presenting four basic lessons derived from combining control theory and experimental implementation

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By Andrew Alleyne, Sean Brennan, Bryan Rasmussen, Rong Zhang, and Yisheng Zhang

This article describes different lessons that canbe learned by including experimental aspectsin control system research. Several keylessons are identified, and then each lesson isdeveloped within the context of a particularexperimental system. A variety of physical

experimental systems are used to illustrate that the keylessons need not all be found in the same system, butshould one be working with a variety of systems, it is likelythat one or more of these issues would arise. The actual

experimental systems incorporate the fields of vehicledynamics, air conditioning and refrigeration, and fluidpower. However, it is felt that the main points of this arti-cle can easily be applied to many other fields.

BackgroundFrom a historical perspective, experimental aspects of con-trol systems significantly predate their mathematicalanalysis [l]. Between the 1950s and the 1980s, however, agreat deal of emphasis was placed within academia on the

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Presenting four basic lessons derived from combining control theory and

experimental implementation.

October 2003200272-1708/03/$17.00©2003IEEE

IEEE Control Systems Magazine

October 2003 21IEEE Control Systems Magazine

analytical aspects of feedback control. These included thevaluable concepts we now take for granted such as con-trollability, observability, stability, optimality, realizations,and robustness [2]. It is only within the past two decadesthat the research pendulum has swung, and we have seenan increased interest in experimental and applicationaspects of controls. Examples of this are the creation ofjournals such as IEEE Transactions on Control System Tech-nology, IFAC Control Engineering Practice, and IEEE/ASMETransactions on Mechatronics. Additionally, conferencesaimed at implementation and experimental aspects of con-trol have recently developed, including the IEEE Confer-ence on Control Applications, the IEEE/ASME Conferenceon Advanced Intelligent Mechatronics, and the IFAC Con-ference on Mechatronic Systems.

The focus of this article is on the role of physical exper-iments in control system research, particularly withinacademia, and how experiments and theoretical analysiscan be performed in a synergistic fashion. Prior to detail-ing particular experiments and insights gained, we differ-entiate between two types of approaches to experiments.We believe there is a difference between what we define ascontrol validation experiments and control technology exper-iments. Although this may seem to be semantic, we clarifythe distinction in the discussion. The reader should knowthat we are not advocating one versus the other, butrather we are merely making an observation. As will beseen in later sections, we believe both are valuable.

Control validation experiments are physical systemsconstructed with the purpose of testing or demonstrating aparticular control technique or set of techniques. Care isoften taken in the design of the hardware and software sothat the key relevant attributes, and only those key attrib-utes, are present in the final experimental system. ln thissense, the experiment that supports the research of con-trol analysis and synthesis is effectively secondary.Aspects of the experiment violating the control re-searcher’s assumptions are removed by design iterations.An example of this is to size the actuation system so thatsaturation is not an issue, unless the control methodologybeing investigated explicitly provides saturation compensa-tion. A specific physical example of a control validationexperiment is wheeled mobile robots [3], [4] that utilizedead reckoning and encoder readings of the wheels todetermine position. Several of these systems design thewheels to minimize slip, and they operate at low speed soas to maintain a kinematic representation of the system.Therefore, the physical systems retain a level of fidelity tothe analytical models that several path-planning and con-trol algorithms utilize. Other specific physical examples areinverted pendulum systems [5], [6], where the uncertaintyis small and the model form is well known.

The motivation for control validation experimentsincludes the demonstration and validation of a theoretical

concept. It is often valuable to show that the theoreticalconstruct can have application to physical systems. How-ever, one problem with complete justification is that thephysical systems used for demonstration are usuallydesigned to work well with the theory. Therefore, the theo-ry may not transfer as well to plants dissimilar to thedemonstration system. Control validation experiments canalso be valuable for determining the practical limitationsof a particular algorithm and can point the researcher innew directions to further refine their techniques. Finally,there is usually some level of excitement associated withdemonstrating a physical device to others in the field.

Control technology experiments occur when a physicalsystem, designed and built a priori, needs to be controlledand is presented to the researcher warts and all. Such acase is representative of industrial practice, and a greatdeal of effort must go into understanding the physical sys-tem and determining the best control approach. Often thefundamental physical process cannot be changed, andundesirable plant characteristics have to be accountedfor. A successful example of this is the control of internalcombustion engines. Delays, combustion kinetics, andtime-varying system dynamics led researchers to considerkey advances such as controlling in the crank angledomain [7], [8] to achieve specific control metrics.

The primary motivation for conducting control technol-ogy experiments is to determine the benefits that embed-ded intelligence has on engineered products and services.Reducing vehicle emissions by orders of magnitude, as aresult of tight air-fuel ratio control, has had a tremendoussocietal impact [9]. The same is true for the servo controlsthat allow data storage densities to achieve their currenthigh levels [10]. Additionally, in the process of developingcontrollers for engineered systems, it is possible to devel-op fundamental understanding of key dynamical phenome-na that can be useful well beyond the field of control.Finally, by examining the control of actual engineered sys-tems, it is possible to identify key factors that limit controleffectiveness such as sensor locations and actuationauthority. These factors can then be used in systemredesign, as was the case when disk drives changed fromlinear to rotary voice coil motors in the late 1960s [10].

The LessonsWhether the reader is interested in control validationexperiments or control technology experiments, we pre-sent four basic lessons learned from combining controltheory and experimental implementation. There are clear-ly more points that could be made, and although the fol-lowing are open to a healthy debate, we choose to focushere on a particular subset due to space constraints.These key lessons include a subset of the most relevantones developed during the 1999 NSF Workshop on theIntegration of Modeling and Control for Automotive Sys-

tems [11]. Although the lessons learned originated fromautomotive applications, we believe they hold true formany controlled physical systems.

