Two-Degree-of-Freedom Vehicle Modeling with State Observer and Control Analysis

Application of State Observers in Vehicle Control Systems

Modern vehicle control systems frequently employ state observers to estimate key state variables that cannot be directly measured, such as yaw rate and sideslip angle. Vehicle dynamics modeling based on the two-degree-of-freedom (2-DOF) model serves as the fundamental approach for studying lateral vehicle motion. This model simplifies the vehicle to the motion of front and rear wheels, describing lateral and yaw movements through state-space equations. In code implementation, the 2-DOF model typically involves defining mass, inertia, cornering stiffness parameters, and constructing state matrices using vehicle physical parameters.

Core Function of State Observers: Reconstructing System States

When sensors cannot directly measure certain states (such as tire slip angles), state observers combine known input signals (like steering wheel angle) and measurable output signals (like lateral acceleration) for state estimation. Common observer design methods include Luenberger observers and Kalman filters, which effectively handle system noise and measurement errors. The Kalman filter implementation typically involves two main stages: prediction (using system dynamics) and update (incorporating new measurements). The observer gain matrix is crucial for balancing estimation speed and noise rejection.

Control Strategy and Animation Visualization

In path tracking control, the state estimates provided by the observer are compared with the reference path. A composite control strategy combining feedforward and feedback components calculates the required front wheel steering angle. Animation demonstrations visually show the deviation between the vehicle's actual trajectory and the reference path, as well as the convergence process between observer-estimated states and true states. This visualization is significant for understanding control system performance. The animation implementation often uses real-time plotting functions to update vehicle position and states at each simulation time step.

Key implementation aspects include establishing an accurate 2-DOF model, designing appropriate observer gain matrices, and selecting suitable control algorithm parameters. Through simulation animations, one can observe the system's response characteristics at different speeds and the observer's estimation effectiveness under various road adhesion coefficients. These visualization results provide valuable reference for control system debugging and parameter optimization. The simulation code typically involves setting up vehicle parameters, defining control laws, and implementing real-time state estimation algorithms with visualization updates.