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This paper presents a collaborative control system for an electric vehicle chassis based on a centralized and hierarchical control architecture. The centralized controller was designed for the suspension and steering system, which is used for improving ride comfort and handling stability; the hierarchical controller was designed for the braking system, which is used for distributing the proportion of hydraulic braking and regenerative braking to improve braking performance. These two sub-controllers function at the same level of the vehicle chassis control system. In order to reduce the potential conflict between the two sub-controllers and realize a coordination optimization of electric vehicle performance, a collaborative controller was built, which serves as the upper controller to carry out an overall coordination analysis according to vehicle signals and revises the decisions of sub-controllers. A simulation experiment was carried out with the MATLAB/Simulink software. The simulation results show that the proposed collaborative control system can achieve an optimized vehicle handling stability and braking safety.

To improve vehicle performance further, more and more active control systems such as the anti-lock braking system (ABS), active suspension system (ASS) and electric power steering (EPS), have been developed and many of them have been commercially utilized for nearly three decades [

The key of the integrated vehicle chassis control research is control architecture, which can be divided into three main kinds: decentralized, centralized and hierarchical architecture [

Recently, the research on integrated control of chassis system is fairly common in conventional vehicles, but seldom done in electric vehicles. In this paper, a coupling of electric vehicle subsystems is provided for cornering regenerative braking conditions, ASS, EPS and electro-hydraulic braking systems are taken as the research object, and a collaborative control system which contains both centralized and hierarchical architecture is designed and the corresponding collaborative control strategy of an electric vehicle chassis system is established, which includes a centralized controller for the suspension and steering system based on Linear-Quadratic Gaussian (LQG) theory and a hierarchical controller for the braking system. The simulation results showed that the designed collaborative control strategy could provide a trade-off control among subsystems and improve the overall performance of electric vehicle further.

The vehicle dynamics includes the movement and rotation on the lateral, vertical and longitudinal directions; therefore, the vehicle lateral, vertical and longitudinal dynamics must be considered for a complete vehicle model. The vehicle dynamics model adopted here contains 14 degrees of freedom as shown in

Vehicle dynamics model: (

The 14 degrees of freedom includes heave, pitch, roll of sprung mass, vehicle yaw, lateral and longitudinal motion, four wheels vertical and rotation movement. According to Newton’s law, the motion equations of the vehicle are derived as follows:

(1) Sprung mass heave movement:
_{s}_{s}_{i}

(2) Sprung mass pitch movement:
_{ys}_{s}_{f}_{r}

(3) Sprung mass roll movement:
_{xu}_{f}_{r}

(4) Vehicle yaw movement:
_{z}_{zx}_{yi}

(5) Vehicle longitudinal movement:
_{xi}

(6) Vehicle lateral movement:

(7) Four wheels’ vertical movement:
_{1i}_{0i}_{ui}_{ui}

(8) Four wheels’ rotation movement:
_{wi}_{wi}_{w}_{bi}_{mi}_{zi}

(9) The ground braking force can be calculated as:
_{xbi}

The total suspension force can be calculated as:
_{i}_{si}_{bi}_{2i}

Supposed that the roll angle _{f}_{r}

The shaft-assisted EPS system is used in this paper, a rack and pinion transmission is designed as the steering transmission. Its structure is shown in

Electric power steering system structure.

According to Newton’s law, the governing equations of motion for the EPS are derived as follows [

(1) Motion equations of steering shaft are expressed as:
_{s}_{s}_{s}_{s}_{d}_{s}_{r}_{s}

(2) Motion equations of rack and pinion are expressed as:
_{r}_{r}_{r}_{m}_{m}_{kp}_{r}_{s}

(3) Motion equations of the assist motor are expressed as:
_{m}_{m}_{m}_{a}_{v}_{m}

In this paper, the ABS model is established according to its work principle, namely the process of cylinder supercharging, pressure maintaining and decompressing as follows [_{w}_{f}_{i}_{d}

The brushless DC motor has the characteristics of low speed and high torque. From a control point of view, as the current of each phase is a square wave, the inverter voltage can be simply controlled with a DC PWM wave method [_{m}^{*}_{p}_{r}_{m}_{s}_{s} is phase resistance, _{pwm}

As the only vehicle component generating external force that can be effectively manipulated to affect vehicle motions, tyres are crucial for vehicle dynamics and control [_{v}_{h}_{z}

