# Adaptive Model Predictive Control-Based Energy Management for Semi-Active Hybrid Energy Storage Systems on Electric Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. The Hybrid Energy Storage System Modeling

#### 2.1. LiB Model

_{bb}approximate the voltage source of the LiB, in which E is a constant evaluated as the open circuit voltage (OCV) value when the LiB is fully discharged. V

_{bb}represents a linear relationship between the variation of source voltage and variation of remaining source energy, just like a capacitor approximately, and C

_{bb}is corresponding capacity. C

_{bp}and R

_{bp}reflect the electrode polarization phenomenon; R

_{bb}is the equivalent dc resistance. V

_{bl}is the cell terminal voltage, P

_{b}is pack power, n

_{b}is cell number in pack.

_{init}is the value of BSOC when the simulation starts, which is set as 0.7. Q

_{b}is the LiB cell nominal capacity.

_{bb}:

_{bb}/b, E = a [32]. V

_{bb}and V

_{bp}are two states expressed by:

_{bl}is expressed by:

_{b}is obtained:

_{b}is the only manipulated variable of the HESS.

_{bp}, R

_{bb}and R

_{bp}are fitted under different BSOC (0.1 as interval). As BSOC is limited to [0.2, 0.9], R

_{bb}, R

_{bp}and C

_{bp}are evaluated by taking an average within the range. The bi-directional DC/DC converter is simplified as an efficiency module with constant efficiency of 95%.

#### 2.2. UC Model

_{0}and C

_{1}) and the part reflecting electrode kinetics (R

_{ub}, R

_{up}and C

_{up}). In the main energy storage part, C

_{0}and C

_{1}are connected in parallel. C

_{0}is characterized by constant capacitance, and C

_{1}is characterized by capacitance varying linearly with the voltage V

_{ub}. They characterize the nonlinearity of the source jointly. In the electrode kinetics part, R

_{ub}represents the Ohmic resistance, while R

_{up}and C

_{up}represent polarization resistance and polarization capacitance separately.

_{ub}and V

_{up}are two states calculated by:

_{ub,max}is 2.8 V according to the manual.

_{ul}is expressed as:

_{u}is represented as:

_{u}is replaced by P

_{d}− P

_{b}, indicating that P

_{b}and P

_{d}decide the working conditions of UC jointly. V

_{ub}, i

_{u}and V

_{ul}reveal strong nonlinearity, and standard state space model is insufficient to characterize the model precisely.

## 3. AMPC-Based Energy Management Implementation

_{b}and i

_{u}have real solutions, the following two expressions are added to outputs:

_{bb}and V

_{ub}who have engineering constraints are also added to outputs. Besides, as state estimator is required, the model observability must be guaranteed. To this end, V

_{b}

_{l}and V

_{ul}are added to outputs as measured variables. By this means, two current sensors and two voltage sensors are needed. The final model is with inputs U = [P

_{b}, P

_{d}], internal states X = [V

_{bb}, V

_{bp}, V

_{ub}, V

_{up}] and outputs Y = [V

_{bb}, i

_{b}, V

_{bl}, y

_{b}, V

_{ub}, i

_{u}, V

_{ul}, y

_{u}].

#### 3.1. Control-Oriented Model Implementation

#### 3.1.1. Linearization

_{t}, U

_{t}) by first approximation of Taylor expansion. The linearized plant is described as:

_{0},U

_{0}) − AX

_{0}− BU

_{0}and g(X

_{0},U

_{0}) − CX

_{0}− DU

_{0}are set as measured disturbances with constant inputs of 1, and the new inputs are augmented as U = [P

_{b}, P

_{d}, M

_{d}]. The state space model is augmented as:

#### 3.1.2. Eliminating Direct Feedthrough

_{a}to inputs, as shown in Equation (15). T

_{a}is chosen as one-tenth or smaller of the AMPC sampling time [37,38]. With this method, the original inputs are turned into new states and new inputs are identical to old ones except a slight delay:

_{a}= [V

_{bb}, V

_{bp}, V

_{ub}, V

_{up}, P

_{b}, P

_{d}, M

_{d}], and new inputs are U

_{a}= [P

_{ba}, P

_{da}, M

_{da}]. The delay in the inputs intrinsically causes a slight model mismatch, which AMPC is good at dealing with.

