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Two-wheeled self-balancing vehicle system is a kind of naturally unstable underactuated system with high-rank unstable multivariable strongly coupling complicated dynamic nonlinear property. Nonlinear dynamics modeling and simulation, as a basis of two-wheeled self-balancing vehicle dynamics research, has the guiding effect for system design of the project demonstration and design phase. Dynamics model of the two-wheeled self-balancing vehicle is established by importing a TSi ProPac package to the Mathematica software (version 8.0), which analyzes the stability and calculates the Lyapunov exponents of the system. The relationship between external force and stability of the system is analyzed by the phase trajectory. Proportional–integral–derivative control is added to the system in order to improve the stability of the twowheeled self-balancing vehicle. From the research, Lyapunov exponent can be used to research the stability of hyperchaos system. The stability of the two-wheeled self-balancing vehicle is better by inputting the proportional–integral–derivative control. The Lyapunov exponent and phase trajectory can help us analyze the stability of a system better and lay the foundation for the analysis and control of the two-wheeled self-balancing vehicle system.
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