� Lesson 1: Where possible, modeling should be donewithin a control-oriented framework. A rule of thumbdeveloped during the aforementioned workshop wasthat, within this framework, models must be basedon straightforward physics and capture approxi-mately 80% of the relevant dynamic behavior.

� Lesson 2: To avoid a control design quagmire, it is

important to know what the appropriate goal is andwhen the system performance is sufficient to meetspecifications developed prior to the control design.

� Lesson 3: The effects of actuation authority and mea-surement sensitivity choices on achievable closed-loop performance should be well understood.

� Lesson 4: The act of serendipity associated with dis-covery is healthy for research.

At first glance, these four points may sound obviousand vacuous to the reader, but there is an importance andsubtlety to each. The control-oriented framework of Les-son 1 runs counter to many fields of modeling where effortis given toward increasing a model’s accuracy. At somepoint, however, the model should be good enough for amodel-based controller to have a high probability of suc-cess in achieving specified performance goals. The poten-tially controversial quantitative evaluation of modelingsufficiency is the result of a careful thought process aboutknowing when a model is good enough. This subtle point isthe reason why vehicle cruise control works well butengine cold start emissions control does not [11]. In addi-tion to knowing that a model has captured most of thedynamics, it is important to know where the rest of theuncertainty is coming from. Certainly, there are robustcontrol tools that can provide some level of guaranteeswith respect to an uncertainty representation for giventypes of systems. For the practicing control engineer, how-ever, it is sometimes more important to know what causesthat uncertainty, not just that it exists. The knowledge isgreatly aided by the physics-based representation men-tioned above. Should it be difficult to design a controller tomeet performance specifications, the control engineer canwork with structural, design, and power engineers to seewhere the dynamic uncertainty can be reduced via overall

systems-level redesign at a reasonable cost.In Lesson 2, the notion of a well-posed control objective

with a priori specifications may seem obvious until exam-ined closer. Often, difficult control problems may be theresult of an unfortunate problem formulation. Moreover, itis important to understand what constitutes the minimumacceptable performance for a given task. Using a semicon-ductor wafer stage example, the cost associated withreducing the maximum absolute value of the scanning errorfrom 50 to 5 nm can be millions of dollars. Each increase or

relaxation of performance specifica-tions has quantitative effects on thecost and achievable performance ofany overall control system aboveand beyond topics such as asymp-totic versus exponential stability.Lesson 2 becomes particularlyimportant when dealing with con-trol technology experiments. Relat-ed to specifications is the notion in

Lesson 3 of choices associated with actuation and sensing.Cost or physical constraints may limit the number of sen-sors and actuators, their placement within a system, andthe finite actuator power or sensor resolution. As a generalexample, the actuators and sensors should be roughly colo-cated for better performance and easier design [12]. Lesson4 indicates that when doing experiments, one shouldalways keep an open mind to identifying fruitful avenues ofdiscovery. Many of these avenues are revealed only afterconfronting what were initially perceived roadblocks forthe original investigations.

We will examine these four lessons learned within thecontext of several experimental systems developed by ourresearch group at University of Illinois, Urbana-Champaign(UIUC) [13]. These experiments include both control vali-dation experiments and control technology experiments.

Importance of Control-Oriented ModelingThe experimental system examined here is a vapor com-pression cycle, more commonly known as an air-condition-ing or refrigeration cycle. We focus on a transcritical CO2

cycle and its related components, although most commer-cial systems use a subcritical cycle. These systems are com-plex devices due to their nonlinear thermo-fluid behavior,and significant savings in energy can be achieved if they areproperly controlled. Moreover, with the use of alternativerefrigerants such as CO2, it is possible to reduce a key con-tributor to ozone layer depletion. The CO2 cycle is a controltechnology experimental system because the basic thermodynamic cycles of the air-conditioning system have beenwell defined for many decades [14], [15] and the controldesigner may be constrained by the already establishedprocess characteristics.

October 200322 IEEE Control Systems Magazine

Control validation experiments are physicalsystems constructed with the purpose oftesting or demonstrating a particularcontrol technique or set of techniques.

A typical transcritical air-conditioning system consistsof the five components shown in Figure 1. For a more com-plete description of the working principles of this system,see [16]. Unique aspects of this system versus subcriticalones include the internal heat exchanger that increasesthe inherently coupled nature of the dynamics and thesupercritical state of the refrigerant in the gas cooler. Thefour controllable inputs to the system are compressorspeed, expansion valve opening, and the mass flow rates ofair across the evaporator and gas cooler. The outputs ofinterest are the superheat temperature (a measure of effi-ciency), evaporator outlet air temperature (a measure ofcomfort), and the operating pressures.

The dynamics of vapor compression cycle systemsare dominated by the thermal behavior of the heatexchangers that have the slowest dynamics. Often theseheat exchangers are modeled by partial differential equa-tions (PDEs). Subsequent to developing the appropriatePDEs, the overall system is discretized into finite ele-ments and a computationally intensive numerical calcu-lation is performed to obtain accurate steady-statebehavior [17]. The PDE approach to modeling a multi-phase fluid heat exchanger is ill suited for most of thecontroller design tools currently available, particularlycomputer-aided control system design tools for multiple-input, multiple-output (MIMO) controller design. There-fore, it is beneficial to transform the PDE into a low-orderordinary differential equation (ODE) representation as asimplification and approximation for control-orientedmodeling. This approach requires several assumptionsabout the fluid flow in the heat exchangers to simplifythe coupled, nonlinear, PDEs given by the conservationof mass, momentum, and energy. These assumptions areas follows:

� Assumption 1: The heat exchanger is a long, thin, hor-izontal tube.

� Assumption 2: The refrigerant flowing through the heatexchanger tube can be modeled as a one-dimensionalfluid flow.

