温度

A Novel Cascade Temperature Control System for aHigh-Speed Heat-Airflow Wind Tunnel Yunhua Li,Senior Member,IEEE,Chaozhi Cai,Kok-Meng Lee,Fellow,IEEE,and Fengjian TengAbstract—In order to meet stringent temperature-control re-quirements in a high-speed airflow wind tunnel(HA WT)for ther-mal simulation under complicated work conditions such as thermal strength experiment of aero engine blade and dynamic calibration of high temperature thermal coupler,this paper proposes a novel cascade fuzzy-PID(C-Fuzzy-PID)compound control method for regulating the fuel-oilflow rate in the inner loop and temperature in the outer loop.The mathematical models that characterize the dynamics of the heat airflow temperature in the combustor and the fuel-oilflow rate for combustion are derived,upon which the im-proved PID control laws for the inner and outer loops are described. The former employs a fuzzy-PID controller with a predictor for controllingflow rate in the inner loop,which effectively overcomes influences according to its characteristics of large inertia and trans-port lag in fuel-oil supply system on the temperature responses.The latter combines disturbance compensation and a fuzzy-PID feed-back law to suppress influences due to factors such as change in work conditions,disturbances,and time-varying parameter varia-tions.The C-Fuzzy-PID method has been numerically investigated by comparing simulation results against two traditional PID-based methods,as well as experimentally validated confirming that the proposed control algorithm has strong robustness and excellent adaptability for temperature control of an HA WT.Index Terms—Cascade control,fuzzy PID,high-speed heat air-flow simulation,predictive control,temperature control,thermal wind tunnel.I.I NTRODUCTIONT HE high-speed airflow wind tunnel(HAWT)for thermal simulation is an important aerospace experimental system. An HAWT that produces a uniform and controllable tempera-turefield has been widely used in heat-strength experiments of high temperature aeroengine blades and dynamic calibration of thermal sensors[1].Among the challenges in developing an HAWT is the modeling of the dynamic system and the design of a controller capable of regulating temperature and fuel oil with quick response for a wide range of the temperature.Manuscript received August17,2012;revised January14,2013and April 7,2013;accepted April30,2013.Date of publication May30,2013;date of current version July8,2013.Recommended by Guest Editor H.Gao.This work was supported in part by the China Scholarship Council and was partly carried out while thefirst author was with The George W.Woodruff School of Mechan-ical Engineering,Georgia Institute of Technology,as a Senior Research Fellow. Y.-H.Li,C.Cai,and F.Teng are with the School of Automation Science and Electric Engineering,Beihang University,Beijing100191,China(e-mail: yhli@;caichaozhi1983@;tengfengjian@).K.-M.Lee is with The George W.Woodruff School of Mechanical Engineer-ing,Georgia Institute of Technology,Atlanta,GA30332-0405USA(e-mail: kokmeng.lee@).Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TMECH.2013.2262077In an HAWT,the mixing of the aviation kerosene with air and their subsequent burning in the combustor results in a complex physicalfield;the thermal-flied environment being simulated is a high-speed airflow of high temperature.The high-temperature airflowfield is governed by theflow rate ratio between the kerosene and the air supplied to the combustor.In practice,the outlet airflow temperature of the HAWT for a specified air-flow speed is adjustable when conducting experiments.Thus, the output temperature of the combustor,which depends pri-marily on keroseneflow rate,can be theoretically controlled by precisely manipulating theflow rate of the fuel oil feeding to the combustor.However,variations in the input airflow along with inadequate fuel-oil combustion and other unknown fac-tors result in significant temperaturefluctuations which must be considered in the controller design for regulating fuel-oilflow rate and temperature.Prior research generally focused on the design and control of thermal wind tunnels particularly on three aspects:modeling and regulating theflow rate,developing a strategy for controllingflow rate,and designing a temperature control system for the combustion process.Three methods are commonly used forflow rate regula-tion;namely,valve control,variable-displacement pump con-trol,and variable-frequency(VF)drive motor-pump control. Among them,the VF drive control method has been widely studied and applied for its saving-energy superiority.A survey on VF speed-regulating technology in hydraulicfield can be found in Peng et al.