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An engine thermal management system design for military ground vehicle - simultaneous fan, pump and valve control.

ABSTRACT

The pursuit of greater fuel economy in internal combustion engines requires the optimization of all subsystems including thermal management. The reduction of cooling power required by the electromechanical coolant pump, radiator fan(s), and thermal valve demands real time control strategies. To maintain the engine temperature within prescribed limits for different operating conditions, the continual estimation of the heat removal needs and the synergistic operation of the cooling system components must be accomplished. The reductions in thermal management power consumption can be achieved by avoiding unnecessary overcooling efforts which are often accommodated by extreme thermostat valve positions. In this paper, an optimal nonlinear controller for a military M-ATV engine cooling system will be presented. The prescribed engine coolant temperature will be tracked while minimizing the pump, fan(s), and valve power usage. A case study investigates the proposed control strategy's performance in comparison to other methods for temperature tracking and energy conservation. The optimal nonlinear controller offered satisfactory coolant temperature tracking with an average error of 0.35[degrees]C and at least 13% reduction in total cooling power.

CITATION: Tao, X. and Wagner, J., "An Engine Thermal Management System Design for Military Ground Vehicle - Simultaneous Fan, Pump and Valve Control," SAE Int. J. Passeng. Cars--Electron. Electr. Syst. 9(1):2016.

1. INTRODUCTION

Modern ground vehicles apply a variety of electronic sensors, on-board controller systems, and electric driven actuators to regulate the powertrain's operation for improved fuel economy and reduced tailpipe emissions. Advanced control algorithms have been introduced for precise fuel injection, spark delivery, air flow management, and transmission shifting to name a few process to satisfy federal regulations while meeting consumer demands. Applying model-based control strategies for accurate thermal management system operation is a promising approach as vehicle cooling has not yet received thoughtful widespread attention from the automotive engineering community.

In an engine cooling system, the actuators (pump, fans) operate at full rotational speed to reach their maximum heat removal capabilities when the engine load and ambient temperature are high. In this instance, the thermostat valve will be fully open. In contrast, the actuator speeds can be reduced and thermostat valve predominately closed when the thermal load and ambient temperatures are low which promotes passive convective cooling. However, in between these extremes, the thermal management system's operation needs to be optimized for variable heat rejection to achieve temperature tracking with minimal power usage. A medium thermal load under a moderate surrounding temperature provides a space for advanced thermal management controller designs as shown in Fig. 1.

An efficient thermal management system design is essential for powertrain reliability, fuel economy, and performance [1]. In a study by Park and Jung [2], various powertrain cooling system architectures and the accompanying effect on the power consumption has been investigated. The upgrade of mechanical actuators in cooling systems by real time controlled electro-mechanical components facilitates improved efficiency under most operating conditions. A variety of control strategies, applied to advanced vehicle powertrain thermal management systems, have been studied [3][4]. The integration of an electric pump and smart valve for faster engine coolant warm up time and reduced temperature fluctuation has been reported in [5]. Cho et al. [6] explored the benefit of a controllable electric pump for truck engine cooling which offers a significant reduction in power consumption and possible heat exchanger downsize. Page et al. [7] investigated a classical PID controller for the cooling system featuring with multiple electric radiator fans and heat controlled thermostats. A suite of nonlinear control strategies was developed by Salah et al. [8] to adjust the smart valve position and the coolant flow rate to track the desired engine temperature. A differential flatness nonlinear controller has demonstrated improved temperature trajectory tracking performance [9].

The radiator fan(s) has been identified to consume that greater power within engine cooling systems when compared to the other components (pump, smart valve) [10]. Recently, attention has focused on optimizing the fan(s) speed to minimize power usage while rejecting sufficient heat. Wang et al. [11] conducted a detailed experimental analysis of multiple electric radiator fan configurations. A rule of thumb and optimization control strategy for total fan array power minimization based on thermal load was proposed [12]. Within the area of hybrid electric vehicles (HEV), Tao et al. [13] developed a model predictive controller to regulate the compressor speed in vapor compression systems to track cooling air temperature and stabilize core battery temperatures within battery packs. A high fidelity electric motor thermal model was implemented in a heavy-duty HEV cooling system controller which tracked the motor's inner peak temperature [14].

