爱华网In this paper, the Furuta pendulum which is the classic model of the spherical pendulum will be discussed. The issue is to carry the pendulum to the upright position and the make it stable at this inverted position. In this paper, the nonlinear system will be linearised and then simulated by LQR method. 1.Introduction As a controlled plant, the Furuta pendulum is multivariable, open-loop unstable and nonlinear higher-order system. The proof of amount of new real-time control theory all base on Furuta pendulum control method. This method also can be applied in many other issues of stability, even the vertical launching of rockets.[1] Figure1.1 shows the basic structure of the Furuta pendulum, in which, the horizontal one is arm, and the vertical one is pendulum. is the angle between the arm and horizontal axis, while is the angle between the pendulum and vertical axis.[2] Figure1.2 is the simplified structure of the Furuta pendulum. Pendulum, arm, motor, frame and electricity box can be seen clearly in this figure. The pendulum is connected with arm which is controlled by the motor. This makes the system more complicated and unstable. There are two main parts below. First part is to analysis the physical model of the Furuta pendulum and deduce the mathematical model, which means to get the state space of the system. The next part is the core of this report, which is simulation of the system. In this part, LQR control law is the method which we used. 2.Analysis of physical modeland setting up mathematical model of the system
