MPC-Based Precision Cooling Strategy (PCS) for Efficient Thermal Management of Automotive Air Conditioning System

The 3rd IEEE Conference on Control T echnology and Applications (CCT A) August 19–21, 2019, Hong Kong, China MPC-based Pr ecision Cooling Strategy (PCS) f or Efficient Thermal Management of A utomotiv e Air Conditioning System Hao W ang 1 , Y an Meng 2 , Quansheng Zhang 2 , Mohammad Reza Amini 1 , Ilya K olmano vsky 3 , Jing Sun 1 , and Mark Jennings 2 Abstract — In this paper , we propose an MPC-based precision cooling strategy (PCS) for energy efficient thermal management of automotive air conditioning (A/C) system. The proposed PCS is able to pro vide precise tracking of the time-varying cooling power trajectory , which is assumed to match the passenger comfort requir ements. In addition, by leveraging the emerging connected and automated vehicles (CA Vs) technology , vehicle speed preview can be incorporated in our A/C thermal manage- ment strategy for further energy efficiency improvement. This proposed A/C thermal management strategy is dev eloped and evaluated based on a physics-based A/C system model (A CSim) from F ord Motor Company for the vehicles with electrified powertrains. In a comparison with F ord benchmark case over SC03 cycle, for tracking the same cooling power trajectory , the proposed PCS provides 4 . 9% energy saving at the cost of slight increase in the cabin temperature (less than 1 o C ). It is also demonstrated that by coordinating with futur e vehicle speed and shifting the A/C power load, the A/C energy consumption can be further reduced. I . I N T RO D U C T I O N Emerging connected and automated vehicles (CA Vs) tech- nologies are pushing vehicle safety and energy ef ficiency to the next lev el and create unprecedented opportunities and challenges for the control and optimization of the vehicle systems. While previous studies have been focusing on im- proving the fuel ef ficiency via powertrain optimizations ([1], [2], and [3]), vehicle thermal management and its interaction with powertrain control in hot and cold weather conditions hav e not been fully explored. T ypical thermal management systems in ground vehicles include the engine cooling [4], exhaust heat recovery [5], battery and electric machine thermal management [6] [7], and cabin heating, ventilation, & air conditioning (HV AC) system. In light-duty passenger cars, the power consumed by the HV A C system, which creates a comfortable passenger compartment, represents the most significant auxiliary load [8], which can significantly impact the ov erall vehicle fuel efficienc y . In the United States, an estimated 7 billion gallons of fuel is consumed annually for the air conditioning (A/C) system of light-duty vehicles [8]. Over 50% range reduction 1 Hao W ang, Mohammad Reza Amini, and Jing Sun are with the Depart- ment of Naval Architecture & Marine Engineering, University of Michi- gan, Ann Arbor, MI 48109 USA. Emails: { autowang, mamini, jingsun } @umich.edu 2 Y an Meng, Quansheng Zhang, and Mark Jennings are with Ford Motor Company , Dearborn, MI 48124 USA. Emails: { ymeng, qzhang71, mjennin5 } @ford.com 3 Ilya K olmanovsky is with the Department of Aerospace Engineer- ing, Univ ersity of Michigan, Ann Arbor, MI 48109 USA. Email: ilya@umich.edu due to heating the cabin in winter has been observed in EV tests for the UDDS dri ving cycle, which were performed at Ar gonne National Lab [9]. Range reduction due to A/C operation in the summer time is slightly lower for EV as reported in [10], and [11], ho wev er, the impact of A/C operation on vehicle energy consumption is still considerable and the comparison with the heating counterpart can be quite dif ferent for different driving cycles and po wertrain configurations. F or example, re garding the HEV applications, since the cabin heating may utilize the engine coolant heat, its impact on fuel economy may not be as dramatic as the one in the EV applications. Aiming at reducing vehicle-le vel fuel consumption, our previous efforts have been focused on dev eloping energy efficient thermal management strategies for the A/C system. In [12], the analysis of A/C system was performed and the optimal compressor and fan speed controls have been in vestigated. W e also studied the speed sensitivity of the A/C system efficiency in [13], which has been exploited to reduce the A/C system energy consumption via model predicti ve control (MPC). Reference [14] demonstrated the impact of uncertain traffic information on optimizing the A/C ener gy efficienc y and ev aluated the overall vehicle fuel economy ov er different driving cycles. In this paper , a precision cooling strate gy (PCS) is pro- posed, attempting to address the trade-of fs between the occupant thermal comfort and the A/C system ener gy con- sumption [12]. In order to quantify such trade-of fs, a new performance