This research study will examine an engine thermal management system for military ground vehicles, specifically an M-ATV, as shown in Fig. 2. The proposed control strategy will synchronously regulate the radiator fan, coolant pump, and smart valve operations to track the prescribed reference temperature with consideration power consumption. The remainder of this paper is arranged as follows. In Section 2, a lumped parameter thermal model is presented that describes the engine cooling system's thermal behavior. In addition, a suite of actuator models will be developed to estimate the power consumption. In Section 3, an optimal nonlinear controller, with two supplemental controllers, will be designed. A case study with numerical results will be presented and discussed to explore the performance and power consumption for different control strategies in Section 4. Section 5 concludes this work. A complete Nomenclature List and denvation of the desired cooling air temperature at the radiator outlet are offered in the Appendix.

2. LIBRARY OF MATHEMATICAL MODELS

An engine thermal management system, featuring electric driven actuators, will be mathematically modeled to establish a basis for controller designs. The M-ATV proposed cooling system configuration consists of an internal combustion engine (ICE), electric coolant pump, smart valve, variable speed fan, and radiator (refer to Fig. 3). A lumped parameter approach will be pursued to develop the differential and algebraic equations.

2.1. Thermal Dynamics of the Engine and Heat Exchanger

The coolant is circulated by the electric pump through the cooling system as shown in Fig. 3. The smart valve allows a temperature dependent portion of the total coolant flow through the radiator and the remainders goes back to engine directly. The coolant discharges the combustion heat in the radiator via forced convective heat transfer. The governing thermal equation for the coolant temperature change at the engine outlet, [T.sub.h], may be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [M.sub.w,e] is the coolant mass inside the engine. The parameter [c.sub.w] is the specific heat of water. The term [Q.sub.e] represents the engine heat of combustion. The second term on the right side of Eq. (1) is the heat removal attributed to the coolant mass flow rate, [rn.sub.W].

The coolant at the pump's outlet, or engine inlet, is a mixture of the cold and hot coolant streams. The smart valve regulates the coolant mass flow through the radiator and bypass. A portion of the coolant will flow into the radiator and discharge the waste heat to the ambient surroundings. The bypass circuit directs the remaining fluid flow right to pump. In this study, the valve is electrically driven and linearly controlled such that 0 [less than or equal to][K.sub.v][less than or equal to] 100%. When [K.sub.v] = 100%, the valve is

fully open and all the coolant will be directed into the radiator. In contrast, [K.sub.v] = 0% means that the valve is closed and all the coolant is routed through the bypass to the pump.

The the coolant temperature at the pump's outlet, [T.sub.m], is a linear combination of the hot, [T.sub.h], and cold, [T.sub.c], coolant temperatures defined as

[T.sub.m] = (l - [K.sub.v])[T.sub.h]+[K.sub.v][T.sub.c] (2)

The differential equation for cold coolant temperature at the radiator outlet, [T.sub.c], may be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [M.sub.w,r] is the coolant masses inside the radiator, the variable [Q.sub.r] on the right side is the heat transfer from the coolant to the cooling air in the radiator. The term [K.sub.v][m.sub.w][c.sub.p.w]([T.sub.h] - [T.sub.c]) denotes the heat transferred by the coolant flow itself due to temperature differences. Finally, the dynamic change in the cooling air temperature at the radiator outlet, [T.sub.a,o], is modeled as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

In this expression, the parameter [M.sub.a,r] is the air mass inside the radiator control volume, and [m.sub.w] denotes the specific heat of air. The term [T.sub.amb] represents the temperature of the ambient air, which will be delivered through the radiator by the variable speed fan at mass flow

rate, [m.sub.a].