� Assumption 3: Axial conduction of the refrigerant isnegligible.

� Assumption 4: Refrigerant pressure along the entireheat exchanger tube can be assumed to be uniform.

Assumption 4 indicates that pressure drop along the heatexchanger tube due to momentum change in refrigerantand viscous friction is negligible; therefore, the conserva-tion of momentum equations are not needed. The PDEs thatgovern fluid flow can be found in most fluid mechanics text-books [18]. By applying these assumptions, it is possible tosimplify these equations to one-dimensional PDEs. Adetailed explanation of these steps can be found in [19].The resulting equations for fluid flowing through the heatexchanger tube are as follows:Conservation of mass:

∂(ρ A)

∂ t+ ∂(m)

∂z= 0, (1)

Conservation of refrigerant energy:

∂(ρ Ah − AP)

∂ t+ ∂(mh)

∂z= piαi(Tw − Tr), (2)

Conservation of tube wall energy:

(Cpρ A)w∂(Tw)

∂ t= piαi(Tr − Tw) + poαo(Ta − Tw), (3)

where ρ = density of refrigerant, P = pressure of refrigerant,h = enthalpy of refrigerant, pi = inner perimeter (interiorsurface area per unit length), po = outer perimeter (exteriorsurface area per unit length), Tr = temperature of refriger-ant, Tw = tube wall temperature, Ta = ambient air tempera-ture, αi = heat transfer coefficient between tube wall andinternal fluid, αo = heat transfer coefficient between tubewall and external fluid, A = cross-sectional area of the insideof tube, m = refrigerant mass flow, and

(Cpρ A

)w = thermal

capacitance of tube wall per unit length. The governing PDEsare used to derive lumped parameter ODEs to model thedynamics of heat exchangers. The heat exchanger, whichmay be an evaporator, gas cooler, or internal heat exchang-er, is divided into sections with a moving boundary betweenfluid phases. Furthermore, (l)–(3) are integrated along thelength of each tube section. Figure 2 shows a typical condi-tion for the evaporator with the fluid entering as two phaseand exiting as a superheated vapor. The evaporator is mod-eled with two regions: a two-phase region and a superheatedregion. The boundary between these regions is a movinginterface, which is difficult to measure physically.


Gas Cooler

Compressor

InternalHeat

Exchanger

ExpansionValve

Evaporator(Receiver)

Figure 1. A diagram of the transcritical vapor compressioncycle. The major physical components are shown. Thedynamic responses of the compressor and expansion deviceare much faster than those for the heat exchangers.

Details on the development of models for the evapora-tor and other components in the system can be found in[19]–[21]. This procedure is similar to the work of [22] thatexamined the dynamics of subcritical cycles. The resultingsystem models consist of 11 ODEs and several calibratedalgebraic relationships. These include nonlinear dynamicmodels as well as linearized versions. The validity of themodeling approach on this system can be seen in Figure 3.The data for Figure 3 were obtained from a prototype auto-motive transcritical air-conditioning system [23] operatingat highway conditions. This test system is part of an NSF-sponsored Air Conditioning and Refrigeration Center atUIUC; a full description of the experimental system can befound in [24]. As shown in Figure 3, the model is accuratein predicting the dynamics of the system given the correctparameters. Although the 11th-order model does a goodjob of describing the system dynamics, a time-domain sys-tem ID test reveals a significant amount of over-modelingin the process. Figure 4 shows the results of a pseudoran-dom binary sequence of pulse inputs given to all inputs ofthe system along with a fifth-order input–output modelderived with system identification tools. The inputs variedare the expansion valve opening, compressor speed, andboth heat exchanger fans. It is clear that the most control-

oriented model is a lower order one that still providesphysical insight.

In [19], a singular perturbation analysis showed that thedynamics of the energy stored in the refrigerant can beneglected while maintaining a majority of the dynamicalinformation. Singular perturbations were used rather thanbalanced truncation so as to retain physics-based systemknowledge in terms of known states such as temperatureand enthalpy. References [19] and [21] detail a numericalcomparison based on singular values and eigenvalues ofthe original and reduced-order models of the system. Afteran extensive iterative modeling, simulation, and validationprocess, it was determined that the dynamic system orderwas essentially equal to the number of individual heatexchanger wall sections shown in Figure 2 because thesedominated the dynamics of energy storage and release.

Figure 5 shows a comparison of the 11th-order nonlin-ear model with reduced order models and the actual data.As can be seen in Figure 5, the reduced-order models do agood job of reproducing the system’s dynamics. The maxi-mum absolute value of the time-domain model error in Fig-ure 5 is less than 10%, well within acceptable tolerancesfor feedback control design. It should be noted that otherinput–output model pairs were not as accurate as Figure 5

[19] but all were within 20% error when exam-ining the maximum absolute value of the time-domain model error for many different PRBSsignal amplitudes.

Discussions on Lesson 1In achieving these models, several assump-tions and compromises were made. A primaryfocus was to retain the physics-based repre-sentation rather than a numerical balancedtruncation approach to the reduced models. Ingeneral, the choice of assumptions rests withthe user and the particular process. This

choice involves a careful and con-scious tradeoff between accuracy andsimplicity. A low-order model mayhave little use for a thermal systemsdesign engineer, but it may be appro-priate for a control engineer. Howev-er, referring to the begining of thisarticle and [11], 80% accuracy isoften sufficient in the model withfeedback compensating for the 20%uncertainty. Therefore, a tradeoff toforego some accuracy can be advan-tageous for control.

It is important to note that thiscontrol-oriented modeling examplewould be practically impossible toachieve without the experimental


3,460

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0 50 100 150 200 250 300 350 400Time

DataNonlinear ModelLinear Model

Figure 3. Evaporator pressure for step changes in compressor speed. This close fitbetween the experimental and simulation data demonstrates good model accura-cy. A linearized model provides results similar to the more detailed nonlinearmodel for this operating condition.

