Electronic Stability Control Using Individual Wheel Torque

The problem

Stability control prevents spins and plough-outs by applying corrective yaw moments, traditionally with individual friction brakes. EVs with several motors can apply positive and negative torques at each wheel, giving faster and more flexible corrections without wearing brakes. The controller must decide when to intervene, how large the corrective moment should be and how to distribute it while keeping wheels within their friction limits.

Objectives

• Build a four-wheel vehicle plant with independent wheel torques and non-linear tyres.
• Design yaw-rate and sideslip control with intervention thresholds.
• Allocate corrective yaw moment across four wheels with friction and motor constraints.
• Evaluate the controller in sine-with-dwell, lane-change and low-friction tests.
• Compare motor-based stability control with brake-only stability control.

What you need

Key concepts

Sine-with-dwell test

A steering input of a sine wave with a pause at the second peak, used in stability-control regulations to check that yaw rate decays quickly after the steering returns to centre.

Sideslip limit

Large sideslip means the driver has little control. Stability controllers intervene when sideslip or its rate exceeds limits that depend on friction.

Combined slip

A tyre's friction is shared between longitudinal and lateral forces, so adding wheel torque reduces available lateral force. Allocation must account for this.

Control allocation

Finding wheel torques that produce the requested yaw moment and longitudinal force while respecting each wheel's motor and friction limits, often as a constrained optimisation.

Step-by-step guide

1. 1

   Define vehicle, tests and pass criteria

   Use an example four-motor EV with stated motor torque limits, mass, inertia and tyre data. Define tests: sine-with-dwell at increasing amplitude, double lane change on dry and wet surfaces and a low-friction step steer. Write pass criteria modelled on regulatory ideas, such as yaw rate falling below a fraction of its peak within a set time after the dwell, and lateral displacement exceeding a minimum for responsiveness.

   Checkpoint: A test matrix with pass criteria written before any controller design.

2. 2

   Build the plant

   Assemble a dual-track vehicle with Vehicle Dynamics Blockset blocks, four wheels with combined-slip Magic Formula tyres and four torque inputs that can be positive or negative. Add a friction-brake model as a backup actuator. Use a fixed-step solver at 1 ms and log all wheel slips and forces. Check combined-slip behaviour by applying braking torque during steady cornering and confirming lateral force falls as longitudinal slip rises.

   Checkpoint: Uncontrolled sine-with-dwell at high amplitude shows yaw-rate overshoot or a spin, confirming the test is demanding enough.

3. 3

   Build the reference and estimator

   Generate desired yaw rate from a bicycle model with friction saturation. Build a sideslip estimator, for example integrating lateral acceleration minus speed times yaw rate with drift correction, or a kinematic–model blend. Compare estimated sideslip with the plant's true value across manoeuvres. Test the estimator with sensor noise and accelerometer bias, because integration-based estimates drift. Record the error at the end of each manoeuvre and explain any drift, since the controller will rely on this estimate rather than the true value.

   Checkpoint: Sideslip estimate within a stated error of the true value in all test manoeuvres.

4. 4

   Design the yaw and sideslip controller

   Design a corrective yaw moment from yaw-rate error with a PI or sliding-mode law, plus a sideslip term that grows as sideslip approaches its limit. Make gains depend on speed. Check stability margins on a linearised model at several speeds. Limit the corrective yaw moment to what the tyres can provide at the estimated friction. Test the controller in an always-on mode first to check its behaviour before adding intervention logic, and record any oscillation in yaw rate.

   Checkpoint: Linear analysis shows adequate margins, and the controller reduces yaw error in a moderate test without causing oscillation.

5. 5

   Add intervention logic

   Implement a Stateflow chart that activates the controller only when yaw-rate error or sideslip exceeds thresholds, with hysteresis and minimum active time. Add states for actuator fault, where control falls back to friction brakes, and for low speed, where control is disabled. Choose thresholds that avoid intervention during normal driving, and check this with a set of gentle manoeuvres where the controller should stay inactive. Log the active state together with yaw-rate error and sideslip for every test.

   Checkpoint: A scripted test shows activation only during the demanding part of each manoeuvre and correct fall-back to brakes in the fault case.

6. 6

   Allocate the corrective moment

   Write a rule-based allocator that applies negative torque to the inner rear or outer front wheel depending on oversteer or understeer, then improve it with quadprog: minimise deviation from the requested moment and longitudinal force plus a penalty on wheel slip, subject to motor and friction limits estimated from normal loads. Compare the two allocators. Measure the allocator's computation time per step.

   Checkpoint: Both allocators deliver the requested moment when feasible, and the optimised version uses tyre capacity more evenly.

7. 7

   Run the test matrix

   Run all tests with no control, brake-only stability control and motor-based control. Compute pass criteria, peak sideslip, path deviation and speed loss. Plot sine-with-dwell yaw rate for the three cases on one graph. Use the same steering inputs for all three cases. Calculate yaw-rate ratios at the defined times after the dwell and compare them with the pass criteria. Record speed loss, because brake-only control usually slows the vehicle more, and present a summary table with pass or fail for each test and controller.

   Checkpoint: Motor-based control meets the pass criteria in all tests where the uncontrolled vehicle fails, with results tabulated.

8. 8

   Robustness and failure cases

   Repeat tests with friction misestimated, increased mass and one motor failed. Check that the fault logic and brake fall-back keep the vehicle stable. Discuss differences between motor torque and friction brakes, such as response speed and the ability to add positive torque. Script all combinations with sim() and present results as a pass or fail table. For each failure, plot the time history, identify whether the estimator, the controller or the allocator caused it and suggest a design change.

   Checkpoint: A robustness table with pass or fail for each case and an explanation for any failure.

9. 9

   Report

   Present the test matrix, plant, estimator, controller, intervention logic, allocation and results. State clearly that the pass criteria are modelled on regulatory ideas but this is not a certification test, and that results are simulation only. Include the test matrix, pass criteria, controller gains, intervention thresholds and allocation method. Present results as tables with key time histories, compare motor-based and brake-only control in a dedicated section and keep all scripts with the report for reproducibility.

   Checkpoint: A report with complete test results and a clear scope statement.

Testing & validation

• Uncontrolled vehicle fails the demanding tests.
• Sideslip estimator accuracy.
• Intervention logic activates only when needed.
• Pass criteria met with motor-based control across the test matrix.
• Robustness to friction error, mass change and motor failure.

Expected results

A motor-based stability controller with intervention logic and optimised torque allocation that passes sine-with-dwell style criteria in simulation and compares favourably with brake-only control.

Take it further

• Add an online friction estimator to adapt thresholds and limits.
• Integrate stability control with torque vectoring for normal driving.
• Use MPC for combined yaw and sideslip control.
• Test the controller in software-in-the-loop with generated code.

Viva and review questions

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