthogonality(with respect to network effects) across the controller designand implementation design layers. This separation of concernsempowers the model based design process to be extended fornetworked control systems. It should be noted that passivestructures have additional advantages with regard to robustnessin the presence of finite length representations and satura-tion [4] but this paper focuses on network effects that is oneof the most significant concerns in the development of CPSs.

The paper first discusses challenges in applying component-based system design techniques for CPSs in Section II. Thechallenges stem from the heterogeneity of CPSs not onlyin terms of their components but also in terms of essentialdesign requirements. For example, control design typicallydepends on assumptions that neglect the network uncertainties.A major problem for model-based design is decoupling controlspecification from implementation uncertainties. To addressthis problem, we propose a passive control architecture thataccounts for the effects of network uncertainties.

After a brief background on passivity in Section III, wepresent the architecture for a simplified system consisting ofa robotic manipulator controlled by a digital controller over awireless network in Section IV. We focus on the technicaldetails required for implementing the architecture and weoutline the technical results that ensure passivity and stabilityof the overall system. Section V evaluates the passive controldesign for a typical 6 degree-of-freedom robotic arm con-trolled by a digital controller over a 802.llb wireless network.We present simulation results based on a detailed model thatcontains components for the robotic arm, the wireless network,and the digital controller that show that the system operationis insensitive to time-varying delays. We also compare theproposed method with a standard non-passive controller toillustrate the advantages of passive control design. Finally,Section VI presents the main directions of our future work.

II. M ODEL-BASED CONTROL DESIGN FORCPSS

Building systems from components is central in all engi-neering disciplines to manage complexity, decrease time-to-market, and contain cost. The feasibility of component-based

Xenofon Koutsoukos, Nicholas Kottenstette, Joe Hall , Panos Antsaklis, Janos Sztipanovits, “Passivity-Based Control Design of Cyber-Physical Systems,” International Workshop on Cyber-Physical Systems Challenges and Applications (CPS-CA'08), in conjunction with the 4th IEEE International Conference on Distributed Computing in Sensor Systems (DCOSS'08), Santorini Island, Greece, June 11, 2008.

Fig. 1. Simplified CPS design flow.

systemdesign depends on two key conditions: composition-ality - meaning that system-level properties can be computedfrom local properties of components - and composability -meaning that component properties are not changing as a resultof interactions with other components. Lack of composition-ality and composability lead to behavioral properties that canbe verified or measured only by system-level analysis (and/ortesting), which becomes inefficient for real-world complexsystems.

CPSs are inherently heterogeneous not only in terms of theircomponents but also in terms of essential design requirements.Besides functional properties, CPSs are subject to a wide rangeof physical requirements, such as dynamics, power, physicalsize, and fault tolerance in addition to system-level require-ments, such as safety and security. This heterogeneity doesnot go well with current methods of compositional design forseveral reasons. The most important principle used in achiev-ing multi-objective compositionality is separation of concerns(in other words, defining design viewpoints). Separation ofconcerns works if the design views are orthogonal, i.e. designdecisions in one view does not influence design decisionsin other views. Unfortunately, achieving compositionality formultiple physical and functional properties simultaneously is avery hard problem because of the lack of orthogonality amongthe design views.

Figure 1 represents a simplified model-based design flowof a CPS composed of a physical plant and a networkedcontrol system. In a conventional design flow, the controllerdynamics is synthesized with the purpose of optimizing per-formance. The selected design platform (abstractions and toolsused for control design in the design flow) is frequentlyprovided by a modeling language and a simulation tool, suchas Matlab/Simulink. The controller specification is passedto the implementation design layer through a “Specifica-

tion/Implementation Interface”. The implementation in itselfhas a rich design flow that we compressed here only intwo layers: System-level design and Implementation platformdesign. The software architecture and its mapping on the(distributed) implementation platform are generated in thesystem-level design layer. The results - expressed again inthe form of architecture and system models - are passed onthrough the next Specification and Implementation Interfaceto generate code as well as the hardware and network de-sign. This simplified flow reflects the fundamental strategy inplatform-based design [8]. Design progresses along preciselydefined abstraction layers. The design flow usually includestop-down and bottom-up elements and iterations (not shownin the figure).

