A Novel Cascade Temperature Control System for a ... - IEEE Xplore

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IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 4, AUGUST 2013

A Novel Cascade Temperature Control System for a High-Speed Heat-Airflow Wind Tunnel Yunhua Li, Senior Member, IEEE, Chaozhi Cai, Kok-Meng Lee, Fellow, IEEE, and Fengjian Teng

Abstract—In order to meet stringent temperature-control requirements in a high-speed airflow wind tunnel (HAWT) for thermal 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-oil flow 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-oil flow rate for combustion are derived, upon which the improved PID control laws for the inner and outer loops are described. The former employs a fuzzy-PID controller with a predictor for controlling flow rate in the inner loop, which effectively overcomes influences according to its characteristics of large inertia and transport lag in fuel-oil supply system on the temperature responses. The latter combines disturbance compensation and a fuzzy-PID feedback law to suppress influences due to factors such as change in work conditions, disturbances, and time-varying parameter variations. 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 HAWT. Index Terms—Cascade control, fuzzy PID, high-speed heat airflow simulation, predictive control, temperature control, thermal wind tunnel.

I. INTRODUCTION HE high-speed airflow wind tunnel (HAWT) for thermal simulation is an important aerospace experimental system. An HAWT that produces a uniform and controllable temperature field 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.

T

Manuscript received August 17, 2012; revised January 14, 2013 and April 7, 2013; accepted April 30, 2013. Date of publication May 30, 2013; date of current version July 8, 2013. Recommended by Guest Editor H. Gao. This work was supported in part by the China Scholarship Council and was partly carried out while the first author was with The George W. Woodruff School of Mechanical 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, Beijing 100191, China (e-mail: [email protected]; [email protected]; [email protected]). K.-M. Lee is with The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMECH.2013.2262077

In an HAWT, the mixing of the aviation kerosene with air and their subsequent burning in the combustor results in a complex physical field; the thermal-flied environment being simulated is a high-speed airflow of high temperature. The high-temperature airflow field is governed by the flow rate ratio between the kerosene and the air supplied to the combustor. In practice, the outlet airflow temperature of the HAWT for a specified airflow speed is adjustable when conducting experiments. Thus, the output temperature of the combustor, which depends primarily on kerosene flow rate, can be theoretically controlled by precisely manipulating the flow rate of the fuel oil feeding to the combustor. However, variations in the input airflow along with inadequate fuel-oil combustion and other unknown factors result in significant temperature fluctuations which must be considered in the controller design for regulating fuel-oil flow rate and temperature. Prior research generally focused on the design and control of thermal wind tunnels particularly on three aspects: modeling and regulating the flow rate, developing a strategy for controlling flow rate, and designing a temperature control system for the combustion process. Three methods are commonly used for flow rate regulation; namely, valve control, variable-displacement pump control, 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 hydraulic field 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 hydraulic 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 simplicity in structure, low cost, large adjustable range, energy saving, and good control performance, VF speed regulation has become an important flow rate control method [8], [9]. In the community of flow rate control research, Li et al. [10] presented a method for controlling the flow rate of a heat wind tunnel. Li et al. [11] proposed a pulse-and-gliding control strategy to minimize fuel consumption of an automatic car. Apart from traditional methods (such as PID control of hightemperature hydraulic system flow rate in [12]), a few other advanced techniques have been recently proposed. For example, Zhang and Li [13] employed a fuzzy-PID law (without taking into account inertia and pure time delay) for controlling

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LI et al.: NOVEL CASCADE TEMPERATURE CONTROL SYSTEM FOR A HIGH-SPEED HEAT-AIRFLOW WIND TUNNEL

flow rate. A Smith predictor and PID control law was designed in [14] for plants with a pure time delay due to flow 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 developed 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 immune genetic algorithm was trained in [17] for overcoming influences 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 combustor. 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 characteristics and realized nonlinear control of the temperature. To address temperature control of the engine, Salah et al. [23] studied a back-stepping control law for the conventional radiator and a multiple-loop model for the engine thermal management system [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-oil flow rate and the temperature of an HAWT, where the plant is characterized by a wide temperature range from 200 to 1700 ◦ C and high heating rate (with temperature raised from 200 to 1700 ◦ C within 30 s). Additionally, the control law must be able to deal with large thermal and flow 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-oil flow 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 dynamics of fuel-oil flow and the gas temperature in the combustor for a typical HAWT are derived, which provide the essential basis for design analysis and numerical simulation. 2) Along with the new approach for regulating the flow rate of the fuel-oil supply system, a new C-Fuzzy-PID control law (consisting an inner flow rate and an outer temperature

Fig. 1.