[2].Zhao et al.[3]applied VF hydraulic pump to a central air conditioning system achieving good energy saving by means of optimization.Energy-saving problems with a VF hydraulic control have also been studied especially on the uses of VF speed-regulating technology for energy saving in hy-draulic elevators[4]–[6].In an attempt to address speed-tracking problems in the VF hydraulic system,an algorithm combining disturbance compensation with a proportional-plus-derivative feedback controller was proposed in[7]for eliminating errors and nonlinear effects.Due to some advantages including sim-plicity in structure,low cost,large adjustable range,energy saving,and good control performance,VF speed regulation has become an importantflow rate control method[8],[9].In the community offlow rate control research,Li et al.[10] presented a method for controlling theflow rate of a heat wind tunnel.Li et al.[11]proposed a pulse-and-gliding con-trol strategy to minimize fuel consumption of an automatic car. Apart from traditional methods(such as PID control of high-temperature hydraulic systemflow rate in[12]),a few other advanced techniques have been recently proposed.For exam-ple,Zhang and Li[13]employed a fuzzy-PID law(without taking into account inertia and pure time delay)for controlling1083-4435/$31.00©2013IEEEflow rate.A Smith predictor and PID control law was designed in[14]for plants with a pure time delay due toflow meter,which however needs an accurate mathematical model of the plant. Temperature control has many applications.For examples,a cascade neural-PID temperature control system for controlling the temperature of superheated steam boiler steam was devel-oped in[15];an optimal robust minimum-order observer was designed in[16]for high-precision steam temperature control;a back-propagation neural-network PID controller with an im-mune genetic algorithm was trained in[17]for overcoming in-fluences of steam temperature caused by time-delay,inertia and nonlinearities.Dong et al.[18]analyzed the effects of saturated output-feedback dissipative control on the steam temperature in a steam generator.Temperature control is also widely studied for engine thermal management.Widd et al.[19]proposed a predictive method based on physical models for temperature control of a homogeneous charge compression ignition com-bustor.Choukroun et al.[20]improved a traditional PI-based temperature control method for a single-loop engine thermal management system.Cipollone et al.[21]used a proportional valve as an alternative to traditional thermostat and studied its effects with a few control methods.Setlur et al.[22]established a model for heat management of an engine with nonlinear char-acteristics and realized nonlinear control of the temperature.To address temperature control of the engine,Salah et al.[23]stud-ied a back-stepping control law for the conventional radiator and a multiple-loop model for the engine thermal management sys-tem[24].Xu et al.[25]discussed using a genetic algorithm to design PID parameters for temperature control of a multiphase flow wind tunnel.Camporeale et al.[26]developed a nonlinear model for a gas turbine and designed a decoupled temperature controller.Kim and Kim[27]studied fuzzy-PI control for a gas turbine;a similar method was also used by Meza et al.[28] for a robot manipulator.Ho et al.[29]combined fuzzy control with an adaptive sliding mode control for speed control of a hydraulic motor.Li et al.[30]developed a fuzzy-control law for an equivalent nanosatellite radiator earth simulator.This paper addresses problems commonly encountered in designing a controller for simultaneously regulating both the fuel-oilflow rate and the temperature of an HAWT,where the plant is characterized by a wide temperature range from200to 1700◦C and high heating rate(with temperature raised from 200to1700◦C within30s).Additionally,the control law must be able to deal with large thermal andflow inertia,transport time lag,and robust in the presence of significant disturbances. To effectively solve these problems,there is a need to develop a mathematical model that takes into accounts the combined dynamics of fuel-oilflow and combustion,and a method for high-performance temperature control with strong robustness. The rest of this paper offers the following.1)The mathematical models that characterize the dynamicsof fuel-oilflow and the gas temperature in the combustor for a typical HAWT