倒立擺的控制外文翻譯

1、第 1 頁Control of an Inverted PendulumJohnny LamAbstract: The balancing of an inverted pendulum by moving a cart along a horizontal track is a classic problem in the area of control. This paper will describe two methods to

2、 swing a pendulum attached to a cart from an initial downwards position to an upright position and maintain that state. A nonlinear heuristic controller and an energy controller have been implemented in order to swing th

3、e pendulum to an upright position. After the pendulum is swung up, a linear quadratic regulator state feedback optimal controller has been implemented to maintain the balanced state. The heuristic controller outputs a re

4、petitive signal at the appropriate moment and is finely tuned for the specific experimental setup. The energy controller adds an appropriate amount of energy into the pendulum system in order to achieve a desired energy

5、state. The optimal state feedback controller is a stabilizing controller based on a model linearized around the upright position and is effective when the cart-pendulum system is near the balanced state. The pendulum has

6、 been swung from the downwards position to the upright position using both methods and the experimental results are reported.1. INTRODUCTION The inverted pendulum system is a standard problem in the area of control syste

7、ms. They are often useful to demonstrate concepts in linear control such as the stabilization of unstable systems. Since the system is inherently nonlinear, it has also been useful in illustrating some of the ideas in no

8、nlinear control. In this system, an inverted pendulum is attached to a cart equipped with a motor that drives it along a horizontal track. The user is able to dictate the position and velocity of the cart through the mot

9、or and the track restricts the cart to movement in the horizontal direction. Sensors are attached to the cart and the pivot in order to measure the cart position and pendulum joint angle, respectively. Measurements are t

10、aken with a quadrature encoder connected to a MultiQ-3 general purpose data acquisition and control board. Matlab/Simulink is used to implement the controller and analyze data. The inverted pendulum system inherently has

11、 two equilibria, one of which is stable while the other is unstable. The stable equilibrium corresponds to a state in which the pendulum is pointing downwards. In the absence of any control force, the system will natural

12、ly return to this state. The stable equilibrium requires no control input to be achieved and, thus, is uninteresting from a control perspective. The unstable equilibrium corresponds to a state in which the pendulum point

13、s strictly upwards and, thus, requires a control force to maintain this position. The basic control objective of the inverted pendulum problem is to maintain the unstable equilibrium position when the pendulum initially

14、starts in an upright position. The control objective for this project will focus on starting from the stable equilibrium position (pendulum pointing down), swinging it up to the unstable equilibrium position (pendulum up

15、right), and maintaining this state.第 3 頁Let the state vector be defined as:Finally, we linearize the system about the unstable equilibrium(0 0 0 0) T.Note that θ = 0 corresponds to the pendulum being in the upright posit