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Temperature control system of HAWT.

control loops) is presented. The inner loop incorporates a predictive control law to overcome the influences of transport lag in the fuel-oil supply system while the outer loop is designed to suppress disturbances due to the wind speed change. Compared with the traditional PID cascade control, 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 studied by comparing simulation results against two traditional methods, PID-PID and PID-Smith, as well as experimentally evaluated demonstrating its robustness and excellent adaptability. II. SYSTEM DESCRIPTION AND MATHEMATICAL MODEL Fig. 1 shows the temperature control system of a typical HAWT, which consists of three subsystems; fuel-oil supply, combustion, and computer control. The fuel-oil supply subsystem adjusts the flow rate of the aviation kerosene feeding to the combustor. The combustion subsystem mixes the fogged kerosene with preheated air, burns them, and finally forms the heat air flow at a specified temperature. The control subsystem consists of a programmable logic controller (PLC) as a field controller, an industrial personal computer (IPC) as a remote 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-oil flow rate through controlling the VF motor and the proportional valve, and finally 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-oil flow rate (measured by the gear flow meter), where the controlled plant consists of a VF

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modeling 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 Loop

Fig. 2.

Control scheme of the overall system. TABLE I NOTATIONS AND VALUES OF PARAMETERS OF A PLANT

Because 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 voltage of the controller, and the output of the VFD is the voltage across to the stator coil of the VF induction motor. The relationship between input and output of the VFD is linear; when not considering low frequency torque compensation, it can be expressed by UA =Kf Kinv u

(1)

where UA is the output voltage of VFD, Kf is the gain between the frequency f and the input control voltage u of the VFD, and Kinv is the voltage–frequency ratio. Generally, the VF induction motor is operated with a constant voltage–frequency ratio, where the electromagnetic time constant is much smaller than that of rotor dynamics. Denoting ωs as the synchronized angular frequency of the motor, Rs as the phase resistance of the stator side, and Ls and Lre as the stator inductance and equivalent rotor inductance, respectively, and considering that the slip ratio (sL = 1 − np /ns ) of the asynchronous motor is usually less than 5% under the common work conditions, therefore Rre  sL Rs , Rre  sL ωs (Ls + Lre ). Under the aforementioned conditions, the torque Γe (in N · m) acting on the motor shaft, which can be derived from the electromagnetic moment equation of the VF motor, can be approximately written as Γe ≈

3mp UA2 3mp UA2 sL sL = ωs Rre 2πRre f

(2)

where ωs = πns /30; ns = 60f /mp ; np and ns are the actual rotational speed and the synchronous rotational speed of the motor in revolution per minute, respectively. Substituting the expressions of sL and ns into (2) yields Γe =

driver, motor pump, and transmitting line, while the outer loop controls 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. Although classical laws governing the physics of the individual processes may be widely known, the relatively complete

m2p 3mp Kf UA − K 2 np =K1 UA − K2 np . 2πRre 40πRre f

(3)

Mechanically, the moment balance equation on the motor shaft is as follows: Γe =JT

Dp pp π dnp πnp + BT + 30 dt 30 2πηpm

(4)

where pp 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 1.2 MPa and the volume elastic modulus of fuel oil is larger than 1.0 GPa, the output flow rate of the oil supplying the pump can

LI et al.: NOVEL CASCADE TEMPERATURE CONTROL SYSTEM FOR A HIGH-SPEED HEAT-AIRFLOW WIND TUNNEL

Fig. 3.

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Lumped-parameter model of a long pipeline. Fig. 4.