are derived,which provide the essen-tial basis for design analysis and numerical simulation.2)Along with the new approach for regulating theflow rateof the fuel-oil supply system,a new C-Fuzzy-PID control law(consisting an innerflow rate and an outertemperature Fig.1.Temperature control system of HAWT.control loops)is presented.The inner loop incorporates a predictive control law to overcome the influences of trans-port lag in the fuel-oil supply system while the outer loop is designed to suppress disturbances due to the wind speed pared with the traditional PID cascade con-trol,the C-Fuzzy-PID effectively rejects to the influence of the time lag and working conditions change.3)The C-Fuzzy-PID method has been numerically studiedby comparing simulation results against two traditional methods,PID-PID and PID-Smith,as well as experimen-tally evaluated demonstrating its robustness and excellent adaptability.II.S YSTEM D ESCRIPTION AND M ATHEMATICAL M ODEL Fig.1shows the temperature control system of a typical HAWT,which consists of three subsystems;fuel-oil supply, combustion,and computer control.The fuel-oil supply subsys-tem adjusts theflow rate of the aviation kerosene feeding to the combustor.The combustion subsystem mixes the fogged kerosene with preheated air,burns them,andfinally forms the heat airflow at a specified temperature.The control subsys-tem consists of a programmable logic controller(PLC)as a field controller,an industrial personal computer(IPC)as a re-mote controller,flow rate sensors,thermocouples,VF driver, and signal conditioning circuits.Specific control algorithms are implemented on the IPC considering that the operation ability of the PLC is limited.The PLC receives control commands from the IPC,adjusts the fuel-oilflow rate through controlling the VF motor and the proportional valve,andfinally achieves the closed-loop temperature control of the overall system.The block diagram of the overall system is shown in Fig.2. The inner loop controls the fuel-oilflow rate(measured by the gearflow meter),where the controlled plant consists of a VFFig.2.Control scheme of the overall system.TABLE IN OTATIONS AND V ALUES OF P ARAMETERS OF A PLANTdriver,motor pump,and transmitting line,while the outer loopcontrols the temperature (measured by using thermocouples)of the gas in the combustor.The output of the outer loop controller is the input of the inner control system,thus forming a cascade control system.For clarity and completeness,the notations and the values of the plant parameters are given Table I.HAWT is a complicated process concerning fuel regulation and transmission,and its subsequent combustion in air.Al-though classical laws governing the physics of the individ-ual processes may be widely known,the relatively completemodeling of the HAWT as an integrated thermal-mechatronic system for effective temperature control is still underexploited due to the complexity of the overall plant.A.Modeling of Flow Rate in the Inner LoopBecause the fuel-oil supply system is mainly operated in the VF speed-regulating mode,the mathematical model and flow rate control strategy have been setup in this mode.The operation mode of VFD in this system is variable voltage variable frequency,the input control signal is the output volt-age of the controller,and the output of the VFD is the voltage across to the stator coil of the VF induction motor.The rela-tionship between input and output of the VFD is linear;when not considering low frequency torque compensation,it can be expressed byU A =K f K inv u(1)where U A is the output voltage of VFD,K f is the gain between the frequency f and the input control voltage u of the VFD,and K inv is the voltage–frequency ratio.Generally,the VF induction motor is operated with a constant voltage–frequency ratio,where the electromagnetic time con-stant is much smaller than that of rotor dynamics.Denoting ωs as the synchronized angular frequency of the motor,R s as the phase resistance of the stator side,and L s and L re as the stator induc-tance and equivalent rotor inductance,respectively,and consid-ering that the slip ratio (s L =1−n p /n s )of the asynchronous motor is usually less than 5%under the common work con-ditions,therefore R re s L R s ,R re s L ωs (L s +L re ).Under the aforementioned conditions,the torque Γe (in N ·m )acting on the motor shaft,which can be derived from the electromag-netic moment equation of the VF motor,can be approximately written asΓe ≈3m p U 2A ωs R re s L =3m p U 2A2πR re fs L (2)where ωs =πn s /30;n s =60f/m p ;n p and n s are the actualrotational speed and the synchronous rotational speed of the motor in revolution per minute,respectively.Substituting the expressions of s L and n s into (2)yieldsΓe =3m p 2πR re K f U A −m 2p 40πR reK 2f n p =K 1U A −K 2n p .