Design Of Inverted Pendulum Control System Based On The Theory Of Pole

In this paper, expound the background and significance of studying the inverted pendulum system, and the present situation, level and developing trend of the study at home and abroad, and discuss various methods of control over the inverted pendulum system. The first level mathematic model of the inverted pendulum is established by the method of Newton mechanics in the analytical mechanics, and then a double level mathematic model of inverted pendulum is established with the Lagrange equation, and last, the difference of Newton mechanics and Lagrange equation is pointed out. Aiming at the inverted pendulum control system, the hardware system and software system of it is designed systematically, the criterion of controllability and observability for the linear system and the form of the state feed-back question, and the design methods for the system controllers of single input-multiple output and multiple input-multiple output are given respectively, so as to analyze and study the stability of the first level and double level inverted pendulum systems. Based on the theory of pole allocation in modern control theory, the controllers for the first level and double level inverted pendulum systems are designed respectively to simulate and study the first level and double level inverted pendulum systems, and the experiment of controlling the real objects of the first level and double level inverted pendulum systems is conducted. In the simulation experiment of controlling over the first level inverted pendulum, both of the dolly and the pendulum are positioned at zero convergently in their respective displacement curves. In the real object experiment, the swing lever is stabilized in a range of +1°in the end, and the dolly is stabilized within -2cm to +10cm. In the simulation experiment of controlling over the double level inverted pendulum, the whole system is stable dynamically within a small range. The stable range is -3°≤θ₂ -θ₁≤3°for the upper pendulum, -4°≤θ₁≤4°for the lower pendulum, and 0≤r≤9 cm for the dolly. Therefore, the stable control over the upper pendulum, lower pendulum, and the dolly is realized.