2.2. Cooling Actuators - Radiator Fan and Pump

The total power consumption of the cooling system should be reduced to help satisfy the legislated fuel and emissions requirements. Only the power consumed by the radiator fan and the coolant pump will be analyzed, given that the power used by the smart valve is negligible. The radiator heat transfer is directly affected by the cooling air mass flow rate provided by the fan which may be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Where [N.sub.f], is the fan speed, and [C.sub.flow] is the flow rate coefficient. The parameters [D.sub.fan] and [[rho].sub.a] denote the equivalent fan diameter and the cooling air density.

The total air pressure increase due to the fan, [dp.sub.fan] may be calculated as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where the parameter [C.sub.press] is defined as the pressure drop coefficient across the radiator. The fan power consumption rate, [E.sub.fan], is given as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

For a given cooling system, the values of [C.sub.flow],[C.sub.press], [D.sub.fan], and [[rho].sub.a] are constant. Thus, the estimation of the radiator fan power consumption can be characterized as a function of the air mass flow rate so that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

with [k.sub.fan], = [D.sub.fan.sup.-4] [C.sub.pres] [[rho].sub.a.sup.-1] [C.sub.flow.sup.-2], The coolant mass flow rate, [m.sub.w], driven by the electric pump, is dependent on the pump rotation speed, [N.sub.p], such that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

where the term [D.sub.is] is the maximum pump displacement. The parameter [[rho].sub.w] denotes the water density while the variable [N.sub.p] is the pump speed.

The total pressure drop across the radiator and the pipe in the coolant flow is calculate as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where [C.sub.p,rad], and [C.sub.p,pipe] denote the pressure rise coefficients in the radiator and pipe, respectively. The parameter [A.sub.flow] is the coolant flow cross section area in the radiator.

The pump power consumption rate, [E.sub.pump], is defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

The pump's power consumption can be summarized as a function of the coolant mass flow rate given the parameters [A.sub.flow], [C.sub.p,rad], [C.sub.pipe], [D.sub.is] and [[rho].sub.w] for a given cooling system as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

where [k.sub.pump] is defined as [??]

Note that the power consumption of the water pump and radiator fan are both proportional to the cube of the given fluid flow rate.

3. CONTROLLER DESIGNS

An optimal nonlinear controller, based on the thermal model, will be designed to minimize the total power consumption of the prescribed ICE cooling system. For comparison purposes, two other control

strategies will also be introduced including a state flow controller, and a classical PI controller.

3.1. Optimal Nonlinear Control

An optimal nonlinear controller will simultaneously regulate the operation of the coolant pump, radiator fan, and smart valve to track the desired engine temperature while using the theoretically minimum total power. The primary control objective is to stabilize the coolant temperature, [T.sub.h], to the prescribed target value, [T.sub.h,d].

3.1.1. Pump Speed Control

The coolant pump electric motor shaft speed will be controlled by an adaptive nonlinear controller. Define the coolant temperature tracking error as

[e.sub.h] = [T.sub.h] - [T.sub.h,d] (13)

The [T.sub.m] term in Eq. (1) may be replaced by Eq. (2), and divide both side of the equation by[M.sub.w,e] [c.sub.p,w], the coolant temperature change at the engine outlet can be simplified as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

Considering that the waste heat of combustion, [Q.sub.e], is not measurable, an estimation of engine heat generation, [Q.sub.e], is applied in the controller design. So, define the heat generation estimation error as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

The desired target coolant temperature, [T.sub.h,d], is constant. The tracking error dynamic change may be evaluated by computing the time derivative of Eq. (13) so that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

To stabilize the coolant temperature, the control objective can be stated as

[e.sub.h] [less than or equal to] as t [right arrow] [infinity] (17)

To realize this control purpose, a Lyapunov based backstepping adaptive controller may be developed to regulate the pump speed by determining the coolant mass flow rate, [m.sub.w] . First, define the second term in Eq. (3) as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

A Lyapunov function, V, can be selected as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