Quality = 1

Twall,2(t )Twall,1(t )

mouthout(t )•

minhin•

Qualityin > 0 P(t )

Two Phase Single Phase

L1(t ) L2(t )

LTotal

Figure 2. An evaporator with a two-phase flow at the entrance and super-heated vapor at the exit. A conceptual moving boundary separates the twofluid phases and dictates the heat transfer characteristics along the tube.

apparatus [23], [24] that was continu-ally used to verify the model validity.A detailed physics-based knowledgeof the process under study will help inmaking the simplicity/ accuracy trade-off, and understanding the algebraicor dynamic relationships of the sys-tem is best done in conjunction withexperimental data. Assumptions canbe made and tested in simulation andthen compared with experimentaldata to determine whether they arevalid or not. Detailed nonlinear mapsrelating various fluid properties, valvecharacteristics, and compressor effi-ciencies can be found and refined bestwith an experiment to assist the


Measured Output

Fifth-Order Fit: 79.63%

Measured Output


Measured Output


Measured Output


Measured Output


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vap

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ir T

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ir T

emp

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0 200 400 600 800 1,000 1,200 1,400

0 200 400 600 800 1,000 1,200 1,400

0 200 400 600 800 1,000 1,200 1,400

0 200 400 600 800 1,000 1,200 1,400

Figure 4. System identification results for a pseudorandom binary input sequence. All system inputs (compressor, valve, andtwo fan speeds) are varied to get a good MIMO identification. Model matching indicates that a fifth-order overall systemdynamic model is accurate.

3,460

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Figure 5. Evaporator pressure for step changes in compressor speed. The fifth-order linear model is capable of capturing the major system dynamics well, there-by justifying a reduced-order modeling approach.

process. Although it is relatively easy to determine con-trol-oriented models for simple mechanical linkage sys-tems driven by dc motors (e.g., robots), we contend thatexperimentation is a necessary condition for successfulcontrol-oriented model development in complex systemssuch as a vapor compression cycle.

Importance of a Well-Defined Control ObjectiveThe experimental system studied here is a half-car activesuspension as shown in Figure 6 [25]. This experiment fallsunder the category of a control technology experimentbecause the appropriate hardware has been chosen byindustrial practice. Despite initially failing from an econom-ic justification viewpoint, which is another valuable lessonlearned, active suspensions provide an excellent casestudy in the appropriate choice of control objective.Although there has been a wealth of information published

on the control of quarter-car, half-car, and full-car suspen-sions, few of these works have incorporated the dynamicsof the actuator in their analysis. As a result, most of thesepublished works have been relegated to simulation stud-ies, with a few notable exceptions [26]–[29]. In addition, allof the experimental exceptions were limited in theirclosed-loop bandwidth. As it turns out, the actuation is acrucial component in the overall systems analysis. Due topower requirements, coupled with packaging constraints,electrohydraulics are the primary practical choice for afully active system. However, the dynamics of electrohy-draulic systems pose a challenging problem for standardformulations of active suspensions.

Most standard quarter-car formulations of the activesuspension problem consider a system such as that shownin Figure 7, where the system input is assumed to be aforce. This regulation problem is often posed in an optimalcontrol framework such as a linear quadratic regulator[30]. The states are the suspension deflection (zs − zu),tire deflection (zu − xr ), as well as the sprung andunsprung mass velocities. A review of previous optimalcontrol strategies applied to the active isolation problemcan be found in [31]. The resultant control input is adesired force applied to the system, and this force is afunction of the system states. This control law usuallyinvolves an inner force control loop applied directly to theactuator, possibly with some force measurement to act asa feedback as described in [27]. The problem is that elec-trohydraulic actuators are fundamentally limited in theirability to track forces of any reasonable bandwidth.

As explained in [32], typical electrohydraulic systemsare limited in their ability to do force control when inter-acting with an environment possessing dynamics. For atypical electrohydraulic system, the poles of the plant withwhich it is interacting will manifest themselves as thezeros of the open-loop force transfer function. If thesezeros are lightly damped, the achievable bandwidth of anycontroller will be limited. Given the lightly damped modesfor a typical quarter-car system of Figure 7, the force loopzeros will usually be lightly damped. Therefore, the use ofthis actuation to generate a controllable force for activesuspension isolation can be said to be an ill-posed problembecause the loop that any controller will be trying to closewill have zeros near the jω axis that fundamentally limitthe performance of any feedback algorithm. This difficultyis evidenced by the dearth of literature on successfulexperimental active suspensions using electrohydraulicsystems. Additionally, nearly all results to date [26]–[28],including production prototypes [29], are limited to rela-tively low-frequency road disturbance rejection because ofthe bandwidth limitation.

The primary problem with many of the earlier activesuspension investigations was that the control objectivewas not properly defined. If the control objective is formu-


Figure 6. The UC Berkeley half-car active suspension. A full-scale testbed involving actual vehicle components is used forinvestigating controllable suspensions.

ms

mu

bt

ks

kt zr

zu

zs

u

Figure 7. A quarter-car active suspension schematic. A 2-DOF linear system model assumes damping in the tire andan ideal actuator between the wheel and car body.

lated in terms that are favorable to the actuator dynamics,then the problem becomes much easier. As electrohy-draulic systems controlled with directional valves can beapproximated as an integrator from input to position out-put [33], a natural formulation would involve one of veloci-ty or of position tracking. The key to successful problemreformulation is the choice of an appropriate reference sys-tem that the system of Figure 7 should emulate. One effec-tive reference system is the inertial damping approach, orskyhook damping, popularized by Karnopp in the 1970s[34]. Considering the system shown in Figure 7, if the con-trollable actuator were to emulate an inertial damper, theresultant system would appear as follows: The transferfunction between the unsprung mass acceleration, and thesuspension deflection is

zs − zu

zu= − s + 2ζωn

s(s2 + 2ζωns + ω2n)

≡ Gref (s), (4)

where ωn = √ms/ks and ζ = (b/2

√msk). If the control sys-

tem is able to make the actuator track this desired posi-tion, then the overall system will behave as if it wereactually inertially damped. Figure 8 captures the essentialnature of the reformulated control objective. What wasoften posed in the active suspension literature as a regula-tion problem is reformulated as a tracking problem inwhich an appropriate prefilter defines the actuator dis-placement reference signal for the control loop to track.The tracking problem is much easier to solve because thefundamental limitations associated with the force controlhave been eliminated.

