Fig 1.
Structures of the pneumatic–disc–brake and the EMB.
(a) Structure of the pneumatic–disc–brake; (b) Structure of the improved EMB.
Fig 2.
(a) The caliper characteristics provided by the manufacturer; (b) The fitted caliper model after unit conversion.
Fig 3.
EMB system model.
Fig 4.
Overall architecture of the control prototype.
Fig 5.
The relationships between the Fxb and the Fy with the λ.
Fig 6.
Wheel braking pressure control prototype.
Table 1.
Parameters of the EMB system model.
Fig 7.
Back EMF waveform of motor.
Table 2.
The relevant parameters of the vehicle.
Table 3.
The preliminary parameters of the control prototype.
Table 4.
The braking efficiency and stability requirements of the M3 vehicles.
Fig 8.
Parameters coupling relations.
The coupling relations in Fig 8 include the electromagnetic relations, the force relations, the motion relations and the control prototype. Where, the green labeled parameters are the potential decision variables, the gray parameters are the EMB attributes, the purple parameters are the intermediate variables during calculation, and the rest are the input, the output and the feedback of the model.
Table 5.
Parameters and levels.
Table 6.
Results of the range analyses.
Table 7.
Parameters sensitivity sorting.
Table 8.
Value bounds of the decision variables.
Fig 9.
Relationship among chromosomes, individuals and population.
Fig 10.
The flow chart of NSGA–II.
Fig 11.
Co–simulation platform for the EMB parameters optimization.
Fig 12.
Optimal results.
Fig 13.
Individuals under the different MFDD intervals.
(a) MFDD < 0.880 g; (b) 0.880 g ≤ MFDD < 0.885 g; (c) 0.885 g ≤ MFDD < 0.890 g; (d) 0.890 g ≤ MFDD < 0.895 g; (e) 0.895 g ≤ MFDD < 0.900 g; (f) MFDD ≥ 0.900 g.
Fig 14.
Selected individuals.
Table 9.
Selected individuals.
Table 10.
Comparison of the decision variables.
Fig 15.
(a) Braking pressure; (b) Braking torque; (c) Motor speed; (d) Motor torque.
Fig 16.
(a) Vehicle and equivalent wheel velocity; (b) Wheel slip ratios.
Fig 17.
Longitudinal distance–time.
Fig 18.
Deceleration–time.
Fig 19.
LD with time and longitudinal distance.
(a) LD–Time; (b) LD–Longitudinal distance.
Table 11.
Comparison of the indicators.