In recent years, more and more scientists have been interested in research on driving two-wheel bicycles. The problems in two-wheel bicycle control problem are self-balancing, uncertain models, and the impact of noise. In the paper, to solve the self-balancing problem, we use the flywheel method according to the inverted pendulum principle. To overcome the effects of the uncertain model, the impact of noise, we designed the vehicle balance controller according to the robust control algorithm. However, robust controllers often have a high order, which affects the quality during real control. To simplify the robust controller, we propose the use of a model order reduction algorithm. The simulation and experimental results have proved the correctness of the solutions given in the paper.

When there is no driver, balancing the two-wheel vehicle is a challenging but fascinating problem. There are various solutions for maintaining the balance of a two-wheel vehicle. This article presents a solution for balancing a two-wheel vehicle using a flywheel according to the inverted pendulum principle. Since uncertainties influence the actual operating environment of the vehicle, we have designed a robust controller RH∞ to maintain the vehicle equilibrium. Robust controllers often have a high order that can affect the actual control performance; therefore, order reduction algorithms are proposed. Using Matlab/Simulink, we compared the performance of the control system with different reduced-order controllers to choose a suitable low-order controller. Finally, experimental results using a low-order robust controller show that the vehicle balances steadily in different scenarios: no-load, variable load, stationary, and moving.

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Model reduction of a system is an approximation of a higher-order system to a lower-order system while the dynamic behavior of the system is almost unchanged. In this paper, we will discuss model order reduction (MOR) strategies for unstable systems, in which the method based on the balanced truncation algorithm will be focused on. Since each MOR algorithm has its strengths and weakness, practical applications should be suitable for each specific requirement. Simulation results will demonstrate the correctness of the algorithms.

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