It should be carefully noted that the reformulation illus-trated in Figure 8 is not specific to the linear inertialdamper reference system of Figure 9. Any suitable refer-ence model could be chosen as long as a well-posed rela-tionship exists between unsprung mass acceleration andactuator displacement. Figure 10 shows the comparison ofan ideal inertially damped system with an experimentalsystem utilizing the reformulation shown in (4).

The details of the experimental system, which is a quar-ter-car analog, are given in [35]. For the inner feedback loopof Figure 8, a model reference adaptive controller [36] wasimplemented. Figure 11 shows the normalized ‖·‖2 ratio of

disturbance and sprung mass acceleration as a function offrequency. Clearly, the experimental performance is veryclose to the ideal. Figure 11 demonstrates excellent broad-band vibration isolation across a relatively wide range offrequencies from 0 to 20 Hz. This meets necessary specifica-tions to cover the 0–15 Hz frequency band that usuallyspans the two primary modes of the suspension system inFigure 7: approximately 1 Hz and 10 Hz. This is even moreinteresting when considering that few experimental activesuspension strategies with electrohydraulic actuators havebeen able to perform at any level above approximately 5 Hz.

Discussions on Lesson 2An ill-posed active suspension control problem with elec-trohydraulic actuators can be made well posed by reformu-lating it in a tracking framework. The experimental aspectto the control system goes beyond the idealized system ofFigure 7 and helps understand the discrepancy betweenthe theoretically achievable performance and that obtainedin practice. Without the experimental aspects, it wouldhave been difficult to develop an explanation regardinglightly damped performance-limiting zeros and then refor-mulate the problem to eliminate them. ln essence, the inclu-sion of experimental efforts into the research allowed us todevelop and refine a well-defined control objective.


zu• •

Inner Feedback Loop

Gref (s) = −s + 2ζωn

s(s2 + 2ζωns + ω2n)

(zs−zu)reference(zs−zu)output

+−

Gcontrol(s) Gplant(s)

Figure 8. A block diagram schematic of problem reformulation. The emulation problem has been recast as a referencetracking problem. The prefilter specifies the closed-loop suspension characteristics.

b

ms

mu

ks

kt

zs

zu

zrbt

Figure 9. An inertially damped quarter car. This passive sys-tem is emulated by the closed-loop active suspension system.Proper emulation makes the vehicle body feel as if it weredamped with respect to a fixed reference.

Appropriate Actuation and Sensing AuthorityThis section focuses on actuation of a load emulator foran earthmoving vehicle power-train testbed. An earthmov-ing vehicle power train is a MIMO fluid power system, inwhich the power distribution needs to be coordinated.With multiple loads competing for the limited total flowand available power in a hydraulic transmission, currentmachines rely on human coordination for different tasks.Active power-train control can be one means to achievebetter performance and less dependence on humans inthe loop. As part of the Caterpillar Electromechanical Sys-tems Laboratory, an earthmoving vehicle power-train sim-ulator (EVPS) was constructed at UIUC as a testbed for

advanced multivariable control of off-highway power trains. Details on thepower-train system and the coordina-tion objective can be found in[37]–[39] along with MIMO H2 and H∞control designs.

This system could be classified asa control validation experiment forthe reason that the EVPS was inten-tionally designed as an abstraction ofan earthmoving vehicle’s powertrain. Several physical aspects wereleft out in the actual design. Oneexample is the ac motor that is con-trolled to emulate either a spark igni-tion or compression ignition enginein real time [38], [39]. Other exam-ples are the load subsystems. In lieuof running an actual vehicle in an off-highway environment, controllableloads emulated by using a pressurerelief valve were imparted to thehydraulic motors representing the

steering, drive, and working implement systems of thevehicle. The working implements on a wheel loader exam-ple would be lift and tilt functions. Cost concerns werethe major factor in the design choice for loading. Moredetails on the loading system can be found in [40], butkey ones will be given here.

We consider only one of the three load loops for thepurpose of exposition. It can be schematically representedas shown in Figure 10. The ac motor, which is controlled tobehave as an internal combustion engine, drives a variabledisplacement pump that sends high-pressure fluid througha controllable valve orifice. The flow valve shown in Figure10 can modulate the flow to a hydraulic motor. The motoris mechanically coupled with a gear pump, cyclinghydraulic fluid in a load loop hydraulically independent ofthe main loop. The load-loop pressure acts as a motorresistance and needs to be controlled by a pressure reliefvalve, termed the load valve, to emulate different loaddynamics. The choice of a hydraulic loading system, ratherthan an electrical one, was largely due to cost. Eddy-cur-rent dynos or ac motors necessary to generate loadtorques and absorb 25 kW on each load node are muchmore expensive than the simple gear pump/valve combina-tion. However, less expensive components come with per-formance tradeoffs that should be evaluated up front inthe experiment design process.

