Drivability-Related Discrete-Time Model Predictive Control of Mode Transition in Pre-Transmission Parallel Hybrid Powertrains
Abstract
:1. Introduction
2. Powertrain Configuration
3. Powertrain Modeling
3.1. Simulation-Oriented Model
3.1.1. Engine
3.1.2. Clutch
3.1.3. Motor
3.1.4. Transmission
3.1.5. Final Drive
3.1.6. Driving Axle Shaft
3.1.7. Longitudinal Vehicle Dynamics
3.2. Control-Oriented Model
4. Controller Design
4.1. Optimization Objectives
4.2. Control Principle
4.3. Equilibrium State
4.4. Control-Oriented Discrete-Time State Space Model
4.5. Optimization Problem Formulation
4.6. Optimization Solution
- Solve the optimization problem without inequality constraints:
- Check whether obtained in Step 1 satisfies the inequality constraint (46). If not, by introducing a Lagrange multiplier, compute , the clutch torque command and the motor output torque command :
- Check whether or not obtained in Step 2 satisfies the inequality constraints (47) and (48). If not, calculate the clutch torque command and the motor output torque command :
5. Results and Discussion
5.1. Parameter Selection
- Firstly, solve the following Riccati equation for finding the Riccati matrix :
- Secondly, compute the state feedback gain matrix :
- Thirdly, calculate the optimum input vector for the current sampling instant:
5.2. Performance in Nominal Conditions
5.3. Comparison with Conditions Without DMPC
5.4. Robustness
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
CPPHP | Clutch-based pre-transmission parallel hybrid powertrain |
DMPC | Discrete-time model predictive control |
HEV | Hybrid electric vehicle |
DLQR | Discrete-time linear quadratic regulator |
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Description | Symbol | Value |
---|---|---|
Engine time constant | 0.1 s | |
Lumped moment of inertia of the engine and the driving parts of the clutch | 0.15 kg·m2 | |
Equivalent radius of the clutch | 0.1 m | |
Coulomb force | 348.4 N | |
Stiction force | 1636.1 N | |
Stribeck velocity | 22 m/s | |
Macroscopic damping coefficient | 0.001 Ns/m | |
Clutch actuator time constant | 0.01 s | |
Stiffness coefficient | 108 N/m | |
Microscopic damping coefficient | 106 Ns/m | |
Motor time constant | 0.001 s | |
Lumped moment of inertia of the driven parts of the clutch, the rotor of the motor and the primary shaft of the transmission | 0.05 kg·m2 | |
Gear ratio | 4 | |
Transmission efficiency | 0.98 | |
Lumped moment of inertia of the secondary shaft of the transmission | 0.01 kg·m2 | |
Final drive ratio | 5 | |
Final drive efficiency | 0.98 | |
Lumped moment of inertia of the final drive and the differential | 0.01 kg·m2 | |
Equivalent stiffness coefficient of the axle shafts | 6000 Nm/rad | |
Equivalent damping coefficient of the axle shafts | 400 Nms/rad | |
Vehicle mass | 1250 kg | |
Entire moment of inertia of the vehicle body and the tires | 10 kg·m2 | |
Wheel radius | 0.3 m | |
Rolling resistance coefficient | 0.01 | |
Gravitational acceleration | 9.8 m/s2 | |
Road slope | 0 | |
Drag coefficient | 0.3 | |
Frontal area | 2 m2 | |
Air density | 1.25 kg/m3 |
Test | Proposed Solver | Quadprog (Interior-Point-Convex) | Quadprog (Active-Set) |
---|---|---|---|
1 | 0.030 ms | 3.985 ms | 1.221 ms |
2 | 0.032 ms | 3.989 ms | 1.271 ms |
3 | 0.031 ms | 3.891 ms | 1.228 ms |
4 | 0.032 ms | 3.913 ms | 1.262 ms |
5 | 0.033 ms | 3.960 ms | 1.251 ms |
Test | Proposed Solver | Quadprog (Interior-Point-Convex) | Quadprog (Active-Set) |
---|---|---|---|
1 | |||
2 | |||
3 | |||
4 | |||
5 |
Description | Symbol | Value |
---|---|---|
Initial engine output torque | 0 Nm | |
Initial rotational speed of | 285 rad/s | |
Initial normalized normal force | 0 | |
Initial value of the average deflection of the bristles | 0 m | |
Initial motor output torque | 50 Nm | |
Initial rotational speed of | 280 rad/s | |
Initial wheel rotational speed | 14 rad/s | |
Initial torsion of the axle shaft | 0.148 rad | |
Engine output torque required by the energy management system | 60 Nm | |
Motor output torque required by the energy management system | 10 Nm |
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
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Guo, D.; Du, C.; Yan, F. Drivability-Related Discrete-Time Model Predictive Control of Mode Transition in Pre-Transmission Parallel Hybrid Powertrains. Energies 2016, 9, 740. https://doi.org/10.3390/en9090740
Guo D, Du C, Yan F. Drivability-Related Discrete-Time Model Predictive Control of Mode Transition in Pre-Transmission Parallel Hybrid Powertrains. Energies. 2016; 9(9):740. https://doi.org/10.3390/en9090740
Chicago/Turabian StyleGuo, Di, Changqing Du, and Fuwu Yan. 2016. "Drivability-Related Discrete-Time Model Predictive Control of Mode Transition in Pre-Transmission Parallel Hybrid Powertrains" Energies 9, no. 9: 740. https://doi.org/10.3390/en9090740