#### 3.1.3. Model Discretization

#### 3.1.4. LiB Current Fluctuation Suppression

_{b}is expressed by the second row of ∆Y, in which coefficients vector of X

_{a}is expressed by G

_{dib}, coefficients vector of U

_{a}is expressed by H

_{dib}. ∆i

_{b}is expressed as:

_{A}= [V

_{bb}, V

_{bp}, V

_{ub}, V

_{up}, P

_{b}, P

_{d}, M

_{d}, ∆i

_{b}], inputs U

_{a}= [P

_{ba}, P

_{da}, M

_{da}] and outputs Y

_{A}= [V

_{bb}, i

_{b}, V

_{bl}, y

_{b}, V

_{ub}, i

_{u}, V

_{ul}, y

_{u}, ∆i

_{b}], as well as control-oriented model matrices G

_{A}, H

_{A}and C

_{A}.

#### 3.2. Optimization Problem

_{ba}is the only manipulated variable, P

_{da}and M

_{da}are measured disturbances, i

_{b}, i

_{u}, V

_{bl}and V

_{ul}are measured outputs, V

_{bb}, V

_{ub}, y

_{b}, y

_{u}and ∆i

_{b}are unmeasured outputs.

_{y}is the number of outputs, p is prediction horizon, w

_{j}is the weight of jth output, ${\rho}_{\epsilon}$ is the constraints violation penalty weight, and ε is the slack variable at interval k. J involves a trade-off between the output reference tracking and constraint violation by weighting, and corresponding QP decision is [U

_{a}(k|k) U

_{a}(k + 1|k) … U

_{a}(k + p − 1|k) ε]. The first part of J represents the output reference tracking with weight matrix w

_{j}, while the second part shows the constraint violation with weight ${\rho}_{\epsilon}$. When ${\rho}_{\epsilon}$ increases, ε tends to be smaller or zero, meaning J is more inclined to suppress constraint violation. If ε is zero, U

_{a}and Y

_{a}are strictly limited within constraints; if ε is positive, at least one soft constraint is reached. While, when ${\rho}_{\epsilon}$ is smaller, ε tends to be greater, soft constraints are more likely to be activated, and the controller performance can be substandard. S

_{y,j}and s

_{u}are scaling factors (SFs) whose roles are to scale inputs and outputs to the same magnitude. ECRs are nonnegative parameters used to soften inputs and outputs constraints, the larger the ECRs are, the greater constraints violation are allowed to obtain optimal solution.

_{Au}is coefficient matrix of P

_{ba}, and H

_{Av}is coefficient matrix of [P

_{da}, M

_{da}], the model in Equation (22) is rewritten as:

_{au}= P

_{ba}and U

_{av}= [P

_{da}, M

_{da}], based on Equation (23), the predicted output is:

_{au}into Equation (25), the predicted output is expressed as:

_{Au}is coefficient matrix of P

_{ba}from H

_{A}, H

_{Av}is coefficient matrix of [P

_{da}, M

_{da}] from H

_{A}. As shown in Equation (26), G

_{A}, H

_{A}(H

_{Au}and H

_{Av}) and C

_{A}are used by QP solver for calculation.

_{b}are not set for they are limited intrinsically by the limitation of V

_{bb}and i

_{b}, and their ECRs are set as 1 by default. V

_{bb}is limited to the range of 0.18 V~0.81 V based on BSOC constraints, both constraints leave some margin and can be violated, ECR

_{1,min}and ECR

_{1,max}are set as 1. Constraints for i

_{b}are −3.2 A~6.4 A according to the manual, the lower bound is strictly limited by the manufacturer, while the upper bound can be set as high as 10 A in our experiment, ECR

_{2,min}is 0 and ECR

_{2,max}is 1. Constraints for V

_{bl}and V

_{ul}are not set for they are intrinsically limited by other states, corresponding ECRs are set as 1. Outputs y

_{b}and y

_{u}must be non-negative, and the constraints are not allowed to be violated. Considering linearization error, the lower bounds for y

_{b}and y

_{u}are set as 0.5, ECR

_{3,min}and ECR

_{6,min}are 0. V

_{ub}is limited to meet the voltage range of DC bus, cell voltage range is thus between 1.5 V~2.7 V. As the energy stored in the UC increases exponentially with V

_{ub}, the upper bound would be violated slightly by absorbing much energy, which is acceptable, ECR

_{4,max}is 1. While the lower bound would be violated severely by even delivering little energy, which is unacceptable, ECR

_{4,min}is 0. Constraints for i

_{u}are −1200 A~1200 A and can be violated, for huge current do not harm the UC cell obviously, ECR

_{5,min}and ECR

_{5,max}are 10. Constraints for ∆i

_{b}are not set for the constraints of i

_{b}intrinsically avoid severe variation of ∆i

_{b}, meanwhile weights for i

_{b}and ∆i

_{b}prevent them from wide variation.