(3)Mechanically,the moment balance equation on the motor shaft is as follows:Γe =J Tπ30dn p dt +B T πn p30+D p p p 2πηpm(4)where p p is the output pressure of the pump in pascal.According to the continuity equation describing the flow rate of the volumetric chamber in the output port of the pump,and neglecting the influence of the compressibility of the fuel oil while considering that the pressure of the fuel oil is less than 1.2MPa and the volume elastic modulus of fuel oil is larger than 1.0GPa,the output flow rate of the oil supplying the pump canFig.3.Lumped-parameter model of a long pipeline.be approximately written as follows:q fuel =160D p n p −C p p p (5)where q fuel is actual flow rate of oil supplying pump,m 3/s .Since the energy loss of the long fuel-oil pipeline from the pump to the combustor nozzle of the HAWT is the pressure loss,it must be modeled to account for its influences.Moreover,there are also dynamic influences of the fluid inductance and capacitance of the pipeline,as well as the throttling resistance of the nozzle in the ing the lumped parameter method [13]to model the long pipeline system (in terms of its fluid resistance R ,capacitance C ,and inductance L as shown in Fig.3),the equation characterizing the transfer functions of the pipeline can be written asp 2(s )q 2(s ) =1+LCs 2−(R +Ls +RLCs 2)−Cs 1+RCs p 1(s )q 1(s )(6)where C =πd 2l4βe ;L =4ρf u e l l πd 2;R =R 1+R 2,R 1=128μl πd 4,R 1and R 2are the liquid resistance of the pipeline liquid or the nozzle,respectively.The resistance R N of the nozzle in Fig.3is obtainable from linearizing its pressure/flow rate relationship:q 2=C d A2p 2/ρfuel (7)where C d is the discharge coefficient,and A is the effectiveflow area of the hole.Linearizing (7)about the operating spout pressure ¯p 2(which is generally a measurement value at starting frequency)leads to (8)for a constant area nozzle holeΔq 2=K c Δp 2where K c =C d ¯A√2ρfuel ¯p 2.(8)There are six nozzles in the combustor,and the liquid resis-tance at the spout can be obtained according to the principle of resistance parallel as follows:R 2=16K c =16∂p 2∂q 2=√2ρoil ¯p 26C d A .(9)Neglecting the compressibility of fuel oil and consideringC =0in (6),and we can obtainq 1=q 2=q fuel =P pLs +R 1+R 2.(10)Combining (1)to (10)yields a transfer function between the oil fuel flow rate q fuel and the VFD input voltage u as follows:G 0(s )=q fuel (s )u (s )=b o ω2n s 2+2ζωn s +ω2n(11)Fig.4.Energy transfer diagram in a combustor.where ω2n =1J T C p L [(1+C p R )(B T +30πK 2)+d 2P R 40π2ηm ;2ζωn =1J T (B T +d 2P40π2ηm C p )+1+C p R C p L +30πK 2;and b o ω2n =K 1d p2πJ T C p L .To account for the pure time delay τexisted in gear flowmeter,the output flow rate q s of the flow meter is expressed byq s (s )=e −τs q fuel (s ).(11a)B.Modeling of Temperature in the Outer LoopFig.4illustrates the energy transfer in the combustor,where the gas temperature in the combustor is the controlled variable in the outer loop.Formulated using a lumped parameter approach,the gas tem-perature T (assumed uniform in the combustor)is governed by the law of energy conservation given in (12)along with the individual contributions of the heat powers Q (W)defined in (12a)–(12e)in terms of temperatures (◦C):V ρp c pdTdt=Q fuel +Q air −in −(Q air −ex +Q water +Q wall )(12)Q fuel =Hρfuel q fuel(12a)Q air −in =ρair −in q air −in c p 1T in (12b)Q air −ex =ρe q ex c pe T (12c)Q wall =hA c (T f −T ∞)(12d)andQ water =ρw q w c w (T w −T w 0)(12e)where Q oil is the heat power released by combustion of thefuel oil into the combustor;Q air −in and Q air −ex are the heat power brought into and out the combustor by the airflow and the exhaust gas,respectively;and Q wall and Q water are the power due to conduction heat transfer through the combustor wall and that due to heat circulation of the cooling water,respectively.T in is the temperature of the airflow entering the combustor;T f is the temperature of the inner combustor wall;T ∞is the ambient temperature;T w 0and T w are the temperature of the cooling water flowing into and out of the combustor,respectively;and ρe ,q ex ,and c pe are the density (kg /m 3),flow rate (m 3/s),and specific heat capacity (J/(kg ◦C))of the exhaust gas flowing out of the combustor.Substituting (12a)–(12e)into (12)yields V ρp c p dT dt =Hρfuel q fuel +ρair −in q air −in c p 1T in −ρex q ex c p 2T −KA 1(T f −T ∞)−ρw q w c w (T w −T w 0).