Regenerative and Friction Brake Blending Strategy

The problem

Regenerative braking recovers energy, but the motor can only provide limited torque, the battery cannot accept charge when full or cold, and braking only the driven axle can upset stability. The brake controller must blend regenerative and friction braking smoothly so the driver gets the same deceleration for the same pedal input. This project designs and tests such a blending strategy.

Objectives

• Model vehicle longitudinal dynamics, the motor's regenerative limits and friction brakes.
• Design series and parallel blending strategies with a stability-based axle split.
• Implement mode logic in Stateflow for battery-full, low-speed and emergency conditions.
• Compare energy recovered and deceleration tracking on standard drive cycles.
• Check that blending transitions are smooth enough for driver comfort.

What you need

Key concepts

Series and parallel blending

In series blending, regeneration is used first and friction fills the remainder. In parallel blending, friction and regeneration act together in a fixed ratio. Series recovers more energy but needs brake-by-wire.

Ideal brake force distribution

The front–rear split that locks both axles at the same time for a given deceleration, shifting forwards as deceleration increases because of load transfer. Braking a rear axle too hard risks instability.

Regenerative torque limit

Limited by motor torque and power curves, battery charge power limit (lower when SOC is high or the pack is cold) and a fade-out at low speed where regeneration becomes ineffective.

Deceleration tracking

The driver expects the same deceleration for the same pedal position regardless of how it is produced, so the total of regen and friction must follow the demand closely.

Step-by-step guide

1. 1

   Define vehicle and limits

   Choose an example front-wheel-drive compact EV with mass, CG height, wheelbase, wheel radius, motor peak torque and power, gear ratio, battery charge power limit against SOC and temperature, and friction-brake capacity. Set requirements: deceleration tracking error within a small band, no rear-axle lock before front, and smooth transitions with limited jerk. Record values in a parameter script labelled as example data.

   Checkpoint: A parameter script and requirements table, including the charge power limit map.

2. 2

   Build the longitudinal vehicle model

   Model m·dv/dt = F_traction − F_brake − F_roll − F_aero − F_grade, with F_roll = m·g·Crr, F_aero = ½·ρ·Cd·A·v² and dynamic axle loads from load transfer, Fz,front = m·g·lr/L + m·a·h/L in braking. Add a battery SOC integrator from motor electrical power. Use a fixed-step solver with a 1 ms step for brake dynamics. Check load transfer by comparing front axle load under braking with the formula.

   Checkpoint: A coast-down test with no brakes matches a hand calculation of deceleration from road load within a few per cent.

3. 3

   Model motor regeneration and friction brakes

   Model available regenerative torque as the minimum of the motor torque curve at current speed, the battery charge limit converted to torque, and a low-speed fade-out ramp between, for example, 10 and 5 km/h. Model friction brakes on each axle as a first-order actuator with a time constant of tens of milliseconds and a pressure-to-torque gain. Check the friction model alone by applying a pressure step and comparing torque.

   Checkpoint: Available regen torque plotted against speed and SOC has the expected shape, falling to zero at high SOC and low speed.

4. 4

   Design the blending strategies

   Convert pedal position to total demanded deceleration. For series blending, assign as much as possible to regen on the front axle, limited by available regen and by the front share allowed by the ideal distribution, then add friction to make up the rest on both axles. For parallel blending, use a fixed regen fraction. Implement both as Simulink subsystems selectable by a parameter.

   Checkpoint: For a constant demand, the sum of regen and friction force equals demand in both strategies.

5. 5

   Add Stateflow mode logic

   Create a chart with states for normal blending, battery-limited (SOC above a threshold or cold pack), low-speed fade-out, and emergency braking (demand above a threshold, where regen is dropped and friction follows the ideal distribution for maximum stability). Use hysteresis on SOC and speed thresholds and rate limiters on torque handovers to keep jerk low. Test the chart with scripted inputs before connecting it to the vehicle.

   Checkpoint: A scripted scenario passes through each state with transitions at the intended conditions and no chattering.

6. 6

   Add a driver model and run drive cycles

   Add a PI driver that follows IDC, MIDC and WLTP speed traces by commanding accelerator and brake pedal. Run each cycle with series and parallel blending, and with friction-only braking as a baseline. Log regenerated energy, friction energy, SOC and speed error. Tune the driver gains once on WLTP and keep them fixed for all strategies so differences in energy come from blending, not from driving style. Check that brake pedal use is similar across strategies.

   Checkpoint: Speed tracking error within a small band on all cycles, and regenerated energy is zero for the friction-only baseline.

7. 7

   Compare energy recovery

   Compute the share of braking energy recovered and the net energy consumption in Wh/km for each strategy and cycle. Explain why urban cycles like IDC offer more recoverable energy than steady highway driving. Repeat at high initial SOC to show the battery-limited mode reducing recovery. Compute recoverable braking energy as the kinetic energy removed by braking minus road-load losses, so the recovered share has a clear reference. Present results per cycle and per strategy in a single table.

   Checkpoint: A table of recovered energy and Wh/km with series blending recovering the most on urban cycles.

8. 8

   Check feel and stability

   Apply pedal steps and ramps and measure deceleration tracking error and jerk during regen-to-friction handovers, especially at the low-speed fade-out and when SOC crosses the threshold. Check the front–rear braking split against the ideal distribution and confirm the rear axle never exceeds its share at high deceleration. Use the rate of change of deceleration as the jerk metric and compare it with a stated comfort limit. Plot the braking split on the ideal distribution diagram for a range of decelerations.

   Checkpoint: Jerk during handovers within the chosen limit and braking split plots staying on the stable side of the ideal curve.

9. 9

   Report

   Present the models, blending strategies, mode logic, energy results and feel and stability checks. State the limitations: no tyre slip model, so ABS interaction is not represented, and actuator models are simplified. Suggest coupling with an ABS slip controller as the next step. Include energy results, handover plots and the Stateflow chart, and describe test scenarios fully so results can be reproduced. Recommend a strategy with its conditions, for example series blending when brake-by-wire is available.

   Checkpoint: A report comparing strategies on energy, feel and stability with clear recommendations.

Testing & validation

• Coast-down deceleration against hand calculation.
• Force sum equals demand in every blending mode.
• Stateflow scenario test through all modes.
• Energy recovered and Wh/km on IDC, MIDC and WLTP.
• Jerk and braking-split checks at handovers and high deceleration.

Expected results

A brake blending controller with Stateflow mode logic that recovers more braking energy than parallel blending while keeping deceleration tracking, handover jerk and axle split within limits.

Take it further

• Add a wheel-slip model and integrate with an ABS controller.
• Model a rear-wheel-drive or dual-motor vehicle and compare stability constraints.
• Make regen depend on battery temperature from a thermal model.
• Add one-pedal driving and compare driver workload and recovered energy.

Viva and review questions

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