Research Of Modeling And Balance Control For A Flywheel Inverted Pendulum

Inverted pendulum system simulation and physical control experiment is a typical scheme which used in verifies a certain control theory or method in control field. It is important means for the control of a certain unstable system and feedback control theory in deeply understand. At present, inverted pendulum balance control research mainly concentrated on the model which pendulum fixed in motion trolley, the balance of control pendulum through trolley motion. However, it is seldom for the research of flywheel inverted pendulum, especially it's control method research is being primary stage, and need to be further exploration and research.This paper researches the modeling of flywheel inverted pendulum system and related issues of motion balance control. And the achievement is as follows:First: The model of the flywheel inverted pendulum based on the Lagrange equationIn this paper we establish the dynamic model of the flywheel inverted pendulum system. The flywheel inverted pendulum is abstracted to a system that is composed of a circle flywheel, and a uniform quality bar. Then we establish a dynamic model of flywheel inverted pendulum using Lagrange equation under some assumption and simplification. We verified the system model through the simulation, and analyze the system's stability and controllability at last.Second: The design of linear quadratic optimal controller of flywheel inverted pendulum systems.We linearized the nonlinear mathematic model of flywheel inverted pendulum system at the balance point,and design linear quadratic optimal regulator controller for the flywheel inverted pendulum to control the balance of the inverted pendulum. In the Matlab/Simulink environment, the simulation experiments indicate that the controller is effective when the inclined angle of system in a certain range, and the controller is non-effective out the range.Third: The design of fuzzy controller based on packet control.Taking the nonlinear mathematic model of flywheel inverted pendulum system as control object, the four input variables of fuzzy controller is decoupled into two groups according to close degree of each input variable relation. Then for fuzzy control rules are designed respectively to reduce the number of fuzzy rules. The simulation experiments indicate the fuzzy controller can reduce the overshoot and adjusting time, and enhance system robustness.Fourth: the flywheel inverted pendulum motion control experiments based on virtual prototype.In order to verify model and control algorithm, virtual reality technology have been introduced, and ADAMS software have been used to do three-dimensional simulation experiment. Firstly, the open-loop response of the model and mathematical model established in this paper are compared to further verify the correctness of the latter model. Secondly, applied PD control on three-dimensional model of flywheel inverted pendulum, so as to establish the necessary foundation for the subsequent physical system control. At last, its control system have been created in the Matlab, and used the flywheel inverted pendulum at virtual reality environment as the controlling object, united simulation control experiment of Adams and Matlab have been completed. Achieved the flywheel inverted pendulum balance control, and then further verified the control algorithm.Fifth: physical experiment of flywheel inverted pendulum system.Through to the flywheel inverted pendulum system design, processing, installation and debugging of the hardware circuit, the flywheel inverted pendulum control system and perceptual system has been a deep understanding. Based on the earlier simulation research, for physical systems control provides theoretical basis and the reference data. Experimental results show that the pendulum of flywheel inverted pendulum system which deviates from the vertical position swinging positive and negative sixteen degrees control is effective, and the flywheel inverted pendulum system has a certain anti-interference ability.Our research in this paper is imbursed by Project 2007-AA04Z226 supported by China's 863 Program, Project 60774077 supported by NSFC, Project KZ200810005002 supported by Beijing Municipal Education Commission, Funding PHR (IHLB). The research work in this thesis is of significant reference value on robot research.