metric, discharge air cooling power (D ACP), is defined as follows: P DAC P ( t ) = c p ( T cab ( t ) − T discharg e ( t )) W bl ( t ) , (1) where c p is the specific heat capacity of air , T cab represents the av erage cabin temperature, T discharg e represents the discharge air temperature, namely , the temperature of the air after the heat exchange with the ev aporator , and W bl represents the air flow rate into the cabin deli vered by HV AC blower . Note that the D A CP in (1) is defined for the case when A/C is running in the recirculation mode, which is also the simulation condition in vestigated hereafter . If fresh air mode is considered, T cab should be replaced by T amb (ambient temperature). The integral of D A CP over time is referred to as the discharge air cooling energy (D ACE) and it is denoted by E DAC E . A key assumption behind this definition is that there exists a time-varying trajectory of P DAC P ,targ that, if it is precisely tracked, the occupant 1 comfort requirement can be satisfied. In the definition, two major v ariables, temperature and flow rate of the cooling air , are considered to primarily impact the comfort. Compared with the average room temperature, which is commonly used as the performance metric in building HV A C control [15], [16] and also in our previous works [13], [14], [17], the choice of P DAC P accounts for special characteristics of the automotiv e A/C system. In a passenger vehicle, occupants sit close to the vents and directly feel the temperature and the amount of air flo w . The occupants’ sensation to A/C is therefore not directly correlated to a verage cabin temperature but instead may be better captured by the ne w performance index proposed here. W e note that realistic occupant comfort requirements are much more complicated than the P DAC P ,targ metric defined here and that research is currently ongoing to define better performance metrics for guiding the design of HV A C control systems in automotiv e applications. Besides the precise tracking of P DAC P ,targ which is intended to pre vent ov er-cooling of the cabin, the idea similar to [13] of exploiting the speed sensitivity of A/C system efficiency will also be pursued. Specifically , the work presented in this paper may be directly compared with our previous work done in [13] since they both explore the speed sensitivity of the A/C system and apply the model predictive control (MPC) design framework. Howe ver , the proposed MPC-based PCS has the follo wing features that differentiate it from that of [13]: 1) A ne w performance metric, D A CP , is proposed instead of applying av erage cabin temperature in [13] and [14]. The proposed PCS is designed to precisely track the prescribed and possibly time-varying trajectory of D A CP . 2) A new predictiv e model structure is proposed which, unlike the one used in [13], takes into account the transient effect of air flow rate on ev aporator wall temperature. 3) The proposed PCS coordinates the A/C operation with vehicle speed by simply manipulating the design parameters in the cost function of the MPC prob- lem. Note that in our pre vious work, such a coor- dination was achieved by manipulating the operating constraints, which requires additional design efforts. The rest of the paper is organized as follows. Section II introduces the A/C system in a power-split HEV and the physics-based system model. Next, the predictive model dev elopment is described in Section III. The design pro- cedures of the PCS are detailed in Section IV. Section V presents the simulation results of the proposed strategy , which demonstrates energy sa ving potentials, follo wed by the conclusions in Section VI. I I . S Y S T E M D E S C R I P T I O N A N D H I G H - FI D E L I T Y AC S I M M O D E L A. A/C System in P ower-split HEVs A typical A/C system configuration for power -split HEVs is considered in this paper , see Fig. 1. There are two major loops within the A/C system, the v apor compression loop shown in yellow and the air supply loop shown in dark blue. In this HEV configuration, battery directly supplies the electrical po wer for the electrically driven compressor and the electric ducted fan (EDF), which consume most of the energy in the A/C system. Assuming a charge sustaining operation for the battery , the ener gy consumed by the A/C system will be e ventually supplied from the fuel energy , con verted by the engine and the power split device (PSD). Fig. 1. Schematic of the A/C system in a power -split HEV B. A CSim Model and Speed Sensitivity Analysis Physics-based modeling of the A/C system can be very challenging [18], especially for modeling the vapor com- pression cycle shown in Fig. 1. In this study , we utilize the Ford A/C system model, which is referred to as ACSim, for control design and validation purposes. General system schematics are illustrated in