The time-domain road input model, which is mainly divided into integral white noise and filtered white noise, is used to generate random road roughness input. The filtered white noise can be a true reflection of the actual situation which road spectrum approximates horizontal within a low frequency range [_{0} is the road roughness coefficient, _{0} is the lower cutoff frequency,

For the chassis system control, the centralized controllers are established for the subsystems (normally two) which have close relationship and high coupling effect according to their own dynamics in order to enhance the degree of integration, the hierarchical controllers are established for such subsystems that have exact coupling relationships and are difficult to control in a centralized way. The decentralized controllers are established for those subsystems that are difficult to control in a centralized way or in a hierarchical way according to their own dynamic effects. The centralized, hierarchical and decentralized controllers are all usually regarded as the low-level sub-controllers, and an extra upper controller is responsible for the unified control of the sub-controllers, to coordinate the control conflicts and improve the overall performance of the chassis system. Herein, we define this kind of chassis control method as the collaborative control.

In this paper, the collaborative control strategy of ASS, EPS and electro-hydraulic braking system is given as follows: a centralized controller is designed for ASS and EPS without considering the impact of the electro-hydraulic braking system, and it can simultaneously analyze and optimize the control target under the coupling effect of electric vehicle lateral dynamics and vertical dynamics during the steering process, and a hierarchical controller is designed for electro-hydraulic braking system without considering the interaction with ASS and EPS.

When the three subsystems are coupled to each other, the above two controllers are regarded as the same level and coordinatively controlled by another collaborative controller. The electric vehicle chassis system collaborative control scheme is shown in

Electric vehicle chassis system collaborative control scheme.

The ASS actuator force and tyre vertical load change are calculated by the collaborative controller according to the signals acquired from the electric vehicle chassis system model to realize a trade-off between ride comfort, braking performance and handling stability. As a result, the collaborative controller must coordinate and assign the control force or torque (correction force of the suspension Δ_{s}_{b}

For the ASS, as the vehicle body pitch motion is caused by braking, the designed correction force of the suspension Δ_{b}_{max} is the maximum braking torque of the hydraulic brake, _{max} is the maximum active suspension force.

For the electro-hydraulic braking system, the front axle load is decreased due to the correction force of the suspension Δ_{b}_{f}_{r}_{sf}_{sr}

For the EPS, as the road lateral force coefficient was decreased during cornering braking, the over-steering tendency will be increased according to the original designed assist characteristics, therefore, the correction torque of the assist motor Δ_{s}_{z}_{1}, Δ_{z}_{2} are the aligning torque of the left front and right front wheels, respectively.

The LQG controller which can observe output of ASS and EPS is designed according to the Equations (1)–(4), (6), (7), (10)–(14), and the state vector is constructed as:

In Equation (27), model noise _{0} is model noise covariance matrix, _{0} is measurement noise covariance matrix. Kalman filter optimal state estimator can be constructed according to the above system state space equations:
_{0} was obtained by the algebraic equation as follows:

The output vectors of ASS+EPS systems should be designed for the control target to make the vehicle have good handling stability, ride comfort and steering portability. It should reduce the vehicle’s vertical acceleration, pitch angle, roll angle, lateral acceleration, yaw rate, suspension travel, steering shaft measured torque and angle, in addition should minimize the control input vector for easy control. Performance index functional was designed based on the above consideration as follows:
_{i}_{i}

According to the optimal control theory, Linear Quadratic Regulator (LQR) optimal control law is

In this paper, the target of the electro-hydraulic braking system controller is designed for guaranteeing the braking performance and safety, therefore, the dominant role of ABS control and the subsidiary role of motor control are played during braking, furthermore, a logic threshold controller based on slip rate is designed for ABS control, taking the slip rate threshold upper limit is 0.16, the lower limit is 0.11, the specific control process is shown in

Electro-hydraulic braking control strategy.

The simulation experiments were carried out with collaborative and individual control respectively, and the model parameters are listed in ^{−5} dB, the input torque of steering shaft is 2 N·m step input and the vehicle initial braking speed is 10 m/s.

After repeatedly debugging, it could achieve a better control effect with the weighting coefficients of ASS+EPS systems as follows: _{1} = 100, _{2} = 50, _{3} = _{4} = 80, _{5} = 100, _{6}~_{9} = 20, _{10} = 80, _{11} = 120, _{1}~_{5} = 0.0005, _{0i} = 10^{−3}, _{0i} = 10^{−7}. The simulation results are shown in

As shown in _{s}

Simulation parameters.