Effectiveness of the platform-based design largely dependson how much the design concerns (captured in the abstractionlayers) are orthogonal, i.e., how much the design decisionsin the different layers are independent. Heterogeneity causesmajor difficulties in this regard. The controller dynamics istypically designed without considering implementation sideeffects (e.g. numeric accuracy of computational components,timing accuracy caused by shared resource and schedulers,time varying delays caused by network effects, etc.). Timingcharacteristics of the implementation emerge at the confluenceof design decisions in software componentization, systemarchitecture, coding, and HW/network design choices. Compo-sitionality in one layer depends on a web of assumptions to besatisfied by other layers. For example, compositionality on thecontroller design layer depends on assumptions that the effectsof quantization and finite word-length can be neglected and thediscrete-time model is accurate. Since these assumptions arenot satisfied by the implementation layer, the overall designneeds to be verified after implementation - even worst -changes in any layer may require re-verification of the fullsystem.

An increasingly accepted way to address these problemsis to enrich abstractions in each layer with implementationconcepts. An excellent example for this approach is True-Time [9] that extends Matlab/Simulink with implementationrelated modeling concepts (networks, clocks, schedulers) andsupports simulation of networked and embedded control sys-tems with the modeled implementation effects. While thisis a major step in improving designers’ understanding ofimplementation effects, it does not help in decoupling designlayers and improving orthogonality across the design concerns.A controller designer can now factor in implementation effects(e.g., network delays), but still, if the implementation changes,the controller may need to be redesigned.

Decoupling the design layers is a very hard problem andtypically introduces significant restrictions and/or overdesign.For example, the Timed Triggered Architecture (TTA) orthog-onalizes timing, fault tolerance, and functionality [10], but itcomes on the cost of strict synchrony, and static structure.In an analogous manner, we propose to encompass passivityinto traditional model-driven development processes in orderto decouple the design layers and account for the effect of

network uncertainties.Our approach advocates a concrete and important transfor-

mation of model-based methods that can improve orthogo-nality across the design layers and facilitate compositionalcomponent-based design of CPSs. By imposing passivityconstraints on the component dynamics, the design becomesinsensitive to network effects, thus establishing orthogonality(with respect to network effects) across the controller designand implementation design layers. This separation of concernsempowers the model-based design process to be applied fornetworked control systems. Network effects need not be con-sidered at the controller design layer and the theoretical guar-antees about stability and performance are independent of theimplementation uncertainties. Further, stability is maintainedeven in the presence of disturbance traffic in the network.

The remaining of the paper presents in detail a sim-plified system consisting of a robotic arm controlled bya digital controller over a wireless network. We focus onthe controller design layer and we manually generate Mat-lab/Simulink/TrueTime models of the overall system and an-alyze the behavior using simulations. Our results support theadvantages of the passive control architecture regarding theorthogonality between the control design and the network un-certainties. Implementing an end-to-end tool chain for passivecontrol design of systems consisting of multiple plants andmultiple controllers communicating over wireless networks isa subject of current and future work.

III. B ACKGROUND ON PASSIVITY

There are various precise mathematical definitions for pas-sive systems [7]. Essentially all the definitions state that theoutput energy must be bounded so that the system doesnot produce more energy than was initially stored. Strictly-output passive systems and strictly input passive systems withfinite gain have a special property in that they arel2-stable.Also, passive systems are Lyapunov-stable in terms of allobservable states. Passive systems have a unique propertythat when connected in either a parallel or negative feedbackmanner the overall system remains passive. By simply closingthe loop with any positive definite matrix, any discrete timepassive plant can be rendered strictly output passive. This isan important result because it makes it possible to directlydesign low-sensitivity strictly-output passive controllers usingthe wave digital filters described in [4].

When delays are introduced in negative feedback con-figurations, the network is no longer passive. One way torecover passivity is to interconnect the two systems with wavevariables. Wave variables were introduced by Fettweis in orderto circumvent the problem of delay-free loops and guaranteethat the implementation of wave digital filters is realizable [4].Wave variables define a bilinear transformation under whicha stable minimum phase continuous system is mapped to astable minimum phase discrete-time system, and thus, thetransformation preserves passivity.