The Lyapunov function must be positive definite. If its time derivative is negative definite, the coolant temperature tracking error and the heat generation estimation error converges to zero eventually [15]. Assuming that the change of [Q.sub.e] is slow, then the Lyapunov function time derivative can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

A control law, [U.sub.1] may be proposed with the form

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

Replace the second term in Eq. (14) by Eq. (21), so that the dynamic change of the coolant temperature tracking error becomes

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

Now design the heat generation estimate as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

In the next step, substitute Egs. (22) and (23) into Eq. (20), the derivative of the Lyapunov function can be written as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

The Lyapunov function converges to zero with a negative definite time derivative. This indicates that the coolant tracking error, [e.sub.h], can be stabilized by applying the proposed input [U.sub.1] in Eq. (21). The desired coolant mass flow rate in the engine can be solved with Eqs. (19) and (22) as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

3.1.2. Fan Speed Control for Total Power Minimization

The overall objective of the optimal nonlinear controller design is to minimize the total cooling system power consumption. Thus, the operation of the radiator fan must be optimized as it represents the largest electrical power consumption. The cooling air mass flow rate control law is developed by tracking the cold coolant temperature, [T.sub.c], to a desired value, [T.sub.c,d], such that the total power consumption of the pump and fan is minimized with any arbitrary thermal load. Consider the system model in a static condition. It can be observed from Eqs. (3) and (4) that when the time derivatives of the cooling fluids temperatures are zero, the heat transfer rate inside the radiator is proportional to the coolant and air mass flow rates as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)

To facilitate the optimization process, assume that the radiator size is large enough to satisfy the heat removal rate and the heat transfer can be fully developed inside the radiator. Consequently, the cooling air and the coolant temperatures are considered very close to each other at the radiator outlet. An optimization variable, [T.sub.x], to be defined as

[T.sub.x] = [T.sub.a,o] = [T.sub.c] (28)

Substituting Eqs. (26) and (27) into Eqs. (8) and (12), allows the total power consumption rate, E, of coolant pump, [E.sub.pump], and the radiator fan, [E.sub.fan], to be derived as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)

To minimize the total power consumption rate with respect to the fluids temperature at the radiator outlet, [T.sub.x], a desired value of [T.sub.x] can be solved by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (30)

which leads to the result

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (31)

Readers are referred to Appendix A for a detailed derivation of this expression.

Given that the hot coolant temperature is tracked to [T.sub.h,d], and the ambient air temperature, [T.sub.amb], is constant, the desired cooling air temperature at the radiator outlet can be derived by solving Eqs. (30) and (31) so that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (32)

When the coolant and air flow exiting the radiator converges to the desired temperature per Eq. (32), the total power consumption of the pump and fan, E, reaches a minimum point. The radiator fan speed is regulated to track this outlet cooling air temperature, [T.sub.a,o,d] .A nonlinear adaptive controller can be developed in a similar manner as the coolant mass flow rate controller.

Define the radiator outlet air temperature tracking error, [e.sub.a,o], as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (33)

To track the coolant temperature, the control objective can be stated as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (34)

Comparing Eqs. (1) and (4). it may be observed that the procedure to construct the cooling air mass flow rate control law will be similar to the coolant mass flow rate control law. Hence, the desired cooling air mass flow rate in the radiator is finally given as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (35)

Note that in the above expression, there's no [K.sub.v] term involved in the denominator, since the smart valve operation does not affect the radiator air flow.

3.1.3. Smart Valve Position Control

To avoid the potential of localized peak temperatures that exceed established limits inside the engine block, the minimum coolant mass flow rate is established as [m.sub.w,min]. When the target coolant mass flow rate derived from Eq. (25) is smaller than [m.sub.w,min], the smart thermal valve is closed to reduce the coolant flow through the radiator and achieve the target [U.sub.l]. The valve opening, [K.sub.v] may be calculated as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (36)

The fan and pump speed can be easily achieved by solving Nf and N in Eqs. (5) and (8) using the target mass flow rates of the cooling fluids, [m.sub.a,d] and [m.sub.w,d], from Eqs. (25) and (35), respectively. The control diagram of the proposed optimal nonlinear control system is displayed in Fig. 4.