Parameters | Values | Parameters | Values |
---|---|---|---|

_{m} |
0.0035 N·m·s/rad | _{a} |
0.5 N·m/A |

_{s} |
0.0275N·m·s/rad | _{kp} |
10 N·m/rad |

_{r} |
0.0275 N·m·s/rad | _{m} |
626 N·m /rad |

_{s} |
0.1 m | _{s} |
183 N·m/rad |

_{f} |
1.100 m | _{v} |
0.0367 V·s/rad |

_{r} |
1.585 m | _{x} |
10,000 N·m/rad |

_{f} |
1.58 m | _{f} |
0.95 N·m /Pa |

_{r} |
1.60 m | _{f} |
1.185 m |

_{0} |
0.01 Hz | _{r} |
1.500 m |

0.015 | 0.0000009 H | ||

_{0} |
0.000005 m^{3}/cycle |
_{m} |
0.008 H |

_{m} |
7.5 | _{s} |
0.00005 H |

_{r} |
10 | _{r} |
33 kg |

_{f} |
0.35 m | _{s} |
1080 kg |

_{r} |
0.32 m | 1350 kg | |

_{s} |
15 | _{p} |
2 |

_{w} |
15 kg·m^{2} |
0.035 Ω | |

_{zu} |
1598kg·m^{2} |
_{s} |
0.975 Ω |

_{ys} |
2444 kg·m^{2} |
_{s} |
0.007 m |

_{s} |
0.042 kg.m^{2} |
_{w} |
0.303 m |

_{m} |
0.00047 kg.m^{2} |
_{pwm} |
0.0002 s |

_{bi} |
1500 N·s/m(1,2), 1300 N·s/m(3,4) | _{ui} |
200,000 N/m(1,2), 180,000 N/m(3,4) |

_{si} |
17,000 N/m(1,2), 22,000 N/m(3,4) | _{ui} |
40.5 kg(1,2), 45.4 kg (3,4) |

Simulation results of vehicle pitch and roll angle: (

Simulation results of vehicle front wheel corner and yaw rate: (

_{b}

Simulation results of vehicle braking torques: (

Comparison of braking distance.

As shown in

Simulation results of vehicle suspension travel: (

As shown in

Simulation results of vehicle vertical acceleration and lateral acceleration: (

A RMS analysis on the vehicle performance parameters is listed in ^{2} to 2.2312 rad/s^{2}, the braking distance is reduced from 22.5 m to 21.7 m, which demonstrates that the collaborative control system could effectively improve the vehicle handling stability and braking safety.

A RMS analysis on the vehicle performance parameters.

RMS value | Individual control | Collaborative control |
---|---|---|

0.0632 | 0.0478 | |

0.0845 | 0.0653 | |

12.3832 | 10.1294 | |

0.6192 | 0.4055 | |

768.83 | 765.26 | |

787.87 | 805.50 | |

0.0197 | 0.0145 | |

0.0093 | 0.0056 | |

^{2}) |
0.9732 | 0.9657 |

^{2}) |
2.3186 | 2.2312 |

(1) In this paper, a new control architecture named collaborative control is designed based on the combination of centralized architecture and hierarchical architecture; this architecture is able to respond flexibly to the controllers designed for multi-subsystems in vehicle chassis, and furthermore, the reliability and integrated control of the system can be guaranteed.

(2) The two subcontrollers can optimize and improve the control performance of the subsystems, therefore, the collaborative controller can fulfill the coordination optimization of subsystem by only giving the correction and compensation control orders to the two sub-controllers, which have closely coupled functions. A simulation experiment on the typical cornering braking is performed and the results show that the collaborative control system could effectively improve the vehicle handling stability and braking safety.

This work was supported by the National High Technology Research and Development Program of China (2011AA11A228, 2012AA111603, 2011AA11A290) in part, the International Cooperation Research Program of Chinese Ministry of Science and Technology (2011DFB70020) in part, the Program for New Century Excellent Talents in University (NCET-11-0785) in part, the National Natural Science Foundation of China (NSFC: 51075010, 51007003 ) in part, the Key Funding Project of the Beijing Municipal Commission of Education and the Natural Science Funding Project of Beijing (KZ200910005007). The authors would also like to thank the reviewers for their corrections and helpful suggestions.

_{∞}-control of a rack-assisted electric power steering system