#### 3.3. Controller State Estimation

_{A}, H

_{A}and C

_{A}. The model in Equation (22) is augmented with noise vector w(k) and v(k) [26]:

_{2}, SF

_{3}, SF

_{6}, SF

_{7}] considering influence of scaling.

- (1)
- Prediction updating:$${\widehat{X}}_{A}(k|k-1)={G}_{A}{X}_{A}(k-1|k-1)+{H}_{A}{U}_{a}(k)$$$$P(k|k-1)={G}_{A}P(k-1|k-1){G}_{A}^{T}+Q$$
- (2)
- Measurement correction:$${K}_{g}(k)=\frac{P(k|k-1){C}_{A}^{T}}{{C}_{A}P(k|k-1){C}_{A}^{T}+R}$$$${\widehat{X}}_{A}(k|k)={\widehat{X}}_{A}(k|k-1)+{K}_{g}(k)({Y}_{A}(k)-{C}_{A}{\widehat{X}}_{A}(k|k-1))$$$$P(k|k)=(I-{K}_{g}(k))P(k|k-1)$$
_{g}(k) is gain matrix for measurement correction, ${\widehat{X}}_{A}(k|k)$ is the corrected states prediction of current interval, P(k|k) is the corrected error covariance matrix of current interval. It’s obvious that time-varying G_{A}, H_{A}and C_{A}influence the value of K_{g}significantly.

#### 3.4. Measured Disturbance

_{da}and M

_{da}. M

_{da}is a constant set as 1, while P

_{da}is HESS power demand determined by vehicle power balance equation shown below:

_{D}is drag coefficient, A is windward area, δ is correction coefficient of rotating mass, a is vehicle acceleration.

## 4. Results and Discussion

#### 4.1. Sampling Time, Prediction Horizon and Scaling Factor

_{d}) and Ts are determined, prediction horizon (p

_{h}) is calculated by p

_{h}= p

_{d}/Ts. p

_{h}decides how many steps the model prediction is conducted, as p

_{h}increases, the prediction accuracy gradually decreases. p

_{h}also decides the size of the matrices in the QP problem, as p

_{h}increases, the matrices become large and the computation burden is heavy. The AMPC with different Ts and p

_{h}is conducted under UDDS, and the results are shown in Table 3. Finally, Ts is set as 0.1 s, p

_{d}is chosen as 2 s, p

_{h}is 20.

_{b}, P

_{d}, Md] are initially selected as [10,000, 10,000, 1], and SFs for outputs [V

_{bb}, i

_{b}, V

_{bl}, y

_{b}, V

_{ub}, i

_{u}, V

_{ul}, y

_{u}, ∆i

_{b}] are initially selected as [0.0005, 1, 1, 1, 0.01, 10, 1, 1, 1]. Among them, SF of P

_{b}and i

_{u}are found to be sensitive to the simulation results. Table 4 shows the results under different SFs:

_{b}and i

_{u}are reselected as 1000 and 30.

#### 4.2. Model Adaptivity Verification

_{ub}estimation gradually deviates from the real value, and the error is accumulative. This is because the gain matrix solved by SSKF is constant through the simulation, an the state estimation error is not applied to update the gain matrix. For the same reason, excessive deviation happens in the remaining four estimations. In Figure 6, TVKF exhibits a pretty precise estimation. TVKF of AMPC solves gain matrix with updated G

_{A}, H

_{A}and C

_{A}at each control interval, it is obvious that varying G

_{A}, H

_{A}and C

_{A}could approximate the real HESS model better, TVKF thus significantly outperforms SSKF in estimation accuracy.

_{A}, H

_{A}and C

_{A}elements of AMPC under UDDS are shown in Figure 7, in which elements with marked change are shown in bold. It’s obvious that elements variation in three matrices are non-negligible, further indicating that a single model is unable to approximate the real HESS, and SSKF is unable to make accurate estimation.