3.2. State Flow Control

A state flow control strategy has been investigated to simultaneously regulate the radiator fan coolant pump and smart valve. According to Wang and Wagner [16], the coolant temperature responds to different cooling actuator combinations with varying magnitudes and time responses. For instance, the smart valve causes the largest coolant temperature change. In contrast, the pump operation provides a faster temperature variation response time with larger fluctuations. Finally, the temperature change due to the radiator fan requires a longer response time when compared to the valve and pump operation. Since the engine fan uses the most power and the smart valve operation consumes a negligible amount, the state flow control strategy can be designed as shown in Fig. 5.

In the initial state, the valve is half closed and the coolant flow rate is set to a minimum. The radiator fan is operated on due to the high power cost. To facilitate the implementation of the state flow control algorithm, define a series of threshold values of the engine coolant temperature as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (37)

The parameters [T.sub.h,max],[T.sub.h,high], [T.sub.h,low], and [T.sub.h,min] . are selected to determine the operation of the cooling system. When the coolant warms up and reaches its desired temperature value, [T.sub.h,d], the valve will fully open to [K.sub.v] = 1. If the coolant temperature keeps rising up to [T.sub.h,high], then the coolant pump will be switched to its maximum speed. The radiator fan is only switched on to maximum speed when the sensor measurement [T.sub.h] reaches the upper band [T.sub.h,max] .The radiator fan will then continue operating at its maximum speed until the coolant temperature drops to [T.sub.h,d].

When the coolant temperature starts dropping to [T.sub.h,d] the radiator fan will be switched off first. The coolant pump speed is then decreased to its minimum value when the coolant temperature drops to [T.sub.low]. The smart valve is placed in a half open state with [K.sub.v] =0.5 if the coolant temperature continues to drop into the lower band, [T.sub.h,min]. By operating the cooling actuators in this synchronized manner, the engine coolant temperature can be regulated around the prescribed value, [T.sub.h,d].

3.3. Classic PI Control

A classical proportional integral (PI) controller may be designed to simultaneously regulate the fan, pump, and smart valve operations. The coolant pump and radiator fan speeds, as well as the valve opening position, can be stated in the compact form as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (38)

where the proportional, [K.sub.p], and integral, [K.sub.I] gains are positive constants. These values are selected such that the cooling air and coolant mass flow rate are proportional per a constant ratio, r, selected by the Calibration Engineer. The initial input [u.sub.0] is applied at the beginning of each test. The valve opening position, [K.sub.v], has been nominalized to an interval of [0, 1] by dividing the pump speed by its minimum value, [N.sub.p,min]

4. CASE STUDY - NUMERICAL RESULTS

To evaluate the three control methods designed for an engine cooling system, a case study has been conducted using an engine thermal management system will be modeled in AMESim while the controllers in MATLab/Simulink. The simulation results will be presented and discussed to demonstrate the advantages of the optimal nonlinear controller, in comparison to the conventional state flow and the classical PI controllers. The mean average value of the coolant temperature tracking error, and the total energy consumption of the coolant pump and fan will be reported. The system model and controller parameters have been summarized in Table 1.

The military ground vehicle studied is a hybridized mid-size truck equipped with a 7.2 L turbo-diesel engine. Urban assault and convoy escort driving cycles were investigated for cooling performance designs. For each cycle, the engine heat generation rate has been estimated based on the vehicle speed profile, the corresponding fuel consumption rate, and the effective engine propulsion power output. The engine waste heat generation rate, [Q.sub.e], for both driving cycles have been displayed in Fig. 6.

Six tests were conducted in the Case study as shown in Table 2. The target coolant temperature, [T.sub.h,d], is set to be 90[degrees]C. In the Tests 1-3, the urban assault driving cycle is implemented. While Tests 4 to 6, feature the convoy escort driving cycle. The coolant temperature tracking and power consumption of the radiator fan and coolant pump were recorded.

