Control And Study Of Planar Inverted Pendulum Base On Ac Servo System

Inverted pendulum is widely concerned by physical, mechanical, mathematical, and control disciplines as a typical non-linear, multivariable, strong coupling and the natural instability dynamic systems. Many researchers use it as a typical equipment of experiment for teaching and research. It can effectively reflect the stabilization, robustness, mobility, traceability and other crucial issues of system in the control process. Meanwhile, the inverted pendulum has an important engineering background, for example the robot to walk upright, the posture control of space take-off booster, the offshore drilling platform stability control, which use inverted pendulum as physical model.At present, the studies for inverted pendulum mainly focus on single-dimension inverted pendulum and the control of mechanical structural parts of inverted pendulum, while pay little attention to the impact of the drive unit. In this paper, in order to achieve rapid stabilization and tracking control of planar inverted pendulum, the permanent magnet synchronous motor is used as the drive unit for planar inverted pendulum, the drive performance of motor and the dynamic characteristic of inverted pendulum are comprehensively considered.In the paper, we firstly introduce the mechanical structure and mathematical model of permanent magnet synchronous motor, analyse the vector control theory and the voltage space vector pulse width modulation technology, and present the simulation model and the wave curves of permanent magnet synchronous motor vector control system. Meanwhile, we use Lagrange equation to establish the dynamic model of planar inverted pendulum, the non-linear mathematical model of planar inverted pendulum system is non-linear decoupled by using step control in the X axis and Y axis, and we obtain the decoupled non-linear mathematical model of the inverted pendulum in the directions of X axis and Y axis.Then, by considering the drive characteristic of permanent magnet synchronous motor, we adopt three kinds of PID control methods to execute the stabilization and tracking control of the non-linear inverted pendulum mathematical model in the X axis and Y axis. By simulating in the Matlab/Simulink, we choose one of the best performance from three types of PID control methods to carried out the position tracking control of step signal, sine wave signal, cosine wave signal, and compass trace signal on X-Y plane. The simulation results prove that PID control can achieve the stability and tracking control of planar inverted pendulum system. In order to improve the control performance of planar inverted pendulum, by considering the drive performance of permanent magnet synchronous motor, we adopt the fuzzy adaptive PID and the full fuzzy control to carry out the stability and tracking control of planar inverted pendulum system respectively. In the fuzzy adaptive PID control, the position control of the cart use fuzzy adaptive PID controller, and the pendulum swing angle use ordinary PID controller. In the full fuzzy control, firstly the error signals of the four outputs of inverted pendulum are transferred into comprehensive error and error rate, then the fuzzy controller is used to control inverted pendulum. The simulation result proves that by using the fuzzy control, the planar inverted pendulum control system has better robustness and faster responding.Finally, the hardware and software construction processes of the planar inverted pendulum system were introduced. The hardware base on PC and TMS320F2812 as the control core. The software consists of the main program of planar inverted pendulum control, DSP initialization subroutine, motor drive subroutine, cart position and pendulum angle measurement subroutine, and so on.