_{b}, Figure 8b,c is zooms of Figure 8a. In Figure 8b, the LiB current of SMPC is charging and discharging dramatically, which is not observed in AMPC. In Figure 8c, the LiB current of SMPC is fluctuating remarkably around 0 when HESS is charging. Furthermore, the LiB current of SMPC distinctly goes beyond that of AMPC. All the situations mentioned above lead to an increase of LiB Ah-throughput, as shown in Figure 8d. The phenomena indicate that time-varying prediction model matrices as well as accurate state estimation by TVKF significantly improve accuracy of control action calculated by QP solver of AMPC. Besides, as SMPC isn’t able to estimate states precisely, the constraints on V

_{ub}and y

_{u}may be violated, resulting in SMPC failure, which will cause damage to HESS.

#### 4.3. Driving Condition Uncertainty Adaptation Verification

#### 4.3.1. DP and RBC Description

_{b}is calculated by:

_{b}is calculated by P

_{d}− P

_{u}, in which P

_{u}is obtained from USOC variation.

_{d}and USOC are inputs, P

_{b}is the output. P

_{b}

_{,avg}represents the average power delivered by LiB, P

_{b}

_{,char}represents the complementary power supplied from LiB to UC to maintain adequate energy for coming peak power demand. Both of them are tuned and keep constant for all driving cycles. Hysteresis control is shown in Figure 10b, which is designed for preventing USOC from frequent fluctuation round the bounds. The USOC range for hysteresis control is determined based on the UC capacity. As the capacity increases exponentially with USOC, the upper range could be set smaller compared with the lower range. Besides, considering the DC bus voltage constraint, the upper range is chosen as [0.9, 0.92], the lower range is chosen as [0.54, 0.59].

#### 4.3.2. EMSs Results Comparison

_{ub}frequently reaches the lower bound. This situation is dealt with by AMPC very softly, for V

_{ub}lower bound isn’t allowed to be violated. In addition, the AMPC operational mechanism of dealing with hard constraints is shown in Figure 11b,c, which are a zoom from 450 s to 470 s of Figure 11a,d, respectively. We can see from Figure 11b that at about 453 s, when V

_{ub}is around 1.65 V and P

_{d}is 20 kW, P

_{b}starts to increase, while P

_{u}gradually decreases to cope with the upcoming lower bound of V

_{ub}. After about 10 s, V

_{ub}reaches the lower bound softly without going beyond it. By this means, AMPC avoids any hard constraints violation. This mechanism is essential to Ah-throughput minimization, as each violation of V

_{ub}will cause an extra charging process from LiB to UC, which significantly increases LiB Ah-throughput. Besides, pulse power in P

_{u}is observed when transient power demand comes across, as mentioned in introduction. This phenomenon happens several times in Figure 11b, and would inevitably cause damage to LiB if it’s passive, which is exactly what the HESS tries to avoid. Hence, designing LiB as the controlled component is reasonable and necessary.

_{b}of three EMSs under a continuous peak power demand which lasts for about 20 s. With the peak demand, optimal i

_{b}of DP changes gradually and magnitude is satisfactory, for peak power demand is known in advance. While, i

_{b}of AMPC is almost 0 at first to avoid the increase of LiB Ah-throughput, and gradually increases when USOC is about to fall to the lower bound to avoid violation. Though the i

_{b}of AMPC is relatively larger, the duration is shortened significantly by QP solver compared with DP and RBC, and the LiB Ah-throughput is reduced through the simulation greatly, indicating excellent flexibility and adaptation of AMPC. LiB current i

_{b}of RBC keeps nearly constant at first for P

_{b}keeps at P

_{b}

_{,avg}to maintain USOC. At about 200 s, a sudden change in i

_{b}appears when USOC reaches the lower bound, as shown in Figure 12e. This indicates that RBC is rigid in handling operation mode transitions caused by constraints, and adjustment of USOC by constant P

_{b}

_{,avg}is poor. In Figure 12a, i

_{b}of DP and AMPC remain nonnegative, while with RBC, LiB charges several times. One of the phenomena is shown in Figure 12c. Referring to Figure 12e, and we can find that the situation appears due to USOC reaches upper bound, again indicating that constant P

_{b}

_{,avg}can’t adjust USOC flexibly to leave a margin for the braking energy. Consequently, frequent charge obviously increases LiB Ah-throughput, as shown in Figure 12d. As AMPC minimizes i

_{b}, energy in UC is always utilized firstly, and USOC always leaves a margin for braking energy, charging to LiB hardly appear. When the power demand is 0, LiB outputs a very small current to UC with DP, which adjusts USOC to deal with peak power demand. Though RBC designs P

_{b}

_{,avg}to simulate this action, P

_{b}

_{,avg}of RBC can’t be real-time optimized based on future demand as well as control target. In Figure 12e, USOC of AMPC fluctuates mainly at the bottom of the range, whereas USOC of RBC fluctuates mainly at the top of the range, again revealing that with AMPC, HESS can take better advantage of UC as a buffer, and absorb more braking energy to reduce LiB Ah-throughput. As a result, when encountering changing driving conditions, AMPC makes the best use of UC as a buffer, while ensuring UC voltage remains within its range, revealing considerable flexibility and adaptivity. Conversely, RBC is rigid in managing bound problems, meanwhile P

_{b}

_{,avg}can’t be adjusted for real-time, RBC adaptability is poorer and the result is not optimal compared with AMPC.