In Test 1, the optimal nonlinear control strategy developed in the Section 3.3 was implemented. The coolant temperature responses are displayed in Fig. 7a, have been stabilized about the target value within an average error of 0.35[degrees]C. The radiator coolant temperature was tracked to its target value, [T.sub.a,o,d], while minimizing the total actuators energy cost by controlling the radiator fan speed. The mass flow rates of the cooling air and coolant inside the radiator are displayed in Fig. 7b. The energy costs of the pump and are 61.5 kJ, and 162.4 kJ respectively.

In Test 2, the state flow control strategy is applied to regulate the engine cooling system operation. By switching the radiator fan and pump to their maximum speeds whenever the coolant temperature reaches the corresponding threshold, and keeping these actuators operating at the maximum speeds until the coolant temperature is too cold, the coolant temperature suffered frequent fluctuations but remained bounded inside a given range. The average coolant temperature tracking error was 1.33[degrees]C. In comparison to Test 1, the state flow controller requires more actuator energy due to the unnecessary maximum cooling effort.

The coolant temperatures at the engine and radiator outlets and for Test 3 have been displayed in Fig. 8a. Similarly, mass flow rates of the cooling air and coolant inside the radiator have been shown in Fig. 8b. It may be observed that the classical PI controller stabilizes the coolant temperature to the desired 90[degrees]C with a relatively large fluctuation compared to the optimal nonlinear controller in Test 1. The average tracking error was 0.45[degrees]C with pump and fan power costs of 36.5 kJ and 219.6 kJ. The total energy use was 12% higher than the total cooling energy loss in Test 1.

Overall, Tests 1-3 demonstrate that the three control strategies can track the engine coolant to a prescribed desired value with different error magnitudes and cooling energy consumptions. The proposed optimal nonlinear controller and the classical PI controller provide stable temperature tracking performance when viewed against the state flow controller. The cooling energy use of the optimal nonlinear controller is the smallest for the urban assault driving cycle comparing to the other cooling control algorithms.

The engine cooling performance for the different control methods over the convoy escort driving cycle have been investigated m Tests 4-6. The engine coolant temperature in Test 4, was tracked favorably to the target value of 90[degrees]C with an average tracking error of 0.34[degrees]C as shown in Fig. 9. The total cooling system power consumption is 599 kJ

In Test 5, the engine coolant temperature is regulated inside the temperature band of [T.sub.h,max], [T.sub.h,min] by the state flow controller. Fig. 10 displays the simulated coolant temperature responses with cyclical temperature profile. The control strategy shut down the radiator fan when the coolant temperature drops lower than [T.sub.h, d] This action limited the heat removal capacity of the radiator, and consequently, the coolant temperature rose greatly. The temperature tracking error was 1.76[degrees]C, and significantly exceeded Test 4 results. The maximum speed fan and pump operations, without considering the real time heat removal rate requirement, led to a large waste of energy due to unnecessary cooling the fluids. As a result, the total cooling energy cost was much larger than the proposed nonlinear-optimal method.

Finally, the classical PI controller stabilized the engine coolant temperature with an average error of 0.79[degrees]C in Test 6 for the

convoy escort profile. The total energy consumed by the radiator fan and pump was 694 kJ, and 15% higher than Test 4. Overall, the proposed optimal nonlinear control strategy offered better coolant temperature tracking performance and reduced energy consumption for the convoy escort driving cycle.

5. CONCLUSION

The replacement of the mechanical-based actuators in a conventional engine cooling system with electronic computer controlled elements provides the opportunity to improve the thermal management system performance. In this paper, an optimal nonlinear controller has been proposed for a heavy duty M-ATV engine cooling system to simultaneously control the coolant pump, radiator fan, and smart valve. A numerical case study with two driving cycles demonstrates that the nonlinear cooling control strategy offered smaller temperature tracking error and temperature fluctuation. Further, a 14% reduction in total cooling system power consumption was realized when compared to the conventional state flow controller and the classical PI controller. The proposed engine cooling control strategy provides advantages that merit further study and field testing.

