Control System Design Of Double Inverted Pendulum System Based On Two-wheeled Self-balancing Vehicle

The double inverted pendulum is a classical unstable system with multivariate,nonlinear and strong coupling.The design of system model and control method is of great significance in the field of control engineering.In this paper,a type of double inverted pendulum system based on two-wheeled self-balancing vehicle is presented,which has simple structure,intuitive image and easy to build.It also provides a new experimental platform for the scientific research of control theory.In this paper,system model and controller of double inverted pendulum control system based on two-wheeled selfbalancing vehicle are mainly carried out.Firstly,the system model is established.The kinematics of system is analyzed and the kinematic model is built for the proposed double inverted pendulum system.To simplify the system analysis process,the dynamic equation of system is obtained by using the Lagrange energy based approach.Considering the small angular swing of the system at equilibrium point,the Taylor series expansion at the equilibrium point is used to linearize the dynamic equation.The system state space model is set up by selecting the system state variables.Next,the unknown parameters contained in the system model are determined.By using the physical experiment,the rotational inertias of the bar and the vehicle body are measured by the pendulum method for the small angle swing at the equilibrium point,respectively.The parameter identification model of the vehicle body and wheel is established,and the data collection platform is set up to obtain the input and output data of the vehicle body parameter identification model.The rotation inertia of the vehicle body is identified by employing the recursive least square method,and the identification result is compared with the experimental measurement results.The validity of the identification model and math is verified,and then the rotation inertia of the wheel is identified by the same method.Finally,the observability and the controllability are analyzed for the system described by state space model.The LQR controller is designed for the presented system.For the optimization selection of the weighted matrix in the LQR controller,the LQR controller based on PSO algorithm is designed.The control effects of the LQR controller and the PSO-based LQR controller are simulated and compared in MATLAB.The results show that the PSO-based LQR controller can obtain more optimized weighted matrix and has better control effect than traditional LQR controller for the proposed double inverted pendulum system based on two-wheeled self-balancing vehicle.