Networks consisting of a passive plant and a controller aretypically interconnected using power variables. Power vari-

ables are generally denoted with an effort and flow pair whoseproduct is power. However, when these power variables aresubject to communication delays, the communication channelceases to be passive which can lead to instabilities. Wavevariables allow effort and flow variables to be transmittedover a network while remaining passive when subject toarbitrary fixed time delays and data dropouts. If additionalinformation is transmitted along with the continuous wavevariables, the communication channel will also remain passivein the presence of time-varying delays [5]. More recentlyit has been shown that discrete wave variables can remainpassive in spite of certain classes of time-varying delays anddropouts [6], [11]. In addition, a method which states howto properly handle time-varying discrete wave variables andmaintain passivity has been developed in [7] and is used inour passive control architecture.

IV. PASSIVE CONTROL ARCHITECTURE

This section presents a passive control architecture for asimplified system consisting of a robotic manipulator con-trolled by a digital controller over a wireless network. Thearchitecture accounts for time-varying delays in the network.Specifically, all components are designed to preserve passivityensuring stability of the closed loop system. We present anoverview of the architecture focusing on the technical detailsrequired for the implementation. The theoretical foundationsfor control of passive plants over wireless networks can befound in [12].

A. Robotic System

Our control strategy takes advantage of thepassive structureof a robotic system [13]. The robot dynamics which aredenoted byGrobot(τ) in Figure 2 are described by

τ = M(Θ)Θ + C(Θ, Θ)Θ + g(Θ). (1)

The state variablesΘ denote the robot joint angles,τ is theinput torque vector,M(Θ) is the mass matrix,C(Θ, Θ) isthe matrix of centrifugal and coriolis effects, andg(Θ) is thegravity vector.

Despite the complexity of robotic manipulators, simplecontrol laws can be used in a number of cases. A fundamentalconsequence of the passivity property is that a simple in-dependent joint continuous-time proportional-derivative (PD)control can achieve global asymptotic stability for set-pointtracking in the absence of gravity [14]. Therefore, we employa PD controller but we consider a discrete-time equivalentimplementation that communicates with the robotic system viaa wireless network. To compensate gravity, we select as thecontrol commandτu = τ − g(Θ). Then it can be shown thatthe robot is apassive dissipative system which is alsolosslessin which all supplied energy is stored as kinetic energy in therobot [15].

Furthermore, the robot can be made to bestrictly-outputpassive by adding negative velocity feedback [7]. Therefore,

Fig. 2. Proposed Wireless Passive Control Architecture

we select the control commandτu to have the following finalform

τu = τ − g(Θ) + ǫΘ, ǫ ≥ 0.

The gravity compensation and the velocity damping are im-plemented locally at the robotic system and it can be shownthat the gravity compensated system with velocity dampingdenotedG : τu 7→ Θ is passive when ǫ = 0 and strictly-output passive for any ǫ > 0 respectively.

B. Wireless Control Architecture

Figure 2 depicts the proposed wireless control architecture.The robotic systemG : τu 7→ Θ is controlled by apassivedigital controller Gpc : e[i] 7→ τuc[i] using wave variablesdefined by the bilinear transformation denoted asb in Figure 2.The communication of the wave variables is subject to time-varying delays incurred in the wireless network that must beaccounted for in order to ensure passivity and stability of theoverall closed loop system.

The digital controllerGpc is interconnected to the robotvia a passive sampler (PS) at sample rateTs which convertsthe continuouswave variable up(t) to an appropriate scaleddiscretewave variable up[i]. Conversely, apassive hold device(PH) converts the discrete timewave variable vucd[i] to anappropriately scaledwave variable vucd(t) which is held forTs seconds.

The inner-product equivelant sampler (IPES) and zero-order-hold (ZOH) blocks at the input of the digital con-troller are used to ensure that the overall systemGnet :[ΘT

−t(t), τT

d (t)]T 7→ [τT

uc(t), ΘT(t)]T is (strictly output) pas-

sive. Θ−t(t) denotes a (negative) desired velocity profile forthe robot to follow, τuc(t) is the continuous timepassivecontrol command, andτd(t) is a corresponding “disturbance”torque applied to the robots joints.