Fig. 2. This model simulates the entire A/C system for a passenger car and is integrated with the controller module which represents two levels of controls. A higher-le vel controller is inside the climate control panel block, and it reflects the control settings (e.g. blower le vel and temperature set-point) from the real vehicle, which directly affect the occupant thermal comfort. Lower - lev el controllers take the command from the control panel and regulate the beha viors of the physical system via the electric compressor control and the front end air flo w control. Boundary conditions are set according to different simulation requirements. Fig. 2. Schematics of A CSim simulation model Next, the speed sensiti vity of A/C system ener gy consump- tion is demonstrated. In Fig. 3, it can be seen that with almost the same P DAC P trajectories (instantaneous de viation within 2 1% ), the power trajectories for compressor and EDF shift downw ards as vehicle speed increases. Fig. 4 summarizes the total A/C energy consumption ( E tot = E comp + E E DF , where E comp and E E DF represent the energy consumed by compressor and EDF , respectively) for each case shown in Fig. 3. Index values from 1 to 10 correspond to constant vehicle speed values from 0 k m/h to 90 k m/h , respec- tiv ely . As the simulation results show , the total A/C energy consumption is reduced by 13 . 6% comparing case 10 with case 1 , while the cooling performance is kept the same. This observation is consistent with the findings in [13]. This speed sensitivity of A/C system efficienc y will be exploited in the PCS design for reducing the energy consumption. Fig. 3. Sensitivity of the A CSim model responses to vehicle speed. Fig. 4. T otal A/C energy consumption decreases as vehicle speed increases. I I I . S I M P L I FI E D A / C S Y S T E M M O D E L F O R M P C D E S I G N A. Pr edictive Model Structur e Like other high-fidelity A/C system models [18], A CSim model in volv es detailed thermal and fluid dynamics of the refrigerant and has a large number of look-up tables from calibrations, which make it impossible to be used in a controller design. Therefore, a simplified model of the system dynamics is necessary . Specifically , the follo wing discrete- time model structure is proposed to satisfy the requirements for MPC-based design: T ev ap ( k + 1) = f T evap = T ev ap ( k ) + γ 1 ( T ev ap ( k ) − T ev ap,tar g ( k )) + γ 2 ( T ev ap ( k ) − T amb ) W bl ( k ) + γ 3 ( T ev ap ( k ) − T amb )∆ W bl ( k ) + γ 4 , (2) W bl ( k + 1) = f W bl = W bl ( k ) + ∆ W bl ( k ) , (3) T discharg e ( k ) = f T discharg e = γ 5 T ev ap ( k ) + γ 6 T cab ( k ) + γ 7 . (4) In (2)-(4), T cab , T ev ap , T amb , W bl and T discharg e repre- sent the cabin average air temperature, the e vaporator wall temperature, the ambient temperature, the blower air flo w rate, and the discharge air temperature, respectively . All temperatures are in o C and the blower air flow rate has the units of k g /s . The model states are T ev ap and W bl . The model inputs are the incremental blower air flow rate, ∆ W bl , and the e vaporator wall temperature tar get, T ev ap,tar g . The model parameters, γ i ( i = 1 , 2 , ..., 7) , are constants and to be identified for matching the system responses. This predictiv e model is nonlinear because of the multiplicativ e coupling between model states and inputs in (2). Compared with the ev aporator wall temperature model proposed in [13], which is modeled as a first-order system with T ev ap,tar g as an input, air flow ef fects ( W bl and ∆ W bl ) are considered in this work based on the observation that with fixed T ev ap,tar g , T ev ap changes when air flo w changes. B. Model Identification and V alidation Next, the A CSim model is simulated with different ran- dom sinusoidal input signals. The system responses are collected with the sampling time, T s = 3 sec , to iden- tify the unkno wn parameters in (2) and (4). The re- sulting identified parameters are γ = [ γ 1 γ 2 ... γ 7 ] = [ − 0 . 084 , − 0 . 487 , − 1 . 121 , − 1 . 730 , 0 . 729 , 0 . 690 , − 11 . 457] . Fig. 5 provides the validation results of the simplified predictiv e model for matching the outputs from ACSim model. It confirms the good accuracy of the proposed model in modeling the key dynamics of the A/C system. Fig. 5. Model v alidation results of ∆ T evap ( k ) = T evap ( k + 1) − T evap ( k ) and T discharg e ( k ) for given sinusoidal excitations. I V . M P C - B A S E D P R E C I S I O N C O O L I N G S T R A T E G Y ( P C S ) In this section, the problem formulation of the proposed PCS is described, whose objectiv e is combining the mini- mization of ov erall A/C energy consumption and the tracking error with respect to the target P DAC P ,targ trajectory . As may be observed in Fig. (3), the compressor power is dominant as compared with the EDF power . Therefore, we