Requirement

Hello and welcome to MAE Learning .In this tutorial we will see how to develop ABS control system and below you can see key requirement.

  • 1st of all we need to detect wheel slip when the difference between wheel speed and vehicle speed exceeds 20%.
  • 2nd we need to prevent wheel lock by modulating brake pressure.
  • At last we should maintain vehicle traction and steering control during braking.
  • APPLY (high pressure) while slip is small.
  • Switch to RELEASE (low pressure) when slip > 20%.
  • Return to APPLY after slip falls back below 15% (a little hysteresis so it doesnโ€™t chatter).

Slip definition used here (common in ABS):

where V = vehicle speed, W = wheel speed (same units), and ฯต\epsilonฯต is a tiny number to avoid divide-by-zero.
We flag slip if slip_ratio > 0.20 (20%).

Model Logic as Described

Blocks Used

  • Sum, MinMax, Divide โ†’ to calculate slip ratio
  • Relational Operator โ†’ to detect Slip > 20%
  • Saturation โ†’ to limit slip to the range of [0,1]
  • Stateflow Chart โ†’ to implement Control strategy (Apply โ†’ Release โ†’ Apply)

Logic Behavior

  • When braking starts if slip > 20% โ†’ Brake Release mode is activated.
  • When slip is < 15% โ†’ Brake is re-applied.
  • This hysteresis band (15โ€“20%) ensures that brakes do not switch on/off rapidly.

Wheel Speed & Vehicle Speed Inputs

  • Constant / Signal Source blocks โ†’ represent vehicle speed and wheel speed.
  • Sum Block ร  This gives the slip numerator: how much faster the vehicle is moving compared to the wheel. calculate the slip ratio (Wheel Speed โ€“ Vehicle Speed)/Vehicle Speed.
  • MinMax block ร  This ensures that when the vehicle is stopped or nearly stopped, we donโ€™t divide by zero.
  • Divide block ร  Compute slip ratio

Relation to Logic:
These signals feed into the slip detection condition. If slip > 20%, it triggers the ABS control logic.

Slip Detection Logic

Saturation Block

  • So, in this logic, saturation block limits the slip ratio in the [0, 1] range.

Why so?

  • Negative slip does not make sense in case of braking (means wheel speed is more than vehicle speed, which does not happen in physical braking).
  • Slip above 100% is also not practically possible in normal ABS scenario.

Means, saturation block ensures that the value of slip remains in realistic and valid range.

Relational Operator Block

  • This block generates slip flags with hysteresis.
  • Its job is to decide:
    • When will Brake Release trigger happen (when slip > 20%).
    • When will Brake Re-Apply trigger happen (when slip < 15%).

Meaning, the relational operator block tells the ABS when to release and when to apply it again, so that the system remains smooth and stable.

Relation to Logic:

This acts as the trigger condition. When TRUE, it sends a signal to the Stateflow chart to start brake modulation.

Logic Behavior

  • When braking starts, if slip exceeds 20%, Slip_High = true โ†’ ABS enters pressure release phase.
  • ABS stays in release mode until slip drops below 15%, when Slip_Low = true โ†’ ABS can reapply brakes.
  • This hysteresis band (15โ€“20%) prevents rapid oscillations.

Stateflow Chart (Core Control Logic)

Stateflow chart with states:

  • Apply โ†’ Brake pressure increases.
  • Release โ†’ Brake pressure decreases.
  • Re-Apply โ†’ Brake pressure gradually re-engages.

Relation to Logic:
This cyclic strategy is divided: Apply โ†’ Release โ†’ Apply, which does not prevent wheel lock.

Result of the Model Logic

If we talk about the result, when the slip condition is met (i.e. slip is more than 20%), the system automatically starts brake pressure modulation.

  • This modulation is cyclic (Apply โ†’ Release โ†’ Apply), due to which the wheels are not fully locked.
  • And when the wheels keep rotating (rotational movement is maintained).
  • As a result, the steering control and stability of the vehicle remains safe.
  • And this is the main objective of ABS system โ€“ to control and maintain safety during braking.

Consistency Between Requirement, Model, and Result

AspectRequirementModel ImplementationSimulation ResultAlignment
Slip DetectionSlip > 20%slip_raw > 0.2 as Slip_Highslip_raw rises above 0.2Matches perfectly
Slip Release ThresholdSlip < 15%slip_raw < 0.15 as Slip_Lowslip_raw falls below 0.15Matches perfectly
Brake PressureApply โ†’ Release โ†’ Apply cycleStateflow three states with 0.1s timed transitionPulse brakecmd between 1.0 and 0.3Matches well
ABS ActivationON at slip > 0.2, OFF when slip < 0.15Stateflow signals public ABS_ActiveABS_Active signal toggling as expectedFully consistent
Timing and ModulationModulation interval ~0.1safter(0.1 sec) transitions in chartObserved pulse widths โ‰ˆ 0.1sCorrectly modelled

Simulation Graph

Input

Output

Conclusion

The Simulink/Stateflow model design matches and implements the ABS requirements.

  • Slip detection thresholds (20% and 15%) are correctly applied and are logically consistent.
  • Brake modulation occurs in a controlled and timed sequence via the Stateflow chart that matches the real behaviour of the ABS.
  • Simulation results clearly show that the responses to slip, brake command and ABS activation are expected and stable.
  • Overall, the system design, logic and output are completely consistent and suitable for an ABS control system that detects slip > 20% and modulates braking.