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CONTACT INFORMATION

Corresponding author: J. Wagner

Department of Mechanical Engineering, 102 Fluor Daniel Building,

Clemson University, Clemson, SC, 29634, USA

jwagner@clemson.edu

ACKNOWLEDGMENTS

The authors wish to acknowledge the financial and technical support of the U.S. Army Tank Automotive Research Development and Engineering Center (TARDEC), and the Automotive Research Center (ARC) at the University of Michigan and Clemson University.

DISCLAIMER

UNCLASSIFIED: Distribution Statement A. Approved for public release.

Reference herein to any specific commercial company, product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or the Department of the Army (DoA). The opinions of the authors expressed herein do not necessarily state or reflect those of the United States Government or the DoA, and shall not be used for advertising or product endorsement purposes.

APPENDIX

APPENDIX A: DERIVATION OF DESIRED COOLING AIR TEMPERATURE AT THE RADIATOR OUTLET

As discussed in Section 3.1.2, the cooling air temperature at the radiator outlet can be treated as design variable for the optimized fan speed controller design. To minimize the total power consumption rate with respect to the fluids temperature at the radiator outlet, [T.sub.x], a desired value of [T.sub.x] can be solved by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (A.1)

where [??]. Now, Eq. (A1) can be written fater taking the partial derivative as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (A.2)

Now divide both sides of this expression by [??], and then move the second term on the left side to the right side so that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (A.3)

This expression may be re-arranged to express temperature on one side as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (A.4)

Thus, the design variable [T.sub.x] may be defined such that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (A.5)

which is same as Eq. (31). Based on this analysis, the ideal temperature for the air and coolant at the radiator outlet is not influenced by the radiator heat removal rate, [Q.sub.r]. Consequently, the proposed desired temperature, [T.sub.x], per Eq. (31) is a function of the valve position, [K.sub.v], that minimizes the total

power consumption, E.

APPENDIX B: DEFINITIONS/ABBREVIATIONS

[A.sub.flow]    Flow cross area                     [m.sub.2]
[c.sub.p]       Air specific heat                   j/([degrees])
[c.sub.p,w]     Water specific heat                 J/([degrees])
[C.sub.press]   Pressure drop coefficient           -
[C.sub.p,rad]   Pressure drop coefficient           -
[C.sub.p,pipe]  Pressure drop coefficient           -
[C.sub.flow]    Pressure drop coefficient           -
[dp.sub.fan]    Fan pressure increase               Pa
[dp.sub.w]      Pump pressure increase              Pa
[D.sub.fan]     Equivalent fan diameter             mm
[D.sub.is]      Pump displacement                   mL
[e.sub.a,o]     Air temperature tracking error      [degrees]C
[e.sub.h]       Coolant temperature tracking error  [degrees]C
E               Total power consumption             kJ
[E.sub.fan]     Fan power consumption               kJ
[E.sub.pump]    Pump power consumption              kJ
[k.sub.e]       Controller feedback gain            -
[k.sub.fan]     Power consumption gain              kJ/([Kg.sup.3])
[k.sub.pump]    Power consumption gain              kJ/([Kg.sup.3])
[K.sub.I]       Integral feedback gain              -
[K.sub.P]       Proportional feedback gain          -
[K.sub.v]       Valve open percentage               -
[m.sub.a,d]     Desired air mass flow rate          kg/s
[m.sub.a]       Air mass flow rate                  kg/s
[m.sub.w,d]     Desired coolant mass flow rate      kg/s
[m.sub.w]       Coolant mass flow rate              kg/s
[m.sub.w,min]   Minimum coolant flow rate           kg/s
[M.sub.a,r]     Air mass in radiator                kg
[M.sub.w,e]     Coolant mass in engine              kg
[K.sub.w,r]     Coolant mass in radiator            kg
[N.sub.f]       Fan speed                           RPM
[N.sub.P]       Pump speed                          RPM
[N.sub.p,min]   Minimum pump speed                  RPM
[Q.sub.e]       Engine heat generation              kW
[Q.sub.e]       Estimated heat generation           kW
[Q.sub.e]       Estimation error                    kW
[Q.sub.r]       Radiator heat removal               kW
r               Constant ratio                      -
t               Time instance                       sec
[T.sub.a,o]     Outlet air temperature              [degrees]C
[T.sub.a,o,d]   Desired outlet air temperature      [degrees]C
[T.sub.amb]     Ambient temperature                 [degrees]C
[T.sub.c]       Cold coolant temperature            [degrees]C
[T.sub.h]       Hot coolant temperature             [degrees]C
[T.sub.h,d]     Desired coolant temperature         [degrees]C
[T.sub.h,max]   Temperature threshold in state      [degrees]C
                flow controller design
[T.sub.h,high]  Temperature threshold in state      [degrees]C
                flow controller design
[T.sub.h,low]   Temperature threshold in state      [degrees]C
                flow controller design
[T.sub.h,min]   Temperature threshold in state      [degrees]C
rt,min          flow controller design
[T.sub.m]       Mixed coolant temperature           [degrees]C
[T.sub.x]       Designed radiator temperature       [degrees]C
[u.sub.0]       Initial PI controller input         -
[U.sub.1]       Intermediate input                  -
V               Lyapunov function                   -
X               Optimization variable               -
[[rho].sub.a]   Air density                         kg/[m.sup.3]
[[rho].sub.w]   Water density                       kg/[m.sup.3]
[epsilon]       Control constant                    -
[infinity]      Infinity                            -