decide to use the predicted compressor power in the cost function to reflect the ov erall system energy consumption in the proposed nonlinear MPC (NMPC) problem. According 3 to [15], P comp can be estimated by: P comp = c p C O P ( k ) ( T cab ( k ) − T discharg e ( k )) W bl ( k ) , (5) where c p = 1008 J / ( kg · K ) is the specific heat capacity of air at constant pressure, C O P represents the A/C system coefficient of performance [19]. Note that, COP may be time- varying, howe ver , in the MPC problem formulation, it is as- sumed to be constant over the prediction horizon and will be updated based on current measurements at the beginning of each control iteration. Fig. 6 shows the comparison between the compressor power estimated using (5) and the actual compressor power computed by ACSim, which is based on the thermo-dynamics of the vapor-compression refrigeration system. Fig. 6. Estimated compressor power based on (5) compared with actual compressor power measured from ACSim. Then, we define the PCS strategy as the follo wing nonlin- ear optimization problem: min ∆ W bl T evap,tar g N p X i =0 ( P comp ( i | k ) + α · ( P DAC P ( i | k ) − β ( i | k ) · P DAC P ,targ ( i | k )) 2 ) , s.t. T ev ap ( i + 1 | k ) = f T evap ( i | k ) , W bl ( i + 1 | k ) = f W bl ( i | k ) , 0 o C ≤ T ev ap ( i | k ) ≤ T ev ap ( i | k ) , 0 . 05 k g /s ≤ W bl ( i | k ) ≤ 0 . 15 k g /s, − 0 . 05 k g /s ≤ ∆ W bl ( i | k ) ≤ 0 . 05 k g /s, 2 o C ≤ T ev ap,tar g ( i | k ) ≤ 10 o C, T ev ap (0 | k ) = T ev ap ( k ) , W bl (0 | k ) = W bl ( k ) . (6) In (6), ( i | k ) denotes the prediction for the time instant k + i made at the time instant k , f T evap and f W bl are from (2) and (3). In the cost function, α and β are design parameters. In this study , α is set to be a large positiv e constant, e.g., 10 5 , to ensure the tracking performance. While β can be either constant, 1 , or time-varying with respect to vehicle speed previe w , depending on the operating scenarios of the A/C system. Detailed design of β and its impact will be discussed in the next section. P DAC P ,targ and T ev ap represent the target DA CP trajectory and the time-v arying upper bound for T ev ap , respectiv ely , which are assumed to be known ov er the prediction horizon. Constant constraints for other variables are giv en according to the system operating requirements. For the results presented in the next section, the prediction horizon, N p , is set to be 10 . The NMPC problem described by (6) is solved numerically using the MPCT ools package [20]. This package exploits CasADi [21] for automatic dif ferentiation and IPOPT algorithm for the numerical optimization. V . S I M U L A T I O N R E S U LT S A N D P E R F O R M A N C E E V A L U A T I O N S A. Simulation Results on the Simplified Model The performance of the proposed MPC-based PCS is first ev aluated on the simplified system model dev eloped in Section III. In Fig. 7, an example of simulating a typical summer cabin cool-down scenario is sho wn. In order to ensure precise tracking of P DAC P ,targ , constant β = 1 is set. V ehicle speed trajectory from SC03 cycle is applied. It can been from Fig. 7 that all the state and input constraints in red dotted lines are satisfied, and perfect tracking of P DAC P ,targ is achie ved except for the initial transient period. In this simulation, T cab and C O P are assumed to be constant values. Fig. 7. Performance ev aluation of the proposed PCS on the simplified A/C system model. B. Simulation Results on the A CSim Model Next, the proposed control strategy is integrated in closed- loop with the A CSim model. Fig. 8 illustrates the implemen- tation in Simulink ® . The model predictive controller takes sensor measurements, predefined P DAC P ,targ trajectories, and future vehicle speed from the traffic prediction as inputs, solves the optimization problem defined by (6), and provides the control inputs to the ACSim model. In this case study , the proposed MPC controller updates the control inputs e very 3 sec , while the outputs from A CSim model is originally sampled at 0 . 1 sec . The same cabin cool- down process is considered and P DAC P ,targ trajectory is calculated from a Ford benchmark case over SC03 cycle. In addition, a heuristic design of β with respect to the speed profile from SC03 cycle is applied. The dependence of β on different vehicle speed can be seen from Fig. 9. The idea behind such heuristic design of β coincides with the exploration of the speed sensitivity of A/C operation, which is that ener gy efficienc y may be impro ved by shifting the A/C load from lo w efficienc y region (at lo w vehicle speed) to high efficienc y region (at high vehicle speed). In the simulation with time-v arying β , the vehicle speed over the prediction horizon is assumed to be known via connecti vity technology , 4 Fig. 8. Schematics of integrating the