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Modeling & Simulation · MCTE4150 · Fall 2025

Half-Car Suspension Modeling & Simulation

MATLABSimulinkState-SpaceVehicle Dynamics

Brief

How does a road bump feel at the driver's seat?

A half-car model captures what a quarter-car can’t: not just bounce (the body heaving up and down) but pitch (the body rocking front-to-back), plus the independent hop of the front and rear wheels. The goal was to model that behaviour and evaluate the ride a driver actually experiences over a road disturbance.

The Model

Equations of motion, cast into state space.

The sprung body and the front/rear unsprung masses, coupled by suspension springs/dampers and tyre stiffness, give a set of coupled second-order equations of motion. These are assembled into a state-space representation so the whole system can be simulated and analysed with standard linear tools.

Simulation

A single bump, and the ride that follows.

Driving the model with a single road bump and watching the driver/seat displacement and velocity shows the suspension doing its job: an initial deflection that rings down and settles, rather than a harsh single jolt. The state-space form makes it easy to swap in different spring/damper values and compare the resulting ride.

Simulated driver/seat time response to a single road bump: displacement rings up and then decays over several seconds while velocity stays small.
Driver/seat response to a single bump — the displacement oscillates and decays as the suspension dissipates the disturbance.

Value

From equations on paper to a model you can tune.

The project connects derivation, linear-systems theory, and simulation into one workflow — a model you can actually push road inputs through and read ride comfort off of, which is the point of modelling a suspension in the first place.