Energy transfer diagram in a combustor.

be approximately written as follows: (5) 3

where qfuel is actual flow rate of oil supplying pump, m /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 combustor. Using 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 as      p1 (s) 1 + LCs2 −(R + Ls + RLCs2 ) p2 (s) = q2 (s) −Cs 1 + RCs q1 (s) (6) 2 where C = π4βd e l ; L = 4ρπfdu 2e l l ; R = R1 + R2 , R1 = 128μl , R 4 1 πd and R2 are the liquid resistance of the pipeline liquid or the nozzle, respectively. The resistance RN of the nozzle in Fig. 3 is obtainable from linearizing its pressure/flow rate relationship:  (7) q2 = Cd A 2p2 /ρfuel where Cd is the discharge coefficient, and A is the effective flow 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 hole Δq2 = Kc Δp2

Cd A¯ where Kc = √ . 2ρfuel p¯2

(8)

There are six nozzles in the combustor, and the liquid resistance at the spout can be obtained according to the principle of resistance parallel as follows: √ 2ρoil p¯2 1 1 ∂p2 . (9) = = R2 = 6Kc 6 ∂q2 6Cd A Neglecting the compressibility of fuel oil and considering C = 0 in (6), and we can obtain q1 = q2 = qfuel =

Pp . Ls + R1 + R2

(10)

Combining (1) to (10) yields a transfer function between the oil fuel flow rate qfuel and the VFD input voltage u as follows: bo ωn2 qfuel (s) = 2 G0 (s) = u(s) s + 2ζωn s + ωn2

d 2P R 1 30 J T C p L [(1 + Cp R)(BT + π K2 ) + 40π 2 η m ; d 2P 1+C p R 1 30 2 J T (BT + 40π 2 η m C p ) + C p L + π K2 ; and bo ωn =

ωn2 =

where

1 qfuel = Dp np − Cp pp 60

2ζωn =

K 1 dp 2π J T C p L .

To account for the pure time delay τ existed in gear flowmeter, the output flow rate qs of the flow meter is expressed by qs (s) = e−τ s qfuel (s). B. Modeling of Temperature in the Outer Loop Fig. 4 illustrates 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 temperature 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 cp

dT = Qfuel + Qair−in − (Qair−ex + Qwater + Qwall ) dt (12)

Qfuel = Hρfuel qfuel

(12a)

Qair−in = ρair−in qair−in cp1 Tin

(12b)

Qair−ex = ρe qex cp e T

(12c)

Qwall = hAc (Tf − T∞ )

(12d)

and Qwater = ρw qw cw (Tw − Tw 0 )

(12e)

where Qoil is the heat power released by combustion of the fuel oil into the combustor; Qair−in and Qair−ex are the heat power brought into and out the combustor by the airflow and the exhaust gas, respectively; and Qwall and Qwater are the power due to conduction heat transfer through the combustor wall and that due to heat circulation of the cooling water, respectively. Tin is the temperature of the airflow entering the combustor; Tf is the temperature of the inner combustor wall; T∞ is the ambient temperature; Tw 0 and Tw are the temperature of the cooling water flowing into and out of the combustor, respectively; and ρe , qex , and cp e are the density (kg/m3 ), flow rate (m3 /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 cp dT dt = Hρfuel qfuel + ρair−in qair−in cp1 Tin −

(11)

(11a)

ρex qex cp2 T − KA1 (Tf − T∞ ) − ρw qw cw (Tw − Tw 0 ).

(13)

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According to the law of quality conservation (with negligible quality change of gas in the combustor), we have ρex qex = ρfuel qfuel + ρair−in qair−in .

(14)

The mass flow rate of the input air ρair−in qair−in is much larger than the mass flow rate of the oil fuel ρfuel qfuel in the actual burning process. So, we can consider ρex qex ≈ ρair−in qair−in , and also can consider cp1 ≈ cp2 ≈ cp . Assume that the temperature of combustor wall Tf = αT and cooling water temperatures in export Tw = βT , then (13) can be simplified as

Fig. 5.

Fuzzy PID predictive controller.