Table 1. Parameter Values and Simulation Specifications.

Parameter                   Value   Unit

[C.sub.P,W]                 4090    J/(kg[degrees]C)
[C.sub.P]                    994    J/(kg[degrees]C)
[D.sub.fan]                  500    mm
[D.sub.is]                    25    mL
[k.sub.fan]                   78.8  -
[k.sub.pump]                  86.4  -
[k.sub.e]                      2    -
[K.sub.1]                     10    -
[K.sub.P]                    300    -
[K.sub.v,0]                    1    -
[M.sub.a,r]                    0.3  kg
[M.sub.w,e]                    2    kg
[M.sub.w.r]                    2    kg
[N.sub.p,min], [N.sub.p,0]  1200    RPM
[N.sub.fan,0]               2000    RPM
r                              1.5  -
[T.sub.amb]                   30    [degrees]C
[T.sub.h,b]                   90    [degrees]C
[T.sub.h,max]                 93    [degrees]c
[T.sub.h,high]                91.5  [degrees]
[T.sub.h,low]                 88.5  [degrees]c
[T.sub.h,min]                 87    [degrees]c
[[rho].sub.a]                  1.2  [m.sup.3]
[[rho].sub.w]               1000    kg/[m.sup.3]

Table 2. Numerical Study Test Conditions and Simulation Results Test

Test No.  Driving Cycle  Cooling Control Algorithm  Temperature Tracking
                                                    Error, eh
                                                    [[degrees]C]

                                                    Peak

1                        Optimal Nonlinear          3.8
2         Urban          State Flow                 5.9
3         Assault        Classical PI               4.2
4                        Optimal Nonlinear          2.1
5         Convoy         State Flow                 5.3
6         Escort         Classical PI               5.7

Test No.            Coolant Pump      Radiator Fan Energy  Total Energy
                    Energy Cost [kJ]  Cost [kJ]            Cost [kJ]

          Average

1         0.35       61.5              162.4                223.9
2         1.33      311.4             1478.5               1789.9
3         0.45       36.5              219.6                256.1
4         0.34      159.6              439.5                599.1
5         1.76      636.5             3085.4               3721.9
6         0.79       50.8              643.9                694.7


Xinran Tao and John R. Wagner

Clemson University
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Author:Tao, Xinran; Wagner, John R.
Publication:SAE International Journal of Passenger Cars - Electronic and Electrical Systems
Article Type:Report
Date:May 1, 2016
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