MPC-based PCS with ACSim model in Simulink ® . thus the values of β over the prediction horizon are also av ailable. Fig. 10 compares the benchmark case with the NMPC results with constant β and speed-dependent β , respecti vely . As observed from the results, for the constant β case, the NMPC regulates the control inputs to achiev e precise tracking of the P DAC P ,targ trajectories. For the speed- dependent β , the actual P DAC P varies around the target. In addition, clear coordination between the control inputs and vehicle speed can be seen in the speed-dependent β case indicating successful load shift as intended. In this simulation, T cab and C O P are assumed to hav e constant values along prediction horizon for each control iteration and are updated using measurements at e very sampling instant. Additional system responses including the trajectories of P comp , P E DF , T cab and T discharg e are sho wn in Fig. 11. Detailed energy consumptions of different cases are reported in T able I. It can be seen that, compared with the benchmark case, the total A/C energy consumption is reduced by 4 . 9% for the MPC results with constant β . This is because for matching the P DAC P ,targ , the MPC-based controller tends to reduce the air flow ( W bl ) towards the end of the cycle, which results in the same pull-down period of the cabin temperature ( T cab ) but slight increase in final cabin temperature (with difference less than 1 o C ). In other words, the actual cooling capacity of the A/C system is reduced for the MPC case while achie ving the same occupant thermal comfort lev el according to the proposed metric. If we compare the MPC results with speed-dependent β with the ones with constant β , we can see that the energy consumption of the A/C system may be further reduced by 0 . 8% while providing 1 . 1% higher E DAC E . The ener gy sa ving achie ved by A/C load shifting can be ev en higher if designing β optimally instead of designing it in a heuristic way . Fig. 12 reports the elapsed CPU time for each control iteration compared with 3 sec for the MPC sampling time. This result is obtained based on a 2 . 9 GH z W indows computer for the speed-dependent β case considered in this section. Note that the worst case ex ecution time is significantly lower than the av ailable time. These results suggest that our NMPC approach could be computationally feasible ev en in slower ECU as the ECU implementation will be based on highly optimized C-code (rather than Matlab) that, based on our past experience, is likely to offset the processor differences. Fig. 9. Heuristic design of speed-dependent β . Fig. 10. Comparison between the proposed PCS and the benchmark case on the A CSim model (key control variables). Fig. 11. Comparison between the proposed PCS and the benchmark case on the A CSim model (A/C energy consumptions and temperatures) . V I . C O N C L U S I O N S A novel MPC-based precision cooling strategy (PCS) was proposed in this paper to exploit the energy sa ving opportunities for the thermal management of automotiv e A/C system. The proposed PCS was designed to precisely track 5 T ABLE I A / C S Y S T E M E N E R G Y C O N S U M P T I O N C O M PA R I S O N S O F A P P LYI N G C O N S TA N T β = 1 A N D S P E E D D E P E N D E N T β W I T H R E S P E C T T O T H E B E N C H M A R K . E DAC E [kJ] E comp [kJ] E E DF [kJ] E tot [kJ] Benchmark 1378.4 689.4 103.2 792.6 Constant β = 1 1377.7 (-0.1%) 653.4 100.6 754.0 (-4.9%) Spd-dependent β 1392.0 (+1.0%) 647.2 100.6 747.8 (-5.7%) Fig. 12. Elapsed CPU time for computing MPC solution for each control instant on A CSim model. the prescribed and time-v arying trajectory of the dischar ge air cooling power (DA CP), which represents the desired cabin cooling requirement. A physics-based A/C system model, A CSim, dev eloped by Ford Motor Company was adopted as the virtual test bench in this study . T o satisfy the requirements of MPC-based design, a simplified predicti ve model was developed based on the ACSim model responses. Next, the proposed MPC-based PCS was formulated by solving a nonlinear optimization problem, which minimizes (i) the tracking error with respect to the D A CP trajectory target, (ii) the energy consumption of the A/C system. The performance of the proposed PCS was ev aluated in closed- loop with A CSim model. Accurate tracking performance and constraint enforcement on system states and inputs hav e been demonstrated. It was also shown that, comparing with a Ford benchmark case over SC03 test cycle, the MPC-based solution of tracking the same D ACP trajectory sa ves 4 . 9% electrical energy at the expense of slightly increased cabin temperature tow ards the end of the simulation. In addition, by exploiting the vehicle speed previe w , the A/C system energy consumption can be further reduced. 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