V ρp cp dT dt + ρair−in qair−in cp T + KA1 αT + ρw qw cw βT = Hρfuel qfuel + ρair−in qair−in cp Tin + KA1 T∞ + ρw qw cw Tw 0 . (15) Because the inlet air, the inlet temperature, cooling environmental 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 qoil (s) as follows: G1 (s) =

Kp T (s) = qoil (s) Tp s + a

(16)

where a = ρair−in qair−in cp + KA1 α + ρw qw cw β, Kp = Hρfuel , and Tp = V ρp cp . III. DESIGN OF THE CONTROLLERS The following two sections describe the design of the inner and outer loop controllers for regulating the fuel-oil flow rate and gas temperature, respectively. A. Design of a Flow Rate Controller in the Inner Loop As modeled in (11) and (11a) and observed during the debugging of the system, the open-loop transfer function of the inner loop control system has a transport lag due to the flow rate sensor. In addition, the nonlinearity and uncertainty of the motorpump and pipeline also makes it difficult to achieve the desired control effects by simply using a simple fixed-gain PID controller. 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 the flow 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 performance 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 implemented in three steps. In the first 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 fed back

against the reference signal. Based on the computed error and the PID gain parameters that are updated by the fuzzy controller in real time, the final step determines the output of the PID controller. 1) Levinson Predictor: The Levinson predictor method predicts the values of the output variables in the future d steps built upon the moving output average ym of n process historical data. For the predictor output at kth time instant in (17), the predicted value of d step ahead is given by (18): ym (k) = −

n 

ai y(k − i)

(17)

i=1

ym (k + d|k) = −a1 ym (k + d − 1|k) − · · · − ap−1 ym (k + 1|k) − ap y(k) − · · · − an y(k + d − n). (18) In (17) and (18), the optimal forecasting parameters, {ai } where i = 1, ..., n, are predetermined using a recursive leastsquares 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 simple fixed-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 the flow 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 (ΔKp , ΔKi , and ΔKd ) 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)

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TABLE II PARAMETERS VALUES OF AN INNER CONTROLLER

Fig. 6.

Structure of an outer loop temperature controller. TABLE III PARAMETERS VALUES OF AN OUTER CONTROLLER

where λ is the correction factor, its adjustment law is λ = λ1 |E| + λ2 λ, λ1 , λ2 ∈ [0, 1]

(20)

where λ1 and λ2 are selected according to the impact weights of the error on the control system performance. Using (19), the output of the fuzzy PID controller is calculated, upon which the incremental PID gains are determined with a defuzzier. The fire-membership function μF (u) for the fuzzy control output of each fuzzy rule can be determined as μF (u) =

5  5  i=1

μ(i,j ) (u)μi (e)μj (ec)

IV. SIMULATIONS (21)

j

where μi (e), μj (ec), and μ(i,j ) (u) denote the triangular membership functions. Calculation of the defuzzier formula (based on the method in [30] and [31]) can be written as  5 5   u= μF (uk )uk μF (uk ) (22) k =−5

change of the wind speed is determined by combustion theory and empirical experience.

k =−5

where u denotes the output of the fuzzy controller after defuzzier, and it has three gains of fuzzy PID. B. Design of Temperature Controller in the Outer Loop As seen in (15), changes of the airflow, cooling water flow 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 a fixed rotational speed in practice, the change in flow 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 (say 1000◦ C) must be tested for a range of wind speeds (say 0.6, 0.8, and 1 Ma). 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 from 0.6 to 0.8 Ma. In order to accomplish this control objective, a compound controller has been designed as shown in Fig. 6, which combines compensation for wind speed change with a fuzzy PID for temperature control. The fuzzy-PID temperature controller has the same structure for the fuzzy-PID flow rate controller in the inner loop. The compensation coefficient to reflect the

In order to evaluate the effectiveness of the improved CFuzzy-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, predictor, 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 fueloil flow rate loop and outer temperature loop are PID controlled; and 3) PID-Smith cascade control law, where the inner loop uses PID with a Smith predictor and outer loop adopts PID. In order to realistically simulate the wind tunnel temperature, the target temperature is initially set to 400◦ C, and then increased to 800◦ C after 50 s. The C-fuzzy-PID control law is evaluated numerically in the following simulation cases. 1) Case A: Temperature responses to step command: To compare the step response of three kinds of control laws, the time lag is set to 3 s [see Fig. 7(a)]. 2) Case B: Effect of pure time delay: To investigate the effect of pure time delay in the inner loop flowrate transfer function of the system, the time delay is increased from 3 to 5 s, while other simulation conditions remain unchanged [see Fig. 7(b)]. 3) Case C: Effect of working condition (wind speed): Working 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 from 0.4 to