The load valve actuator used to generate the hydraulicresistance is a two-stage pressure relief valve whose char-acteristics are relatively insensitive to flow change. Thegoal in this case is to emulate an actual load as if thehydraulic gear motor were part of a real earthmoving vehi-


Figure 10. An electrohydraulic powertrain schematic with a load emulator. Thehydraulic motor/pump combination emulates a physical load coupled to thepower train. The electric motor is controlled to behave as an internal combustionengine, and the variable displacement pump acts as a variable transmission.

Figure 11. Transmissibility ratios. The closed-loop emula-tion strategy allows the experimental system to behave likean ideal inertial damper over a broad range of frequencies.The high-frequency deviation from ideal performance is dueto actuator bandwidth limits.

1

0.8

0.6

0.4

0.2

00 5 10 15 20

Ideal Ratio

Experimental Ratio

Acc

eler

atio

n R

MS

Rat

io

Disturbance Frequency [Hz]

cle. As the load valve can only absorb power, however, itdepends on the output speed of the hydraulic gear motorto generate a desired load. This objective has been cast[41], [42] into a unique control framework that we termresistive control. The performance of the controller is sole-ly dependent on its ability to act as a resistive load, withthe assumption being that the engine supplies enoughpower such that part of it can be dissipated. A generaliza-tion of the resistive framework is shown in Figure 12.

We define the driving subsystem as the source and thedriven subsystem as the load. Figure 12 shows a sourcesystem GS under an actual load GL. Within the context ofthis discussion, the source system represents the wheelmotors and the load system includes the environment(rolling resistance, road grade plus vehicle weight, andbearing friction) that provides resistance to the motion ofthe wheel motors for this earthmover example. The drivingsignal yd (wheel motor speed) and the loading signal yr

(load torque on wheel) define the boundary between thesource and the load. dS is an exogenous signal into thesource, such as the net flow coming from the main pumpinto the motor.

The goal of the controller is to emulate the actual loadGL by shaping the dynamics from dS to yS so the source(i.e., wheel) thinks it is attached to an actual load (i.e.,environment). For a controller to manipulate the closed-loop dynamics from dS to yS , it can use dS as a feedfor-ward signal and yS as a feedback signal, assuming thecontroller has access to both measurements. The follow-ing discusses the controller taking only yS to generate theloading signal, creating a one degree-of-freedom (DOF)feedback design. A two-DOF design using both dS to yS

with both feedback and feedforward elements can also beconsidered as in [41].

If possible, it is more desirable to use only the drivingsignal yd as shown in Figure 13, where the components arespecific to this earthmoving vehicle example. In this case,the interconnection of the source and the emulator repre-sents that of the source and an actual load. Ga representsthe actuator dynamics. The main idea is to emulate theload, that is, to let K ∗ Ga = GL , so that the closed-loopdynamics will match the reference system. When thisapproach works, it is the most straightforward way toemulate a load and is convenient for emulating complexloads, nonlinear loads, or loads with time-varying parame-ters because the controller preserves the original repre-sentation of the actual load.

As detailed in [41], it is necessary for the actuator to besignificantly faster than the desired closed-loop bandwidthof the emulator. Figure 14 shows time- and frequency-domain results for both a direct and a resistive controlapproach for load emulation. In contrast to a resistiveapproach, the direct controller assumes that a torque sig-nal is the controller output, and this torque can be directly

applied to the system regardless of the reference input.Direct control would occur if the pump and valve of theloading loop in Figure 10 were replaced by a direct drive acmotor with associated power electronics and cooling cir-cuits. Both direct and resistive controllers assume thesame controllable actuation bandwidth, and both utilize anH∞ control design procedure [41].

As seen in the frequency responses for direct controlin Figure 14, where an arbitrary input can be appliedindependently of the external reference, the closed-loopsystem performance rolls off as the actuator loses band-width. However, for the resistive control approach asso-ciated with the load emulation, the closed-loop responseapproaches the open-loop plant response at high fre-quencies. This indicates that the closed-loop systembecomes independent of controller design and actuatorbandwidth at high frequencies. This phenomenon canalso be seen in the time-domain responses of the system.For direct control, the closed-loop system response canbe made to track the reference model speed throughouta step change in driving torque. For the resistive control,the speed briefly tracks the open-loop model at the startof the step change in input torque and then settles downto track the reference model. The initial response of theresistive controller indicates that the system behaves


Figure 12. The concept of source and load in resistive con-trol. The load affects the power source that, in turn, affectsthe generation of the load. In a resistive case, the load canaffect only the rate of energy dissipation and cannot indepen-dently add energy. A detailed explanation can be found in[41].

Figure 13. One-DOF feedback load emulation. Direct mea-surement of the source output is used by the controller to setthe prescribed load on the source system. The controller con-tains a model of the load dynamics in addition to other infor-mation.

like the open-loop dynamics for high-frequency signals.The eventual convergence to the reference model indi-cates the resistive approach tracks well for lower fre-quencies. The unique phenomena illustrating theconvergence of the closed-loop behavior to the open-

loop dynamics in Figure 14 is specific to the class ofresistive systems such as the EVPS load emulator in Fig-ure 10, many types of engine test dynamometers [44], andother hardware-in-the-loop testbeds [45].

Discussion on Lesson 3A control engineer should thoroughly understand howthe choice of actuation and sensing methods affects theclosed-loop performance. In the case of resistive sys-tems, an understanding of how the indirect nature of theactuation affects the high-frequency system behaviorwould not have been discovered had it not been for the

EVPS experimental load controller. A specific controlproblem for an experimental apparatus thus resulted in abasic and fundamental insight into a unique aspect ofhow actuation bandwidth limitations affect closed-loopsystem dynamics. Typically, one assumes that actuator

rolloff implies a rolloff in closed-loop behavior. In this case, how-ever, actuator rolloff impliesconvergence to open-loop plantbehavior. By understanding theunderlying phenomenon, it is pos-sible to appropriately specify thevalve bandwidth necessary toachieve a desired emulation task.In doing so, the costs associated

with the load aspect of this control validation experi-ment could be reduced by an order of magnitude overcompeting technologies while still meeting the systemperformance specifications based on the maximum loaddynamics bandwidth.

