Research On Stability Control For Linear Double Inverted Pendulum

Inverted pendulum system is a complex multi-variable, highly nonlinear, strong coupling, rapidly moving and absolutely instable system. We must take effective control method in order to make it stable at near the equilibrium position. On the one hand, inverted pendulum control process can effectively reflect much of the key control problems, such as the non-linear problem, the system robustness problem, the dynamic problem, the stabilization problem and the tracking problem. Therefore, the inverted pendulum control is of great theoretical significance. On the other hand, any control problem with fulcrum under its barycenter is similar to an inverted pendulum model. Therefore, study on the control of inverted pendulum system also has an important practical significance.In this thesis, linear quadratic optimal control which was optimized with genetic algorithms and fuzzy control which was optimized with genetic algorithms were studied on the linear double inverted pendulum which was produced by Shenzhen Googol Company.The main research work are as follows:1. An introduction of the inverted pendulum control study background and status was given. A double inverted pendulum nonlinear mathematical model of physical systems was set up using Lagrange's equation. Two types of linear approximation methods were used to deal with the nonlinear mathematical model and two types of linear models were obtained. The analysis of the characteristics proved that linear double inverted pendulum system is a naturally unstable system but completely controllable near the equilibrium position.2. We optimized the optimal state weighted array of linear quadratic optimal control and obtained the optimal state feedback matrix, so we realized linear quadratic optimal control optimized with genetic algorithm. We made use of the optimal state feedback matrix to to deal with dimensionality reduction of linear double inverted pendulum state variables. Then we constructed the basic two-dimensional fuzzy controller and used genetic algorithm to optimize parameters of the linear double inverted pendulum system, such as quantitative factors and scale factor, so we realized fuzzy control optimized with genetic algorithm. In the MATLAB environment, we made simulation analysis on the linear double inverted pendulum control system according to these two methods. At the same time we analyzed the impact of linear approximation on the system dynamic performance and steady-state performance.3. Using MATLAB RTW toolbox for real-time control, we constructed real-time fuzzy control platform. We used the control algorithm module to generate code to download to real-time kernel, to drive external hardware devices and to realize stability control of the double inverted pendulum. Using Borland C++ 3.1 to develop real-time fuzzy control procedures and generate an executable program file, we realized stability control of the double inverted pendulum in DOS environment.Simulation studies on the linear double inverted pendulum system and physical control showed that linear quadratic optimal control optimized with genetic algorithm and fuzzy control optimized with genetic algorithm, were able to realize stability control of the double inverted pendulum. Compared with the first method, the second method not only had good dynamic performance and steady-state performance, but also had better robustness.