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Proceedings of the 1003 I E E EInternational Conference 00 Robotics &AutomationTaipei, Taiwan, September 14-19,2003

Modeling and Control of a Monopropellant-BasedPneumatic Actuation System'Eric J. Barth, M ichael A. Gogola, and Michael GoldfarbDepartment of Mechanical Engineering, Vanderbilt University, Nashville, TN 37235

AbstractThis work d escribes the modeling and control of a proposedactuation system that is capable of pressurizing a chambervolume via the cataly tic decomposition of a liquid monopro-pellant con trolled by a bina ry onloff propella nt valve. Tw odesign configurationsof the actuation system are presentedand common portions of both are energetically modeled.Th e parameters of the resulting dynamic model are mean-ingful physical properties of either the propellant or thesystem. A model-based switching controller is then appliedto the task of pressure tracking. Model validation and con-troller perform ance are shown experimentally.1 IntroductionOne of the most significant challenges in the developm entof an autonomous human-scale robot is the issue of powersupply. Perhaps the most likely power supplyiactuatorcandidate system for such a robot wo uld be a lithium vari-ant battery and DC motor combination. This type ofsystem, however, w ould. have to carry an inordinateamount of battery weight in orde r to perform a significantamount of work for a significant period of time. A state-of-the-art example of a human-scale robot that utilizeselectrochemical batteries combined with DC mo-torharmonic drive actuators is the Honda Motor Corpora-tion humanoid robot model P3, which weighs 130 kg,carries 11.5 kg of batteries and provides approximately15-25 minutes of operation, depending on its workload.Operation times of this magnitude or smaller are not un-common and represent a major technological roadblockfor designing mobile robots that can operate power-autonomously for extended periods of time.One alternative to using batteries and DC motors is todirectly convert stored chemical potential energy intomechanical work through the pneumatic domain. In par-ticular, liquid chemical fuels have high thermodynamicenergy densities, and this thermal energy can be extractedas mechanical energy through the expansion of gaseousproducts. Control of power across a required bandwidthcan be achieved through the use of pneumatic servovalves that control the flow of the hot gaseous productsinto a pneum atic piston. Thoug h several possibilities ex-ist for the generation of gases, monopropellant liquid fu-els are well suited for this type of system. Monopropel-lants are a class of fuels that rapidly decompose (orchemically react) in the presence of a catalytic material.Unlike combustion or hypergolic reactions, no mixing orignition is required. This results in a simple, low weightenergy converter system. A monopropellant-based system

0-7803-7736-2/03/$17.0002003 IEEE

provides a good solution to the design trade-offs betweenfuel energy density and system weight for the scale ofinterest. As such, the authors have been developingmonopropellant-powered actuators for use in self-powered human-scale robots, and in particular, have beenpursuing two configurations for converting the storedchemical energy of a monopropellant into controlled me-chanical work. The first configuration controls the flowof the liquid monopropellant through a catalyst pack andinto a centralized high-pressure hot gas reservoir, thencontrols the piston output by controlling the flow of hotgas from the reservoir into and out of a pneumatic cylin-der. This approach, called a centralized configuration, isdepicted schematically in Fig. 1. The authors have re-ported preliminary experimental findings characterizingthe energetic capability of this system in [ I , 21. The sec-ond configuration controls the piston output by preciselycontrolling the direct injection of liquid monopropellantthrough the catalyst pack and directly into each chamberof the cylinder. This approach, called direct injection, isdepicted schem atically in Fig. 2. Both the centralized anddirect injection configurations entail the control of twofluids. For the centralized configu ration, a liquid mono-propellant controller maintains a desired reservoir pres-sure via the control of a binary fuel valve, and a hot gasflow controller utilizes a proportional spool valve to con-trol the piston output via control of the gas f low into andou t of the cylinder. For the direct injection configuration,a liquid monopropellant controller controls the pressuriza-tion of each cylinder chamber via a binary fuel valve, anda hot gas flow controller controls the depressurization ofeach cylinder chamber via the hot gas exhaust flow.This paper treats the development of the controllers forthe monopropellant control loops. Specifically, both con-figurations require pressure control via a binary controlvalve with the chemical reaction dynamics in the controlloop. Therefore, both approaches require the develop-ment of a dynamic model of the chamber pressurizationthrough the monopropellant reaction dynamics, and addi-tionally require a methodology that can control a pressureacross those dynamics with a binary (i.e., non-proportional) control input. Specifically, this paper de-scribes such a model and controller, and shows experi-mental data of pressure tracking that demonstrates boththe validity of the model and the effectiven ess of the con-trol method.

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Fig. I. chematic of the centralized monopropellan1 actuation systemwith a dashed box drawn around those components energetically mod-eled.