Serendipitous Discovery and New PathsThis section studies on-road automotive vehicles. Unlikeother investigations into vehicle control that take a con-trol technology experiment viewpoint [46]–[49], we willdetail a control validation experiment viewpoint. For thestudies given in [46]–[49], full-sized vehicles were

instrumented and interfaced. Thisapproach involves a large capitalinvestment in the vehicles, controlelectronics, and testing facilities.Additionally, safety concerns need tobe addressed in the full-sized vehicleexperiments. To circumvent the costand inherent danger in testingaggressive vehicle controllers usingfull-sized vehicles, a scaled vehicletestbed was developed as an evalua-tion tool to bridge the gap betweensimulation studies and full-sizedhardware. This testbed is known asthe Illinois roadway simulator (IRS),shown in Figure 15. Previous scaledvehicle experiments, such as [50],had mainly involved moving thevehicles along a fixed surface, whichnaturally incurs a host of interfacingand sensing issues. The IRS movesthe road while the vehicle is heldfixed with respect to inertial space,which simplifies interfacing andimplementation. The design inspira-tion for the IRS came from compara-tive locomotion studies done by


Control technology experiments occurwhen a physical system, designed and builta priori, needs to be controlled and ispresented to the researcher warts and all.

Figure 14. Performance comparison of direct control and resistive control. Athigh frequencies, the dynamics of the resistive controlled system converge to open-loop plant dynamics. For direct control, the closed-loop dynamics roll off with theactuation bandwidth at high frequencies.

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biologists on different types of animals [51]–[53]. Furtherdetails on the IRS design and construction can be foundin [54] and [55].

The IRS is a control validation experiment becausecareful design eliminated many of the details associatedwith an actual vehicle. There is no internal combustionengine, and accurate inertial sensing is readily available.Additionally, the dynamics of the vehicle are confined to aplane because the pitch, roll, and heave modes have beendesigned out. Similar to motivations stated earlier, the goalof the IRS was to provide a physical system to demonstrateparticular control algorithms. The system was designed tomake it easier to illustrate these concepts.

There are several vehicle control concepts that havebeen developed with the IRS. These include a four-wheel-steer (4WS) or differential wheel torque approach we termdriver-assisted control (DAC) [55]. The goal is to utilize therear-wheel steering or torque differential between left andright wheels to give the driver a specified response fromthe steering input to vehicle yaw rate. As such, the vehiclecan attain any handling characteristic within physical con-straints such as tire-road friction.

Subsequent to developing controllers and implement-ing them on the IRS, it was imperative to justify that theresults obtained were valid on a full-sized vehicle. To justi-fy the validity of the controller design and the corre-sponding results, it was necessary to put the model andcontroller structure into a framework that is independentof physical size. This led to the use of dimensionlessanalysis [56]. The ability to compare scale experiments tofull-sized vehicle experiments relies primarily on the con-cept of dynamic similitude. The Buckingham Pi theorem[57] provides a useful tool to study dynamical systems ina dimensionless framework. It states that the solution to adifferential equation can be made invariant with respectto the dimension space spanned by the parameters in thedifferential equation. This property is exploited throughnondimensionalizing the differential equation by groupingthe parameters into (n − m)-independent dimensionlessparameters called pi-groups, where n is the number ofparameters and m is the dimension of the unit space occu-pied by the parameters. For two systems modeled by thesame differential equations, the systems are dynamicallysimilar if the pi-groups associated with the differentialequation are numerically the same for both systems.

Application of the Buckingham Pi theorem to the classicbicycle model vehicle dynamics yields the pi groupings

�1 = aL, �2 = b

L, �3 = Cαf L

mU2,

�4 = Cαr LmU2

, �5 = Izm2

, (5)

where m = vehicle mass, Iz = vehicle moment of inertia,

V = vehicle longitudinal velocity, a = distance from the center of gravity (C.G.) to front axle, b = distance fromC.G. to rear axle, L = vehicle length, a + b, Cαf = corneringstiffness of front two tires, and Cαr = cornering stiffness ofrear two tires.

Derivation and explanations of the vehicle pi parame-ters are given in more detail in [55] along with the dynamicsimilitude analysis proving similarity between IRS and full-sized vehicles.

There are key advantages to examining the vehicledynamics in the pi-space versus a dimensional state orparameter space. It is well known that the vehicle dynam-ics change significantly with both velocity and corneringstiffness. In [58], it is shown that for a given vehicle, �4 is


Figure 15. The IRS system: a mechatronic analogy to thewind tunnel for scaled aircraft. The vehicle remains fixedwith respect to inertial space while the roadway moves.

Figure 16. Parameter root loci. A nondimensional dimen-sional framework illustrates a duality between two differentparameter variations. Cornering stiffness and longitudinalspeed have the same effect on vehicle dynamics.

usually proportional to �3. Therefore, both velocity andcornering stiffness variations correspond approximately tovariations in a single parameter, namely, �3. This is shownin Figure 16 where the open-loop system eigenvalues areshown with respect to the two different parameters: veloci-ty (represented by “o”) and cornering stiffness (represent-ed by “x”). For the variation of the system roots withrespect to cornering stiffness, the ratio of front to rear cor-nering stiffness was assumed to remain the same.

These plots, similar to a root locus for controllerdesign, demonstrate that the effect of road-friction varia-tions on the underlying vehicle dynamics is dual to theeffect of velocity variations. Therefore, these systemparameter variations can be combined. By examining thesystem in a dimensionless framework, we were able tosee the duality between velocity and road-friction. Theuse of the IRS as a control validation experiment wasvital in directing us to consider these scaling issues thatthen led to a new discovery associated with the basicdynamics of vehicles.