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0.2 Ma meanwhile keeping other simulation conditions unchanged [see Fig. 7(c)]. 4) Case D: Effectiveness of disturbance rejection: A disturbance, which is set to 0.2 V for the input signal of VFD, is added to the inner loop system at t = 100 s [see Fig. 7(d)]. B. Discussions of Simulation Results Some observations can be made from the simulated results. As illustrated in Fig. 7(a), although all three methods yield an overdamped temperature response to step changes, the fuzzyPID method significantly improves the response time over both traditional PID-PID and PID-Smith control methods. The PIDSmith has a slightly shorter settling time than that of PID-PID as it incorporates Smith predictor to compensate the time lag in the inner loop. Fig. 7(b) illustrates that an increase in time delay causes an overshoot and lengthens the settling time. The fuzzy-PID controlled system exhibits an excellently short settling time as compared to the PID-PID and PID-Smith cascade control methods despite the fact that it yields a slightly larger overshoot in the response. It is interesting to note that that the PID-PID offers a better transient response (both overshoot and settling time) than that of the PID-Smith method in this case. This is because Smith predictor depends on an accurate mathematical model; the control performance degrades when the plant models experience parameter variations. The ability to handle changes in working condition can be examined in Fig. 7(c). Unlike the traditional PID-PID algorithm and PID-Smith method, there is nearly no impact on the temperature response under the control of the C-Fuzzy-PID law. This is because the C-Fuzzy-PID eliminates the impact through disturbance compensation control which achieves. It is worth noting that the temperature responses of the PID-PID and PIDSmith methods are very close in this case; this is because a work condition change only influences the outer loop, and the outer loop of these methods uses the same PID control. Apart from the wind speed change, there are also system disturbances caused by other factors such as flow field fluctuation in the wind tunnel and pressure fluctuation in the oil supply system. Fig. 7(d) displays simulation results illustrating the effects of the disturbance added to the inner loop system at t = 100 s. As seen in Fig. 7(d), while all three temperature responses are perturbed immediately after the disturbance was exerted, the disturbance has significantly less effects on the C-Fuzzy-PID controlled system than on the PID-PID or the PID-Smith controlled systems; both the overshoot and settling time of the C-Fuzzy-PID system are much smaller than its two counterparts for the same disturbance. Therefore, one can conclude that the C-Fuzzy-PID controller is theoretically superior among the three methods in rejecting disturbances. Fig. 7(d) further demonstrates that the PID-PID performs better than the PID-Smith in terms of smaller temperature fluctuations and shorter settling time with the same reason explained in Case B. Fig. 7. Results of comparative studies of three control laws. (a) Comparison of step responses, Case A, τ = 3 s, 0.4 Ma. (b) Effect of pure time delay, Case B, τ = 5 s, 0.4 Ma. (c) Effect of airflow wind speed, Case C, τ = 3 s, 0.2 Ma. (d) Inner loop disturbance rejection, Case D, τ = 3 s, 0.2 Ma.

V. EXPERIMENTS Fig. 8 shows the subsystems of the HAWT system on which experiments were conducted to evaluate the control methods

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Fig. 8. Main subsystems of HAWT. (a) PLC control cabinet. (b) VFD control box. (c) Valves collocation of oil circuit. (d) Hydraulic pump supply.

developed in this paper. Developed by an aviation research institute in China, the HAWT system consists of a hydraulic pump station, fuel-oil regulating and assigning circuit, PLC control cabinet, VFD control box, and remote IPC. There are two motor pumps and two VFDs in the experimental system, which provide the aviation kerosene fed to the primary and preparatory combustors of the three different wind tunnels. The temperature of the high-temperature gas in the combustor as a result of fuel-oil combustion was controlled by the methods developed in this paper. In order to compare against simulations and conduct experiments similar to actual system operations, the gas in the combustor was allowed to reach the steady-state temperature of 400◦ C before an experiment was conducted. In the first experiment, a reference step command of 400◦ C was issued to raise the gas temperature to 800◦ C. In the second experiment, the temperature rose from 400 to 800◦ C with the wind speed set at 0.4 Ma, and the wind speed was then changed to 0.2 Ma at the instant t = 40 s. The temperature data measured in the main combustor of the wind tunnel for the first and second experiments are plotted in Figs. 9(a) and (b), respectively. As shown in Fig. 9(a), the temperature raised about 3 s after the step command was issued validating that the system model has a pure time delay in the system. In both experiments, the temperature curves in Figs. 9(a) and (b) reached the expected value with no overshoot demonstrating that the C-Fuzzy-PID control method can effectively suppress the impact caused by change of the wind speed. As seen in the measured temperature data in Fig. 9(b), the temperature in the combustor experienced only a slight change when the wind speed is reduced, and promptly restored to the set value of 800◦ C within a short time. This illustrates that although the reduction of wind speed causes a rise in temperature, the designed controller is robust in rejecting disturbances (caused by the change of working conditions) and the