#### 4.4. Weights

_{b}and ∆i

_{b}are to minimize simultaneously, w

_{2}and w

_{7}should be adjusted. Fix w

_{2}at 1, and set w

_{7}as 1, 5, 10 and 20, simulation results are shown in Figure 13. From Figure 13a we can see that, weight adjustment significantly influences the AMPC control performance. When w

_{7}increases, i

_{b}changes more and more slowly, LiB Ah-throughput increases for this reason and accumulative ∆i

_{b}absolute reduces, as shown in Figure 13b,d, while, when w

_{7}is 20, the trend has been broken. As shown in Figure 13a,c, i

_{b}fluctuates severely at 100 s~500 s, ∆i

_{b}absolute inevitably increases. As a result, both Ah-throughput and accumulative ∆i

_{b}absolute significantly increase during this period, as shown in Figure 13b,d. The accumulative ∆i

_{b}absolute when w

_{7}is 20 is nearly the same with that when w

_{7}is 5, which is conflicting with the original target of increasing the weight. The situation arises for two reasons: (1) to suppress i

_{b}change; (2) to provide energy to UC so that UC could face huge power demand fluctuation. To satisfy two conditions simultaneously, i

_{b}absolute has to retain high magnitude and changes drastically between positive and negative. As a result, when w

_{7}is too big, it’s difficult to obtain optimal solution within all constraints.

_{w}= w

_{7}/w

_{2}, simulation results under different w

_{2}and k

_{w}are listed in Table 7 and Table 8. No matter how much w

_{2}is, when k

_{w}remains unchanged, LiB Ah-throughput and accumulated ∆i

_{b}are always the same, indicating that k

_{w}is the only decision variable no matter how w

_{2}and w

_{7}change.

_{w}increases from 0.1 to 20, LiB Ah-throughput increases gradually as well, while accumulated ∆i

_{b}first decreases then increases, and the minimum value appears when k

_{w}is 10 or 15. As LiB Ah-throughput when k

_{w}is 10 is significantly smaller than that when k

_{w}is 15, we can conclude that k

_{w}should not exceed 10 when both goals are optimized. Based on analysis above, when setting w

_{2}as 1, and if the ∆i

_{b}is to taken into account, w

_{7}should be set between 5 and 10 (e.g., k

_{w}range is between 5 and 10). The proposed AMPC is capable of optimizing multiple objects simultaneously by appropriate weighting, and it’s suitable for designing EMS of HESS which usually includes various targets.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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- QP Solver. Available online: https://cn.mathworks.com/help/mpc/ug/qp-solver.html (accessed on 13 May 2017).

**Figure 5.**States values estimated by SSKF of SMPC. (

**a**) V

_{bb}estimation; (

**b**) V

_{bp}estimation; (

**c**)V

_{ub}estimation; (

**d**) V

_{up}estimation; (

**e**) ∆i

_{b}estimation.

**Figure 6.**States values estimated by TVKF of AMPC. (

**a**) V

_{bb}estimation; (

**b**) V

_{bp}estimation; (

**c**) V

_{ub}estimation; (

**d**) V

_{up}estimation; (

**e**) i

_{b}estimation.

**Figure 8.**Simulation results comparison of AMPC and SMPC. (

**a**) LiB current comparison. (

**b**) LiB current comparison between 320 s and 390 s; (

**c**) LiB current comparison between 1170 s and 1220 s; (

**d**) LiB Ah-throughput comparison.

**Figure 11.**Power distributionof AMPC. (

**a**) Power distribution; (

**b**) Power distribution between 450 s and 470 s; (

**c**) V

_{ub}variation between 450 s and 470 s; (

**d**) V

_{ub}variation.