C. Wave Variables

The continuous robot input and outputwave variablesvucd(t), up(t) ∈ R

m depicted in Figure 2 are related to the

corresponding torque and velocity vectorsτucd(t), Θ(t) ∈R

m as follows:

1

2(uT

p (t)up(t) − vT

ucd(t)vucd(t)) = ΘT(t)τucd(t).

The wave variable vucd(t) and velocity measurementΘ(t)are considered inputs and thewave variable up(t) and de-layed control torqueτucd(t) are considered outputs and arecomputed as follows:

[

up(t)τucd(t)

]

=

[

−I√

2bI

−√

2bI bI

] [

vucd(t)

Θ(t)

]

whereI ∈ Rm×m denotes the identitiy matrix.

The digital control input and outputwave variablesupd[i], vuc[i] ∈ R

m depicted in Figure 2 are relatedto the corresponding discrete torque and velocity vectorsτuc[i], Θd[i] ∈ R

m as follows:

1

2(uT

pd[i]upd[i] − vT

uc[i]vuc[i]) = τuc[i]TΘd[i]

Thewave variable upd[i] and control torqueτuc[i] are consid-ered inputs and thewave variable vuc[i] and delayed velocityΘd[i] are considered outputs and are computed as follows:

[

vuc[i]

Θd[i]

]

=

I −√

2bI

√

2bI − 1

bI

[

upd[i]τuc[i]

]

D. Passive Sampler and Passive Hold

The passive sampler denoted (PS,Ts) in Figure 2 and thecorrespondingpassive hold denoted (PH,Ts) must be designedsuch that the following inequality is satisfied∀N > 0:

∫ NTs

0

(uT

p (t)up(t) − vT

ucd(t)vucd(t))dt−N−1∑

i=0

(uT

p [i]up[i] − vT

ucd[i]vucd[i]) ≥ 0. (2)

This condition ensures that no energy is generated by thesampleand hold devices, and thus, passivity is preserved.

Denote eachjth element of the column vectorsup(t), up[i]asupj

(t), upj[i] in which j = {1, . . . ,m}. An implementation

of the PS that satisfies condition (2) is given by

upj[i] =

√

∫ iTs

(i−1)Ts

u2pj

(t)dt sign(

∫ iTs

(i−1)Ts

upj(t)dt).

in which j = {1, . . . ,m}.Denote each jth element of the column vectors

vucd(t), vucd[i] asvucdj(t), vucdj

[i] in which j = {1, . . . ,m}.An implementation of the PH that satisfies condition (2) is

vucdj(t) =

1√Ts

vucdj[i − 1], t ∈ [iTs, (i + 1)Ts].

E. Passive controller

Typically a passive continuous-time PD controller is imple-mented as

e1(t) = (Θd(t) + Θ−t)

τuc(t) = Kpe1(t) + Kd(Θd(t) + Θ−t).

A state-space realization of the controller can be described by

x(t) = Ax(t) + Bu(t) (3)

y(t) = Cx(t) + Du(t). (4)

whereA = 0, B = I, C = Kp = KT

p > 0, D = Kd =KT

d > 0} (all matrices are inRm×m).To obtain a digital controller, we implement the discrete-

time equivalentpassive controller Gpc : e1[i] 7→ τuc[i]computed from the state-space realization (3,4) with samplingperiodTs. The resulting controller is implemented as

x[k + 1] = Φspx[k] + Γspu[k]

y[k] = KsCspx[k] + KsDspu[k]. (5)

where Ks > 0 is a diagonal scaling matrix andu[k] =(Θd[k] + Θ−t[k]). Details for computing the digital controllerand a theoretical result showing that the controller isstrictly-output passive can be found in [12, Section 2.3.1].