Fig. 9. Experimental result of step response of fuzzy-PID cascade control. (a) Step response of fuzzy-PID cascade control when wind speed is 0.4 Ma. (b) Step response while wind speed changed from 0.4 to 0.2 Ma.

temperature control performance of the HAWT is satisfactory with fluctuation kept within ±7 ◦ C. VI. CONCLUSION A successfully developed C-Fuzzy-PID control system (with an inner flow rate and an outer temperature control loops) for temperature control of a HAWT has been presented. The plant models for both loops, which have been derived in closed form for a physical HAWT, have been shown to provide a useful basis for simulation analysis and controller design. The proposed C-Fuzzy-PID has been numerically investigated by comparing simulation results against two traditional methods; PID-PID and PID-Smith. The inner loop, which incorporates a predictive control law, effectively overcomes influences of large inertia and transport lag in fuel-oil supply system on the temperature responses. The outer loop, where the compensation coefficients of the fuzzy-PID law for temperature control can be tuned (based on combustion theory and experiences) to reflect work conditions, provides an effective means to suppress the impact caused by a change in wind speeds. The models and the proposed C-Fuzzy-PID law have been validated experimentally showing that the proposed controller not only can realize precise temperature control, but also can quickly suppress influences caused by a change of work conditions, parameter variation, and disturbances on the plant. The temperature fluctuation of the system is less than ±7 ◦ C. Simulation and experimental results have confirmed that the