The experimental system also provided a motivation fornew research areas in the control of systems that varyover length scales. Motivated by the IRS results, previouswork by [59] examined the concept of robust control with-in a dimensionless framework. The goal was to provide arobust control algorithm that was independent of thelength scale of the plant. Therefore, if the plant changed indimension, the same control law could be used as long asit was appropriately scaled. Reference [58] details a linearmatrix inequality-based robust control approach whereranges are placed on the pi parameters based on a distrib-ution of vehicles examined from the literature. In [59], afrequency domain H∞ controller is designed for vehiclelane tracking in a dimensionless framework. The multi-plicative uncertainty bound for a data set of over 50 repre-sentative vehicles is found to be much tighter, and henceless conservative, with the system description given in thedimensionless framework. This observation leads to lessconservative robust controllers that are able to stabilizeany vehicle in the data set while achieving the prescribedperformance specifications.

Discussion on Lesson 4The justification of what was originally a vehicle controltestbed led to the investigation of a dimensionless vehicle

dynamics and control framework. This serendipitous dis-covery process arises from experiments and theory work-ing together. The idea of a dimensionless framework hasled to other avenues of research, including the apparentduality between cornering stiffness and vehicle velocity, aphenomenon that was qualitatively understood but notpreviously formalized. This discovery process is one of thekey benefits to working with experiments.

ConclusionsThis article is meant to illustratesome of the key lessons to belearned by combining experimentswith control theory and analysis.To demonstrate the breadth ofapplication, different types of con-trol experiments were used toillustrate each lesson. Neither the

lessons nor their exposition were exhaustive, but they didrepresent a core subset of ideas that were identified byover 70 representatives from industry and academia dur-ing an intensive two-day workshop focused on automotivesystems. It is likely that these core ideas could be appliedin a variety of other fields. It is hoped that this expositionprovides the reader with concrete examples they canapply to their own research investigations. Moreover, wehope this will encourage others to generate their own listof best practices or lessons learned that they can sharewith the research community.

There are only positive aspects to the combination ofexperiments with control theory. Certainly experimentscan be expensive to create and maintain; this includesboth capital investment as well as personnel. It may betempting to insist that cheaper simulations can do the jobof demonstrating controller design concepts. However,that would be missing a large part of the picture. One onlygets out of a simulation what one puts in. By involvingactual hardware, the researcher is engaged in a continuouscycle of discovery.

AcknowledgmentsThe support of Caterpillar Inc., Ford Motor Company, NSF,ONR, the University of Illinois, and all the ACRC membercompanies was instrumental in developing the results pre-sented here. This is greatly appreciated.

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Andrew Alleyne received the B.S. degree in mechanical andaerospace engineering from Princeton University in 1989and the M.S. and Ph.D. degrees in 1992 and 1994, respective-ly, from The University of California at Berkeley. He joinedthe Department of Mechanical and Industrial Engineering atthe University of Illinois, Urbana-Champaign, in 1994 andwas appointed to the Coordinated Science Laboratory. Hecurrently holds the Ralph M. and Catherine V. Fisher Profes-sorship in the College of Engineering. His research focuseson modeling and control of nonlinear mechanical systemsand is a mixture of theory and implementation. He is cur-rently an associate editor of the ASME Journal of DynamicSystems, Measurement and Control, and IEEE Control SystemsMagazine, as well as a co-editor for Vehicle SystemDynamics. He can be contacted at M&IE Department and

Coordinated Science Laboratory, University of Illinois,Urbana-Champaign, 140 MEB, MC-244, 1206 West GreenStreet, Urbana, IL 61801, U.S.A., [email protected].

Sean Brennan received B.S. degrees in mechanical engi-neering and physics from New Mexico State University, LasCruces, in 1997. As a National Science Foundation GraduateFellow, he received the M.S. degree in 1999 and the Ph.D.degree in 2002 in mechanical engineering from University ofIllinois, Urbana-Champaign. He is currently an assistant pro-fessor at Pennsylvania State University in the Mechanicaland Nuclear Engineering Department. His theoretical inter-ests include unifying the concepts of scaling and controltheory in the areas of robust and adaptive control, withapplication interests ranging from vehicle chassis control,to mechatronics, to MEMS.

Bryan Rasmussen received the B.S. degree in mechanicalengineering magna cum laude from Utah State University,Logan, in 2000 and the M.S. degree in mechanical engi-neering from the University of Illinois, Urbana-Champaign,in 2002. He is currently pursuing the Ph.D. degree from theUniversity of Illinois. His current research focus is ondynamic modeling and control of thermo-fluid systems.

Rong Zhang received the B.S. and M.S. degrees in 1996 and1998, respectively, from the Department of AutomotiveEngineering at Tsinghua University, Beijing, China. Hereceived the Ph.D. degree in 2002 in mechanical engineer-ing from the University of Illinois, Urbana-Champaign. Hisdoctoral research was on multivariable robust control ofnonlinear systems with application to hydraulic powertrains. He joined General Motors R&D and Planning in 2002as a senior research engineer. He is currently working oncontrol theory technology for the next generation vehiclepower trains.

Yisheng Zhang received the B.S. degree from Beijing Insti-tute of Technology, Beijing, China, in 1996 and the M.S.degree from Tsinghua University in 1999, both in vehicleengineering. He received the Ph.D. degree in mechanicalengineering from the University of Illinois, Urbana-Cham-paign, in 2003. He joined Eaton Corp. in 2003 and is cur-rently working on hybrid electric and other advancedvehicle powertrains.


presenting four basic lessons derived from combining control theory and experimental implementation

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