Swing Up And Stability Intelligent Control Of Linear Single Inverted Pendulum

The control of inverted pendulum system has been long considered as an intriguing problem in control theory and application. Inverted pendulum system is a typical quick, multivariable, nonlinear and unstable system. So it is a classic system that can reflect many problems which exist in control realm. Inverted pendulum is a very important plant. In theory, It is well known as a test bed for new control theory and techniques. And in application many equipments such as aviation, robots can't do without it. The inverted pendulum plant is in common use in control theory teaching and research as it is also so cheap and easy to get. So it is amused and valuable for a senior student to do research on this subject.In this paper, single inverted pendulum is investigated, and we place emphasis on the control of swing-up and stability of the single inverted pendulum. Main research work is declared below:1. First, the composing and working principle of the inverted pendulum is introduced and its mathematic model is built. It is proved that its open control system is instability, but it is controllable and observable on equilibrium point.2. The process of swing-up of the inverted pendulum is analyzed and the method of energy feedback to upswing is introduced.3. PID controller and linear quadratic optimal (LQR) controller is designed. Also, through simulation in Matlab, response of different input and initial conditions of the two methods are compared and studied carefully. The experiments show that PID controller is a simple structure as feedback transfer function. But its control effect is less perfect. LQR controller is a relatively sophisticated methods of modern control theory. Its control effect is relatively perfect. And it can be used in real-time control. Also the complexity of the accused system and the increase of non-linearity will reduce the control performance. So, we should study more effective control methods.4. Research on Fuzzy control algorithm of inverted pendulum system and fuzzy control of swing up is researched. The dimensions of input varieties of fuzzy controller of stability is depressed by designing a fusion function using optimization control theory, rule explosion problem is solved. Based on fuzzy control theory, we design fuzzy adapting PID controller to control pendulum angle in accordance with principle that first control pendulum angle and second control cart displacement. Two dimensional fuzzy controller is used to control cart displacement. It also can avoid rule explosion problem.5. And then, The inverted pendulum fuzzy control system is simulated in Matlab software. The results of simulation from adjusting parameters show that the control method has good control ability.6. Last, the real control is achieved in Real-time Workshop of Simulink environment. The response curves of state variable and the curve of control quantity when the pendulum is swing-up, stable and being disturbed. The result of real-time control show that the swing-up and stable control of single inverted pendulum have good effects and good anti-disturb factors.