F. Passivity of the Closed-Loop System

All elements of the wireless control architecture are imple-mented to ensure passivity. In addition, if the communicationprotocol ensures that

∫ NTs

0

ΘT(t)τucd(t)dt ≥(N−1)∑

i=0

τT

uc[i]Θd[i] (6)

always holds, it can be shown that whenǫc = ǫ = 0 thesystem depicted in Figure 2 ispassive. Furthermore, ifǫc >

0, and ǫ > 0 then the system isstrictly-output passive andLm

2 stable. The proof is based on the fact that all componentsof the architecture preserve passivity and is a straightforwardextension of the results presented in [12]. Condition (6) canbe imposed on the wireless communication protocol by notprocessing duplicate transmissions of wave variables [7].

V. EVALUATION

This section presents preliminary simulation results to eval-uate the passive control architecture for controlling a roboticarm over a wireless network.

A. Experimental Setup

We consider the Pioneer 3 (P3) arm which is a roboticmanipulator built for the P3-DX and P3-AT Activmedia mobilerobots. The P3 Arm has two main segments, the manipulatorand the gripper. The manipulator has five degrees of freedomand the gripper has an additional one. Figure 3 shows thehome position of the P3 arm including the locations for thecenters of gravity using the point mass assumption.

A2 = 0.160m A1 = 0.068m

D4 = 0.137m

A5 = 0.113m

m3

m2

m1

m5

m4=0

Fig. 3. Pioneer 3 Arm

The simulation model includes three main subsystems asshown in Figure 4. The dynamic model of the robotic arm isdescribed by Equation (1) and is derived using the Langrangianapproach for computing the elements of the mass matrix,coriolis and centrifugal vector, and gravity vector [16]. Themodel is implemented as a Simulink block using the “RoboticsToolbox for Matlab” [17] and includes gravity compensationand velocity damping as described in Section IV.

To evaluate the performance of the control scheme over awireless network, we use the “TrueTime Toolbox 1.5” [9].We consider that the controller is inteconnected to the roboticarm via a 802.llb wireless network. The network subsystemcontains three nodes implemented as TrueTime kernel blocks.The first node (node 1) implements the network interfaceof the digital controller and the second node (node 2) theinterface for the P3 arm. A third network node (node 3) is usedas a disturbance node in order to incur time-varying packetdelay as described in [18]. For our simulations, we use the802.11b wireless block in TrueTime with the throughput setto 11 Mbps, which is the theoretical limit of 802.11b, and theremaining parameters set to the default values. The controllerwireless node and robot node are 10 meters apart while thedisturbance node is 5 meters away from both. The packet sizecontains a 120 bit header plus preamble and a payload of 384bits required to fit 6 double precision floating point values.

Fig. 4. Simulation model

Thecontroller subsystem contains two components: a blockfrom the robotics toolbox (jtraj) which provides the referencevelocity trajectory for the robotic arm to follow, and a discretestate-space model of the controller. The controller receivesas input the reference trajectory along with the actual robotvelocity and computes the torque control command for therobot. To demonstrate the advantages of the passive controlarchitecture, we performed two sets of experiments, one usinga non-passive control architecture and one using the passivecontrol scheme presented in Section IV. In all the experiments,the reference provided to the controller commands the robot togo to a position of [1 0.8 0.6 0.4 0.2 0] from the start positionof all joints equal to zero over a 4 sec time interval.

B. Non-passive Control Architecture

In the first set of experiments, we consider a non-passivecontrol scheme. To implement the digital controller, we dis-cretize the continuous-time PD controller described by Eqs.(3)-(4) using a standard zero-order hold operation [19]. Thedigital controller communicates with the robot directly withoutusing wave variables. The gravity compensation and velocitydamping are implemented locally as in the passive controlscheme.

The non-passive system is highly unstable for large con-troller gains. To obtain reasonable results, we set the gains tokp = kd = 3. Figures 5 and 6 show the joint angles of therobotic arm for two different sampling periods. The system isunstable forTs = 0.1 but becomes stable whenTs = 0.05sec.

To simulate the system in the case of time-varying delays,we incorporate the disturbance node. The sampling periodis kept constant (0.05 sec), but the amount of disturbancepackets on the network varies. The disturbance node samplesa uniform distributed random variable in(0, 1) periodicallyevery 0.01 sec. If the value is greater than a disturbance

0 1 2 3 4 5 6

0

0.5

1

1.5

2

2.5

3

Time (seconds)

Th

eta

(rad

ian

s)

Joint 1Joint 2Joint 3Joint 4Joint 5Joint 6

Fig. 5. Non-passive system -Ts = 0.1 sec.

