Application of model reduction for robust control of self-balancing two-wheeled bicycle

Abstract

In recent years, balance control of two-wheeled bicycle has received more attention of scientists. One difficulty of this problem is the control object is unstable and constantly impacted by noise. To solve this problem, the authors often use robust control algorithms. However, robust controller of selfbalancing two-wheeled bicycle are often complex and higher order so affect to quality during real controlling. The article introduces the stochastic balanced truncation algorithm based on Schur analysis and applies this algorithm to reduce order higher order robust controller in control balancing two-wheeled bicycle problem. The simulation results show that the reduced 4 th and 5 th order controller arcoording to the stochastic balanced truncation algorithm based on Schur analysis can control the two-wheeled bicycle model. The reduced 3 rd order controller cannot control the balance of the two-wheeled bicycle model. The reduced 4 th and 5 th order controller can replace the original controller while the performance of the control system is ensured. Using reduced 5 th , 4 th order controller will make the program code simpler, reducing the calculation time of the self-balancing two-wheel control system. The simulation results show the correctness of the model reduction algorithm and the robust control algorithm of two-wheeled self-balancing two-wheeled bicycle.

Control Design for the Ward–Leonard System in Wind Turbines

“…Different order reduction algorithms were used to reduce the order of the 6 th -order controller, and the different resulting controllers were compared to choose the most suitable low-order controller. This study used Moore's balanced truncation algorithm [16], LQG balancing algorithm [17], and Singular Perturbation Approximation (SPA) [18] to reduce the order of the controller. The results of the step reduction are shown in Tables I-III.…”

Application of Zhou’s Balanced Truncation Algorithm for Controlling the Balance of Bicyrobot

“…However, the difficult problem of twowheeled mobile robot is maintaining robot balance when the vehicle is stationary, when the vehicle is moving. Among the two-wheeled mobile robots, the bicyrobot is one of the robots that is of great interest to research [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Using the Model Reduction Techniques to Find the Low-Order Controller of the Aircraft's Angle of Attack Control System

“…In practice, the use of high-order controllers has many disadvantages. Therefore, robust control design is often accompanied by a requirement to reduce the controller order [4][5][6][7][8][9].…”

“…The balanced truncation algorithm has been improved to apply to unstable systems [11], continuous systems [12] and discrete systems [13], or continuous to discrete conversion [14]. Some popular order reduction methods are the method of preserving the dominant point [7] or the optimal method of Hankel [15], etc. Therefore, to find a suitable low-order controller, we need to compare and evaluate the low-order controllers, which are the result of using different algorithms to reduce the high-order controller.…”

“…Using a high-order controller (6 th -order controller) will cause many disadvantages in practice, while using a low-order controller in practice brings many advantages such as easier analysis, much faster simulation, controller synthesis easier [1][2][3][4][5][6][7][8][9]. Therefore, it is necessary to simplify the high-order controller.…”