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C-Fuzzy-PID control algorithm has strong robustness and excellent adaptability. Suggested future work may include a strict theoretical analysis of the proposed C-Fuzzy-PID for the temperature control of HAWT, which takes into account the perturbation of the controlled plant. REFERENCES [1] S. Zhao, L. Liao, and Y. Chen, “1700◦ C Hot wind tunnel for thermal calibration,” Aviation Meas. Testing Technol., vol. 20, no. 4, pp. 3–6, Apr. 2000. [2] T. Peng, B. Xu, and H. Yang, “Variable frequency hydraulic technology development and research,” J. Zhejiang Univ., vol. 38, no. 2, pp. 215–221, Feb. 2004. [3] T. Zhao, J. Zhang, and L. Ma, “On-line optimization control method based on extreme value analysis for parallel variable-frequency hydraulic pumps in central air-conditioning systems,” Building Environ., vol. 47, pp. 330– 338, Jan. 2012. [4] H. Yang, W. Sun, and B. Xu, “New investigation in energy regeneration of hydraulic elevators,” IEEE/ASME Trans. Mechatronics, vol. 12, no. 5, pp. 519–526, Oct. 2007. [5] B. Xu, X. Ouyang, and H. Yang, “Energy-saving system applying pressure accumulators for VVVF controlled hydraulic elevators,” presented at the ASME Int. Mech. Eng. Congr. Expo., Washington, DC, USA, Nov. 16–21, 2003. [6] B. Xu, J. Yang, and Y. H. Yang, “Comparison of energy-saving on the speed control of VVVF hydraulic elevator with and without pressure accumulator,” Mechatronics, vol. 15, no. 10, pp. 1159–1174, 2005. [7] D. Hu, S. Ding, H. Zhu, B. Xu, and H. Yang, “Velocity-tracking control of the variable-speed controlled hydraulic system: Using compound algorithm of PD & feed-forward-feedback control,” in Proc. 3rd IEEE Conf. Meas. Tech. Mechatronics Autom., 2011, pp. 1109–1116. [8] R. Manasek, “Simulation of an electro-hydraulic load-sensing system with AC motor and frequency changer,” in Proc. 1st IEEE Conf. FPNI-PhD Symp., 2000, Slovakia, pp. 311–324. [9] Y. Bian, X. Xu, and L. Zhu, “Variable frequency hydraulic speed control system based on CANopen,” in Proc. 2nd IEEE Conf. Edu. Technol. Comput., 2010, pp. 264–268. [10] Y. Li, C. Cai, T. Liu, and L. Zhang, “Study on control strategies for oil-fuel supply system used in supersonic combustion wind tunnel,” in Proc. Int. Conf. Fluid Power Mechatronics, Beijing, China, 2011, pp. 732–737. [11] S. Li, H. Peng, K. Li, and J. Wang, “Minimum fuel control strategy in automated car-following scenarios,” IEEE Trans. Vehicular Technol., vol. 61, no. 3, pp. 998–1008, Mar. 2012. [12] S. Xu, M. Zhou, and H. Dong, “High temperature hydraulic pump and flow control based on frequency conversion technology,” in Proc. IEEE Conf. Mechatronics Autom., 2010, pp. 1203–1208. [13] L. Zhnag and Y. Li, “Design and Implementation of fuel supply system based on variable frequency speed-regulating technology,” Hydraul. Pneum. Seals, vol. 30, no. 4, pp. 10–12, Apr. 2010. [14] T. Liu, Y. Li, and L. Zhang, “Flow rate predictive control for volumetric type of fuel oil supplying system driven by variable frequency induction motor,” Hydraul. Pneum. Seals, vol. 31, no. 2, pp. 52–56, Feb. 2011. [15] J. Zhang, F. Zhang, M. Ren, G. Hou, and F. Fang, “Cascade control of superheated steam temperature with neuron-PID controller,” ISA Trans., vol. 51, no. 6, pp. 778–785, Nov. 2012. [16] H. Moradi and F. Bakhtiari-Nejad, “Improving boiler unit performance using an optimum robust minimum-order observer,” Energy Convers. Manage., vol. 52, no. 3, pp. 1728–1740, 2011. [17] L. Han and Z. Zhang, “The application of immune genetic algorithm in main steam temperature of PID control of BP network,” Phys. Procedia, vol. 24, pp. 80–86, 2012. [18] Z. Dong, X. Huang, and L. Zhang, “Saturated output feedback dissipation steam temperature control for the OTSG of MHTGRs,” IEEE Trans. Nucl. Sci., vol. 58, no. 3, pp. 1177–1190, Jun. 2011. [19] A. Widd, K. Ekholm, P. Tunest˚al, and R. Johansson, “Physics-based model predictive control of HCCI combustion phasing using fast thermal management and VVA,” IEEE Trans. Control Syst. Technol., vol. 20, no. 3, pp. 688–699, May. 2012. [20] A. Choukroun and M. Chanfreau, “Automatic control of electric actuators for an optimized engine cooling thermal management,” presented at the Soc. Auto. Eng. World Congr., Detroit, MI, USA, 2001.