**Figure 12.**HESS states comparison under UDDS with DP, AMPC and RBC. (

**a**) LiB current comparison; (

**b**) LiB current comparison between 160 s and 220 s; (

**c**) LiB current comparison between 500 s and 640 s; (

**d**) LiB Ah-throughput comparison; (

**e**) USOC comparison.

**Figure 13.**Simulation results with different w

_{7.}(

**a**) LiB current; (

**b**) LiB Ah-throughput; (

**c**) LiB current rate; (

**d**) Accumulated LiB current rate.

Nominal Capacity | 3.35 Ah | Maximum Discharge Current | 6.6 A |

Nominal Voltage | 3.6 V | Maximum Charge Current | 2 A |

Voltage Range | 2.5 V~4.2 V | Specific Energy | 243 Wh/kg |

Rated Capacitance | 650 F | Absolute Maximum Current | 680 A |
---|---|---|---|

ESR_{DC} | 0.8 mΩ | Specific Power | 14 kW/kg |

Voltage Range | 0 V~2.8 V | Specific Energy | 4.1 Wh/kg |

Ah-Throughput/As | p_{d}/s | |||
---|---|---|---|---|

2 | 5 | 10 | ||

Ts/s | 0.1 | 387 | 387 | 398 |

0.2 | 391 | 391 | 400 | |

0.5 | 430 | 429 | 452 | |

1 | 654 | 577 | 712 |

Ah-Throughput/As | SF_{Pb} | |||
---|---|---|---|---|

100 | 1000 | 10,000 | ||

SF_{iu} | 5 | 389.5 | 398 | 551 |

10 | 386 | 390 | 492 | |

20 | 385.5 | 387 | 440 | |

30 | 385 | 386 | 418 |

V_{bb} | V_{bp} | V_{ub} | V_{up} | ∆i_{b} | |
---|---|---|---|---|---|

SSKF | 3.08 × 10^{−4} | 3.88 × 10^{−4} | 0.22 | 2.72 × 10^{−3} | 0.18 |

TVKF | 2.35 × 10^{−7} | 2.55 × 10^{−6} | 5.76 × 10^{−4} | 4.13 × 10^{−4} | 0.05 |

Ah-Throughput/As | AMPC | DP | Difference | RBC | Reduce |
---|---|---|---|---|---|

UDDS | 387 | 371 | 4.3% | 461 | 16.1% |

FTP75 | 635 | 594 | 6.9% | 718 | 11.6% |

India_urban | 462 | 438 | 5.5% | 601 | 23.1% |

NEDC | 605 | 561 | 7.8% | 635 | 4.7% |

HWFET | 850 | 786 | 8.1% | 861 | 1.3% |

Hybrid | 1870 | 1762 | 6.1% | 2000 | 6.5% |

average | / | / | 6.5% | / | 10.6% |

Ah-Throughput/As | w_{2} | |||
---|---|---|---|---|

1 | 10 | 20 | ||

k_{w} | 0.1 | 387 | 387 | 387 |

1 | 388 | 388 | 388 | |

5 | 407 | 407 | 407 | |

10 | 570 | 570 | 570 | |

15 | 761 | 761 | 761 | |

20 | 989 | 989 | 989 |

Accumulated ∆i_{b}/A | w_{2} | |||
---|---|---|---|---|

1 | 10 | 20 | ||

k_{w} | 0.1 | 236 | 236 | 236 |

1 | 217 | 217 | 217 | |

5 | 136 | 136 | 136 | |

10 | 82 | 82 | 82 | |

15 | 82 | 82 | 82 | |

20 | 122 | 122 | 122 |

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## Share and Cite

**MDPI and ACS Style**

Zhou, F.; Xiao, F.; Chang, C.; Shao, Y.; Song, C.
Adaptive Model Predictive Control-Based Energy Management for Semi-Active Hybrid Energy Storage Systems on Electric Vehicles. *Energies* **2017**, *10*, 1063.
https://doi.org/10.3390/en10071063

**AMA Style**

Zhou F, Xiao F, Chang C, Shao Y, Song C.
Adaptive Model Predictive Control-Based Energy Management for Semi-Active Hybrid Energy Storage Systems on Electric Vehicles. *Energies*. 2017; 10(7):1063.
https://doi.org/10.3390/en10071063

**Chicago/Turabian Style**

Zhou, Fang, Feng Xiao, Cheng Chang, Yulong Shao, and Chuanxue Song.
2017. "Adaptive Model Predictive Control-Based Energy Management for Semi-Active Hybrid Energy Storage Systems on Electric Vehicles" *Energies* 10, no. 7: 1063.
https://doi.org/10.3390/en10071063