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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 doesn’t chatter).

Slip definition used here (common in ABS):

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

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Model Logic as Described

Blocks Used

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

Logic Behavior

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

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Wheel Speed & Vehicle Speed Inputs

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

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

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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 → ABS enters pressure release phase.
• ABS stays in release mode until slip drops below 15%, when Slip_Low = true → ABS can reapply brakes.
• This hysteresis band (15–20%) prevents rapid oscillations.

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Stateflow Chart (Core Control Logic)

Stateflow chart with states:

• Apply → Brake pressure increases.
• Release → Brake pressure decreases.
• Re-Apply → Brake pressure gradually re-engages.

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

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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 → Release → 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 – to control and maintain safety during braking.

Consistency Between Requirement, Model, and Result

Aspect	Requirement	Model Implementation	Simulation Result	Alignment
Slip Detection	Slip > 20%	slip_raw > 0.2 as Slip_High	slip_raw rises above 0.2	Matches perfectly
Slip Release Threshold	Slip < 15%	slip_raw < 0.15 as Slip_Low	slip_raw falls below 0.15	Matches perfectly
Brake Pressure	Apply → Release → Apply cycle	Stateflow three states with 0.1s timed transition	Pulse brakecmd between 1.0 and 0.3	Matches well
ABS Activation	ON at slip > 0.2, OFF when slip < 0.15	Stateflow signals public ABS_Active	ABS_Active signal toggling as expected	Fully consistent
Timing and Modulation	Modulation interval ~0.1s	after(0.1 sec) transitions in chart	Observed pulse widths ≈ 0.1s	Correctly modelled

Simulation Graph

Input

Output

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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.

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