Dynamics and Control Research of a Momentum-Wheel-Based Two-Wheeled Self-Balancing Vehicle Based on Cascade PID

Momentum wheel-based two-wheeled self-balancing vehicle represent typical underactuated, nonlinear systems, posing significant challenges for stability control under varying operating conditions. To achieve self-stabilizing control during uniform horizontal motion, a cascaded PID control method is proposed. This approach stabilizes the frame tilt angle via an outer-loop PID controller while simultaneously controlling the handlebar angle and momentum wheel speed through an inner-loop PID controller, thereby enabling constant-speed self-balancing vehicle operation. First, based on the Lagrange method, the five rigid-body Lagrangian functions of the self-balancing vehicle are derived. The nonlinear dynamic equations of the self-balancing vehicle system, incorporating Lagrange multipliers, are established. Using Taylor series expansion, these equations are approximated linearly near the system's equilibrium point, leading to the linearized dynamic equations of the self-balancing vehicle system. Then，building upon this foundation, the model's stability is analyzed using the Lyapunov stability criterion. A cascaded PID controller is designed, employing the self-balancing vehicle's body tilt angle as the outer loop and the handlebar angle and reaction wheel speed as the inner loop, based on key variables such as body tilt angle, handlebar angle, and reaction wheel speed. Finally, MATLAB/Simulink is utilized to simulate the self-balancing vehicle's key variables under the cascaded PID controller. Simulation results demonstrate that under cascade PID control, the self-balancing vehicle recovers to an upright state within 1.5 seconds. The maximum body tilt deviation is controlled within 0.029rad, with system overshoot at 2.9% and steady-state error approaching zero, exhibiting excellent dynamic response and stability. This research provides theoretical justification and simulation validation for the horizontal balance control of two-wheeled self-balancing vehicle.