0 1 2 3 4 5 6−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (seconds)T

het

a (r

adia

ns)



parameter, a packet is sent out over the network. Figure 7shows the network schedule when the disturbance parameteris 0.5. A value of 0 means the node is idle, a value of 0.25means the node is waiting to send, and a value of 0.5 meansthe node is sending data. These values are superimposed tothe node id and are plotted in Figure 7. Figure 8 is a graph ofthe network delay between the controller node and the robotnode caused by the disturbance traffic. When the disturbanceis increased, packet delay is introduced because the controllernode and robot node have to wait for the disturbance node tostop sending as illustrated in the network schedule. Figure 9shows that the time-varying delays have significant effect onthe stability and performance of the robotic arm in the caseof the non-passive control scheme.

C. Passive Control Architecture

The second set of experiments involves the proposed passivecontrol architecture. In this case the control gains are set tokp = 600 and kd = 2.8. Figures 10, 11, and 12 show theresults for sampling periods 0.2, 0.1, and 0.05 sec respectively.When the sampling period is increased, the robot slightlyovershoots its destination but it finally settles to the desiredlocation.

The passive control design not only allows larger controllergains and slower sampling but also ensures that the systemis insensitive to time-varying delays. Figure 13 shows thenetwork schedule and figure 14 the network delay when the

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

Time (seconds)

Wir

eles

s N

od

e S

tate

Fig. 7. Network schedule for disturbance = 0.5.

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04

0.05Node 1 to 2 Network Delay

Time (seconds)

Del

ay (

seco

nd

s)

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04


Time (seconds)

Del

ay (

seco

nd

s)

Fig. 8. Network delay for disturbance = 0.5.

0 1 2 3 4 5 6−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (seconds)

Th

eta

(rad

ian

s)



0 1 2 3 4 5 6−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (seconds)

Th

eta

(rad

ian

s)


Fig. 10. Passive system -Ts = 0.2 sec.

0 1 2 3 4 5 6−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (seconds)

Th

eta

(rad

ian

s)



0 1 2 3 4 5 6−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (seconds)T

het

a (r

adia

ns)



disturbance parameter is 1 and the sampling period of thecontroller isTs = 0.05. Figure 15 shows that the time-varyingdelays have little effect on the stability and performance of therobot as ensured by the theoretical analysis. The simulationsare similar for the larger sampling periods as well. Thisrobustness to time-varying delays stems from the passivityconstraints imposed on all the components of the networkedcontrol architecture.

VI. D ISCUSSION ANDFUTURE WORK

The overall system dynamics of CPSs emerges from the in-teraction among physical dynamics, computational dynamics,

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

Time (seconds)

Wir

eles

s N

od

e S

tate

Fig. 13. Network schedule for disturbance = 1.

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04


Time (seconds)

Del

ay (

seco

nd

s)

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04


Time (seconds)

Del

ay (

seco

nd

s)

Fig. 14. Network delay for disturbance = 1.

0 1 2 3 4 5 6−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (seconds)

Th

eta

(rad

ian

s)



and communication networks. This heterogeneity causes majorchallenges for compositional design of large-scale systemsincluding fundamental problems caused by network uncer-tainties, such as time-varying delay, jitter, data rate limita-tions, packet loss and others. To address these implementa-tion uncertainties, we propose a passive control architecture.The inherent safety of passive systems offers advantages inbuilding CPSs that are insensitive to network uncertainties,thus improving orthogonality across the controller design andimplementation design layers and empowering model-drivendevelopment. We have presented an architecture for a sim-plified system consisting of a robotic manipulator controlledby a digital controller over a wireless network and we haveevaluated the system based on preliminary simulations resultsbased on a detailed model that contains components for therobotic arm, the wireless network, and the digital controllerthat show that the system operation is insensitive to time-varying delays.