Pliquid

liquid propellant valvePrnpellant line

Fig. 2. Schematic o f the direct injection monopropellant actustion syn-tem wi!h a dashed box drawn around thase components energeticallymodeled.2 System Mod elingA s mentioned, the system under consideration for model-ing is that of the catalyst pack and chamber volume. Thechamber volume represents either the pressure reservoirin the case of the centralized system, or the actuatorchamber in the case of the direct injection system. Thegeneral approach taken here is to model these two com-ponents using an energy balance method based on fustprinciples. Given that these two compo nents taken to-gether are at a location where the pneumatic supply en-ergy is generated and stored, it is imperative that such anenergy-based modeling approach is taken. The resultingmodel may be subsequently utilized for system designissues regarding control and efficiency. The task of mod-eling these two components is accomplished by drawing acontrol volume around each, performing an energy (orpower) balance regarding the flux and storage rate of en-ergy in each, and then matching energy flux rate condi-tions at the boundary between the two components.2.1 Modeling the Catalys t PackFigure3 shows a schematic with a control volume drawnaround the catalyst pack. With regard to this control vol-

ume (CV), a power balance relating the rate of energystorage to the energy flux rate across the boundary may hewritten as,(1)

where is the rate of internal energy stored inside theCV , k c , s the enthalpy rate across the CV, Qc0, is theheat flux rate into the CV, and k , s the rate of workdone to the external environment. Assuming the volumeof the catalyst pack is constant results in eo,0 . Inseeking a lumped parameter model of the combined cata-lyst pack / chamber system, and assuming that the flowrestriction between the catalyst pack and the chamber issmall, it is also assumed that ii, s small compared tothat of the chamber. Therefore, this term is neglected inthe power balance equation of the catalyst pack, andhence ci,, 0 . This agrees with intuition in that thepneumatic energy is stored almost exclusively in the lar-ger volume of the chamber. The net enthalpy rate acrossthe boundary may he written as the flow power into theCV minus the flow power out of the CV:The term 43 represents the hydraulic flow power asso-ciated with the supply pressure of the monopropellant,P , , and the volumetric flow rate of liquid monopropel-lant; Q . The term mCc,cpTADTepresents the pneumatic(i.e. compressible gas) flow power, where I , s themass flow rate leaving the catalyst pack, c p is the specificheat at constant pressure, and TAOT s the adiabatic de-composition temperature of the monop ropellant. Therelative magnitude of the hydraulic flow power is as-sumed to be negligible compared to the flow power of thegas leaving the catalyst pack, and therefore P,p = 0 . Thisassumption is contingent upon the mass specific energystored in the monopropellant and becomes increasinglyaccurate as a higher energy density monopropellant isconsidered. For 70% H2 0 2 n steady-state operation witha 4.9 MPa (700 psig) supply pressure, the ratio ofmcdcJADr to P,g is ahout 220, thereby legitimizing theassumption for one particular monopropellant at one par-ticular supply pressure.The catalytic decomposition of a monopropellant resultsin the liberation of heat. To model the heat released, afirst order dynamic is assumed to he associated with themonopropellant finding a catalyst site,where Q, is the heat released by the monopropellant, r,is the time constant, and k is the heat of decomposition

ii,,=fL,Qcn, -w,,

ri,,= 0 3 &CpT*Dr (2)

.,e, +Q, =!Iilgfl (3 )

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minus the heat of vaporization of product liquids. Notethat the steady-state heat release rate for a constant massflow rate agrees with a basic thermod ynamic property kthat can be measured (or looked up) for a given monopro-pellant. Recogn izing this hea t released as heat enteringthe CV, and further assuming that the cataly st pack is wellenough insulted such that the b eat loss in the form of con-duction or convection is small in comparison, it can beStatedThis assumption is also based on a lumped parameter phi-losophy in that the heat loss from the catalyst pack isdwarfed by the heat loss kom the much larger surfacearea of the chamber.The mass flow rate of monopropellant into the catalystpack can be m odeled by the standard hydraulic flow equa-tion.

e, =Q, (4)

where pi is the density of the monopropellant, c is thevalve discharge coefficient, A is the valve orifice area,an d P is the downstream pressure (i.e. the pressure insidethe chamber). Strictly spea king , the flow restriction rep-resented by the discharge coe fficien t is a function of boththe valve geometry aswell as the restriction presented bythe material in the catalyst pack. It is typically acceptablefor discbarge coefficients to be determined experimen-tally. e\

I------+---------- 't7cvCatalyst PackFig. 3. A schematic of the wntrol volume (CV) used to model the cats-1ystpack

high pressure gaseou s products from the reservoir for ac-tuation, or the exhaust and volumetric cha nges in the ac-tuator chamber, will require subsequent modification tothe model). A power balance approach may again hetaken resulting in:

Given a static chamber volume, k, = 0. xpress U , byintegrating dU=mc,dT from a reference internal en-ergy, U,af, nd reference temperature, T4 :

u c h = H c h + &h - c h ( 6 )

"j d U = jrnc,dT (7)"< T