[21] R. Cipollone and C. Villante, “Vehicle thermal management: A model based approach,” in Proc. ASME Internal Combustion Engine Div., Long Beach, CA, USA, 2004, pp. 85–95. [22] P. Setlur, J. Wagner, D. Dawson, and E. Marotta, “An advanced engine thermal management system: Nonlinear control and test,” IEEE/ASME Trans. Mechatronics, vol. 10, no. 2, pp. 210–220, Apr. 2005. [23] M. Salah, T. Mitchell, J. Wagner, and D. Dawson, “Nonlinear control strategy for advanced vehicle thermal management systems,” IEEE Trans. Veh. Technol., vol. 57, no. 1, pp. 127–137, Jan. 2008. [24] M. Salah, T. Mitchell, J. Wagner, and D. Dawson, “A smart multiple-loop automotive cooling system—Model, control, and experimental study,” IEEE/ASME Trans. Mechatronics, vol. 15, no. 1, pp. 117–125, Feb. 2010. [25] T. Xu, X. Pu, and Z. Yuan, “Application of PID parameter setting based on a genetic algorithm in a high-temperature multiphase flow wind tunnel,” J. Eng. Thermal Energy Power, vol. 25, no. 4, pp. 414–417, Apr. 2010. [26] S. M. Camporeale, B. Fortunato, and A. Dumas, “Dynamic modelling of recuperative gas turbines,” Proc. Inst. Mech. Eng., J. Power Energy, vol. 214, no. 3, pp. 213–225, May 2000. [27] J. Kim and S. Kim, “Design of incremental fuzzy PI controllers for a gasturbine plant,” IEEE/ASME Trans. Mechatronics, vol. 8, no. 3, pp. 410– 415, Sep. 2003. [28] J. L. Meza, V. Santib´an˜ ez, R. Soto, and M. A. Llama, “Fuzzy self-tuning PID semiglobal regulator for robot manipulators,” IEEE Trans. Ind. Electron., vol. 59, no. 6, pp. 2709–2718, Jun. 2012. [29] T. H. Ho and K. K. Ahn, “Speed control of a hydraulic pressure coupling drive using an adaptive fuzzy sliding-mode control,” IEEE/ASME Trans. Mechatronics, vol. 17, no. 5, pp. 976–986, Oct. 2012. [30] Y. Z. Li, K. M. Lee, and J. Wang, “Analysis and control of equivalent physical simulator for nano-satellite space radiator,” IEEE/ASME Trans. Mechatronics, vol. 15, no. 1, pp. 79–87, Feb. 2010. [31] E. Kayacan, O. Cigdem, and O. Kaynak, “Sliding mode control approach for online learning as applied to type-2 fuzzy neural networks and its experimental evaluation,” IEEE Trans. Ind. Electron., vol. 59, no. 9, pp. 3510– 3520, Sep. 2012.

Yunhua Li (M’05–SM’12) received the M.S. degree in mechanical engineering from Jilin University of Technology, Changchun, China, in 1988, and the Ph.D. degree in mechatronics from Xi’an Jiaotong University, Xi’an, China, in 1994. He has been a Full Professor of mechanical engineering at Beihang University, Beijing, China, since 1999. He was a Postdoctoral Research Fellow with Beihang University and National Chengkung University from December 1994 to October 1996 and from July 1997 to August 1997, respectively. He has published more than 160 refereed journal and conference papers in journals sponsored by IEEE, ASME, and Elsevier, and four books. He has completed numerous granted research and development projects as the Principal Investigator. His research interests include nonlinearity dynamics, hydraulic and mechatronic servo control, and power transmission and control of aircraft, mobile robots, and vehicles. Dr. Li is currently a Technical Editor of the IEEE/ASME TRANSACTIONS ON MECHATRONICS.

Chaozhi Cai received the B.S. and M.S. degrees in detection technology and automatic equipment from Hebei University of Engineering, Hebei, China, in 2007 and 2010, respectively. He is currently working toward the Ph.D. degree in the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. His current research interests include system modeling, process control, and intelligent control theory with applications.

LI et al.: NOVEL CASCADE TEMPERATURE CONTROL SYSTEM FOR A HIGH-SPEED HEAT-AIRFLOW WIND TUNNEL

Kok-Meng Lee (M’89–SM’02–F’05) received the B.S. degree from the State University of New York, Buffalo, NY, USA, in 1980, and the S.M. and Ph.D. degrees from the Massachusetts Institute of Technology, Cambridge, MA, USA, in 1982 and 1985, respectively. He is currently a Professor with The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA. He was also honored as a Pao Yu-Kong Chair Professor at Zhejiang University. He is currently on leave from Georgia Tech and is a Distinguished Professor with the State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, under the National Recruitment Program of Global Experts. He holds eight patents in machine vision, a three-degrees-of-freedom sphericalmotor/encoder, and a live-bird handling system. His research interests include system dynamics/control, robotics, automation, and mechatronics. Dr. Lee is a Fellow of the ASME. He has received the National Science Foundation Presidential Young Investigator, Sigma Xi Junior Faculty Research, International Hall of Fame New Technology, and Kayamori Best Paper Awards.

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Fengjian Teng received the B.S. degree from the University of Science and Technology of Beijing, Beijing, China, and the M.S. degree in mechatronics from Beihang University, Beijing. He is currently a Research Assistant in the School of Automatic Science and Electrical Engineering, Beihang University. His research interests include hydraulic system design, electrical control, and mechanical design.