Our future work in this area aims at three major directions:

• We are investigating theoretical methods that provide aneffective way to interconnect multiple passive systemsand controllers together and preserve stability in thepresence of time-varying delays and data dropouts as wellas address important concerns such as distortion and lowsampling rates;

• We are developing an integrated end-to-end tool chain

for the model-based design of networked control systemsthat will support modeling, simulation, and model-basedcode generation of networked control applications; and

• We plan to demonstrate and experimentally evaluatethe proposed design technology using a networked tele-operated robotic platform consisting of networked au-tonomous vehicles equipped with robotic arms and hapticpaddles connected via a wireless network.

ACKNOWLEDGEMENTS

This work is partially supported by National Science Foun-dation CAREER grant CNS-0347440 and grant DoD/DTRA-CRANE N00164-07-C-8510.

REFERENCES

[1] C. Desoer and M. Vidyasagar,Feedback Systems: Input-Output Proper-ties. Academic Press, Inc., 1975.

[2] P. Li and R. Horowitz, “Control of smart machines, part 1: Problemformulation and non-adaptive control,”IEEE/ASME Trans. Mechatron.,vol. 2, no. 4, pp. 237–247, 1997.

[3] D. Lee and P. Li, “Passive coordination control of nonlinear mechanicalteleoperator,”IEEE Trans. Rob. Autom., vol. 21, no. 5, pp. 935–951,2005.

[4] A. Fettweis, “Wave digital filters: theory and practice,”Proceedings ofthe IEEE, vol. 74, no. 2, pp. 270 – 327, 1986.

[5] G. Niemeyer and J.-J. E. Slotine, “Towards force-reflecting teleoperationover the internet,” inIEEE International Conference on Robotics andAutomation, 1998, pp. 1909 – 1915.

[6] P. Berestesky, N. Chopra, and M. W. Spong, “Discrete time passivityin bilateral teleoperation over the internet,” inIEEE InternationalConference on Robotics and Automation, 2004, pp. 4557 – 4564.

[7] N. Kottenstette and P. J. Antsaklis, “Stable digital control networksfor continuous passive plants subject to delays and data dropouts,” inProceedings of the 46th IEEE Conference on Decision and Control,2007, pp. 4433 – 4440.

[8] A. L. Sangiovanni-Vincentelli, “Quo vadis sld: Reasoning about trendsand challenges of system-level design,”Proceedings of the IEEE, vol. 95,no. 3, pp. 467 – 506, 2007.

[9] A. C. M. Ohlin, D. Henriksson, “TrueTime 1.5 - reference manual,”Department of Automatic Control, Lund University, Tech. Rep.

[10] H. Kopetz, “The time-triggered architecture,”Proceedings of the IEEE,vol. 91, no. 1, pp. 92 – 126, 2003.

[11] C. Secchi, S. Stramigioli, and C. Fantuzzi, “Digital passive geometrictelemanipulation,” inIEEE International Conference on Robotics andAutomation, 2003, pp. 3290 – 3295.

[12] N. Kottenstette, “Control of passive plants with memoryless nonlinear-itites over wireless networks,” Ph.D. dissertation, University of NotreDame, 2007.

[13] R. Ortega and M. Spong, “Adaptive motion control of rigid robots: Atutorial,” in 27th IEEE Conference on Decision and Control, 1988, pp.1575 – 84.

[14] W. S. Levine,Control System Applications. CRC Press, 2000.[15] W. M. Haddad and V. S. Chellaboina,Nonlinear Dynamical Systems

and Control: A Lyapunov-Based Approach. Princeton University Press,2008.

[16] J. J. Craig,Introduction to Robotics: Mechanics and Control. Addison-Wesley, 1989.

[17] P. I. Corke, “Robotic toolbox for matlab, release 7.1,” CSIRO, Tech.Rep.

[18] A. Cervin, D. Hendriksson, B. Lincoln, and K. Arzen, “Jitterbug andtruetime analysis tools for real-time control systems,” in2nd Workshopon Real-Time Tools, 2002.

[19] P. Antsaklis and A. Michel,Linear Systems. McGraw-Hill, 1997.

passivity-based control design for cyber-physical systemspantsakl/publications/381-cps-ca08.pdf ·...

Documents