(13)According to the law of quality conservation(with negligible quality change of gas in the combustor),we haveρex q ex=ρfuel q fuel+ρair−in q air−in.(14) The massflow rate of the input airρair−in q air−in is much larger than the massflow rate of the oil fuelρfuel q fuel in the actual burn-ing process.So,we can considerρex q ex≈ρair−in q air−in,andalso can consider c p1≈c p2≈c p.Assume that the temperature of combustor wall T f=αT and cooling water temperatures in export T w=βT,then(13)can be simplified asVρp c p dTdt+ρair−in q air−in c p T+KA1αT+ρw q w c wβT= Hρfuel q fuel+ρair−in q air−in c p T in+KA1T∞+ρw q w c w T w0.(15) Because the inlet air,the inlet temperature,cooling environ-mental temperature of combustor wall,and temperature of the cooling water are basically stable and can be seen as a constant in the experimental process for the certain work conditions, so the rear three items of(15)can be considered as a constant item.Taking Laplace transformation of(15)leads to the transfer function between T(s)and q oil(s)as follows:G1(s)=T(s)q oil(s)=K pT p s+a(16)where a=ρair−in q air−in c p+KA1α+ρw q w c wβ,K p= Hρfuel,and T p=Vρp c p.III.D ESIGN OF THE C ONTROLLERSThe following two sections describe the design of the inner and outer loop controllers for regulating the fuel-oilflow rate and gas temperature,respectively.A.Design of a Flow Rate Controller in the Inner LoopAs modeled in(11)and(11a)and observed during the debug-ging of the system,the open-loop transfer function of the inner loop control system has a transport lag due to theflow rate sen-sor.In addition,the nonlinearity and uncertainty of the motor-pump and pipeline also makes it difficult to achieve the desired control effects by simply using a simplefixed-gain PID con-troller.Fuzzy control law and fuzzy rule-based control law have been widely applied in control systems because it relaxes the accuracy requirements on the mathematical model of the plant. According to the system characteristics of a typical HAWT,an improved fuzzy-PID controller with a predictive algorithm is designed for theflow rate control in the inner loop as shown in Fig.5.This new compound fuzzy PID control law is effective in overcoming the effects of time delay on the system.The fuzzy-PID predictive controller achieves its control per-formance through the combined effects of predictive control on the time-delay elimination and rule-based tuning PID gains on the improved system robustness and steady-state accuracy.As illustrated in Fig.5,the fuzzy-PID predictive controller is im-plemented in three steps.In thefirst step,a Levinson predictor is designed to determine the output value of the future d steps from the historical data of the process output.Next,the error is computed by comparing the predicted value that is fedback Fig.5.Fuzzy PID predictive controller.against the reference signal.Based on the computed error and the PID gain parameters that are updated by the fuzzy controller in real time,thefinal step determines the output of the PID controller.1)Levinson Predictor:The Levinson predictor method pre-dicts the values of the output variables in the future d steps built upon the moving output average y m of n process historical data. For the predictor output at k th time instant in(17),the predicted value of d step ahead is given by(18):y m(k)=−ni=1a i y(k−i)(17)y m(k+d|k)=−a1y m(k+d−1|k)−···−a p−1y m(k+1|k)−a p y(k)−···−a n y(k+d−n).(18) In(17)and(18),the optimal forecasting parameters,{a i} where i=1,...,n,are predetermined using a recursive least-squares method.2)Design of a Fuzzy-PID Controller:The three PID gains are generally determined through empirical methods such as process reaction curve criteria;once determined,they cannot be changed throughout the controlling process.Unfortunately, these simplefixed-gain PID controllers will not guarantee the adaptability of the actual fuel supply system to the change of its working conditions.In order to have a good control effect on theflow rate,this paper enhances the PID controller with fuzzy control which adjusts in real time the PID gains according to the state of the linguistic variables(E and EC)of the error e and the error change ec;namely,the inputs of the fuzzy PID controller are e and ec,and the output is the three incremental gains(ΔK p,ΔK i,andΔK d)of the PID control law.When implementing the fuzzy PID control law,the controller inputs(e and ec)are quantified to the specified range(−5,5), upon which the membership degree for each linguistic variable