Vehicle Dynamics - Matlab & Simulink Examples

Explore how a bicycle model captures vehicle dynamics from steering input. Merge front and rear wheels to form the bicycle model and simulate the vehicle response.

Examine vehicle dynamics by modeling lateral acceleration regimes, from rigid-body motion to roll with suspension effects, using a body-fixed frame, then adopt a bicycle model in Matlab Simulink.

Explore the bicycle model for vehicle dynamics, deriving linearized state-space equations with slip angles, tire stiffness, and steering input, to analyze lateral motion and stability.

Explore state-space modeling of a pendulum dynamic system, deriving x1 = theta and x2 = theta dot, with matrix A and MATLAB simulations showing damping toward a stable equilibrium.

Analyze stability of a four-wheel vehicle via state space matrices and eigenvalues of A. Learn how radius of curvature, understeer, neutral steering, and oversteer affect maneuver safety.

Explain vehicle dynamics through oversteer, neutral steering, and understeer, using steady-state analysis and curvature concepts to show how forward speed and characteristic speed affect stability and maneuverability.

Explore how the bicycle model uses front and rear slip angles to explain cornering, lateral acceleration, and stability. Relate understeer and oversteer to slip angles, neutral steering, and centrifugal forces.

Avoid common mistakes in vehicle dynamics modeling with the bicycle model, covering critical and characteristic speeds, tire models, units, and MATLAB/Simulink examples.

Explore slip angle concepts through a Simulink model, using linearized small-slip approximations, state vs signal distinctions, and interactive inputs like steering angle and sine waves to debug vehicle dynamics.

Explore articulated vehicles, including tractors with trailers and fifth wheel hinges, using a bicycle model to analyze yaw and pitch. Compare linearized small-slip dynamics with non-linear extensions and interpret results.

Derive a single degree of freedom model for the trailer angle psi, obtaining a second-order equation with natural frequency and damping to relate slip angle to psi and assess stability.

Examine the three degree of freedom bicycle model for tractor–semi-trailer dynamics, linearize steering and slip angles, and derive the state-space form with the system matrix A to analyze stability.

In chapter 3, the lecture defines bicycle-model steady state as zero change in states, constant velocities, and the angle. It derives the critical speed for non-oscillatory instability using linear algebra.

Explore articulated vehicle instabilities through jackknifing and trailer swing, analyze stability metrics and real-world amplification, study tracking error and offset to reduce rearward amplification with control techniques.

Four wheel steering extends steering to rear wheels, increasing stability and maneuverability. Explore transient versus steady-state behavior, slip angles, and control strategies for rear-wheel actuation.

Analyze the four wheel steering vehicle model, extending the bicycle model with front and rear slip angles, dual inputs, and a state-space formulation for stability analysis.

Explore four wheel steering strategies with a k factor in the bicycle model. See how this reduces sideslip and alters the B and A matrices, affecting stability.

Explore a selection of four wheel steering control strategies for vehicle dynamics, examining how steering inputs shape sideslip angle, stability, and transient behavior using Matlab & Simulink examples.

Examine chapter 4 4ws examples, analyzing front steering inputs, sideslip angle, and curve-fitting methods. Compare strategies that zero sideslip in steady state or transient and relate to a state-space stability analysis.

Simulate a bicycle vehicle model in Matlab using h and k matrices for front and rear steering, achieving zero sideslip and analyzing stability and critical speed.

Analyze roll center and roll axis in an extended bicycle model, linking sprung and unsprung mass, suspension data, and three-degree-of-freedom dynamics to vehicle handling and load transfer.

Explore higher degree of freedom vehicle models beyond the bicycle model by incorporating roll motion, load transfer, wheel rotation, and nonlinear tire models.

Chapter 6 presents a 3-DOF vehicle model with longitudinal, lateral, yaw, and roll dynamics, incorporating sideslip, inertia, and roll stiffness into a state-space framework for simulation.

Explore how road irregularities drive the vertical vehicle response and how suspension dynamics, including bounce, pitch, and roll, govern ride comfort and handling.

Explore the wheel hop behavior of the quarter car model, analyzing unsprung mass, tire stiffness, and suspension damping to derive a 9.4 Hz natural frequency.

Model a two-mass quarter car with sprung and unsprung masses, springs and a damper; derive motion equations and explore undamped natural frequencies for body bounce and wheel hop in state-space.

Explore the quarter car model by deriving hop frequencies, creating road input signals, and building a simulation with a modified output matrix C to map sprung mass displacement and acceleration.

Simulate a quarter-car model in MATLAB using the predefined output matrix c and disturbance inputs to compare hump and bump profiles, analyzing displacement, acceleration, and ride comfort at varying speeds.

Explore transfer functions and state-space models of a quarter-car in matlab, deriving from motion equations and road input, and analyze sprung-mass displacement, acceleration, and suspension force using ss and ss2tf.

Explore the half car model to derive natural frequencies for bounce and pitch motions, using state-space and differential equations, and analyze front and rear suspension stiffness.

Explore the four degrees of freedom Cartercar model with two masses, deriving mass matrices and a state space representation for Matlab simulations.

Explore active suspensions in vehicle dynamics, comparing passive, semi-active, and active systems, and learn how actuators improve ride comfort and handling against higher cost and complexity.

Develop a basic active suspension model using a state-space representation of the sprung mass and suspension travel, with road input as a disturbance and a control input u.

Learn LQR control for vehicle dynamics, deriving input u from state x via gain K to minimize a quadratic cost with weights Q and R, and consider actuator limits.

Design an LQR controller for vehicle dynamics by formulating a quadratic cost with Q and R, solving the Riccati equation for P, and obtaining the gain K in Matlab.

Compare passive, velocity feedback, and LQR active quarter-car controllers using transfer functions and frequency responses for sprung-mass acceleration, suspension travel, and tire deflection, noting invariant points and weight effects.