is then determined.Here,the linguistic variable sets for the inputs and output of the fuzzy controller are chosen as{NB, NM,NS,ZO,PS,PM,PB}and expressed by{−4,−3,−2,−1, 0,1,2,3,4}.Unlike the traditional fuzzy control a Mamdanni’s rule table for fuzzy reasoning,the fuzzy rules for the fuzzy-PID controller are based on analytic formula with an adjusting factor to improve the adaptability of the fuzzy rule as follows:U=[λE+(1−λ)EC](19)Fig.6.Structure of an outer loop temperature controller.whereλis the correction factor,its adjustment law isλ=λ1|E|+λ2λ,λ1,λ2∈[0,1](20) whereλ1andλ2are selected according to the impact weights of the error on the control system performance.Using(19),the output of the fuzzy PID controller is calcu-lated,upon which the incremental PID gains are determined with a defuzzier.Thefire-membership functionμF(u)for the fuzzy control output of each fuzzy rule can be determined asμF(u)=5i=15jμ(i,j)(u)μi(e)μj(ec)(21)whereμi(e),μj(ec),andμ(i,j)(u)denote the triangular membership functions.Calculation of the defuzzier formula (based on the method in[30]and[31])can be written asu=5k=−5μF(u k)u k5k=−5μF(u k)(22)where u denotes the output of the fuzzy controller after de-fuzzier,and it has three gains of fuzzy PID.B.Design of Temperature Controller in the Outer LoopAs seen in(15),changes of the airflow,cooling waterflow rate,and environment temperature would appear as disturbances in the combustor gas-temperature control system.Because the flow rate of the cooling water can be adjusted by a water supply with a regulating valve and a water pump with afixed rotational speed in practice,the change inflow rate of the cooling water is not large.On the other hand,temperature experiments with different wind speeds at the same temperature are often needed. For example,the characteristics of a specimen at a specified temperature(say1000◦C)must be tested for a range of wind speeds(say0.6,0.8,and1Ma).Any switch in wind speed could have a significant influence on the model and control performance of the plant;thus,the control system not only must reject any disturbances quickly to achieve accurate temperature regulation,but also overcome any impact caused by a switch of work condition;for example,a change in the airflow from0.6 to0.8Ma.In order to accomplish this control objective,a compound controller has been designed as shown in Fig.6,which com-bines compensation for wind speed change with a fuzzy PID for temperature control.The fuzzy-PID temperature controller has the same structure for the fuzzy-PIDflow rate controller in the inner loop.The compensation coefficient to reflect theTABLE IIP ARAMETERS V ALUES OF AN I NNER CONTROLLERTABLE IIIP ARAMETERS V ALUES OF AN O UTER CONTROLLERchange of the wind speed is determined by combustion theory and empirical experience.IV.S IMULATIONSIn order to evaluate the effectiveness of the improved C-Fuzzy-PID controller described in Section III,simulations were performed in Simulink according to the mathematical models of HAWT in Section II.The relevant parameters of the plant,pre-dictor,and controllers used in the simulation are,respectively, given in Tables I–III.A.Setting of Simulation Cases and Comparative Control Laws Comparative numerical studies were conducted using three methods.1)C-Fuzzy-PID control law presented in the paper;2)PID-PID cascade control law,where both the inner fuel-oilflow rate loop and outer temperature loop are PID controlled;and3)PID-Smith cascade control law,where the inner loop usesPID with a Smith predictor and outer loop adopts PID. In order to realistically simulate the wind tunnel tempera-ture,the target temperature is initially set to400◦C,and then increased to800◦C after50s.The C-fuzzy-PID control law is evaluated numerically in the following simulation cases.1)Case A:Temperature responses to step command:To com-pare the step response of three kinds of control laws,the time lag is set to3s[see Fig.7(a)].2)Case B:Effect of pure time delay:To investigate the effectof pure time delay in the inner loopflowrate transfer func-tion of the system,the time delay is increased from3to 5s,while other simulation conditions remain unchanged [see Fig.7(b)].3)Case C:Effect of working condition(wind speed):Work-ing condition change in wind speed can be characterized by a change in Mach number.An increase in Mach number will result in a decrease in temperature(and vice versa) while the air-fuel ratio is larger than the optimal air-fuel ratio.To examine the effectiveness of handling impact on the system due to a change in wind speed from0.4to。