Inverted pendulum attached to cart, cart on frictionless surface & axes

In summary, the conversation discusses the behavior of an inverted pendulum attached to a frictionless cart. The initial conditions of the system are set and it is observed that without friction, the pendulum continues to swing back and forth perpetually, always reaching the initial height in a symmetrical angle. There is a suggestion that the motion of the pendulum may appear differently depending on the observer.
  • #1
Number2Pencil
208
1

Homework Statement



As a small verification of a larger problem, I'm trying to determine how the dynamics of an inverted pendulum attached to a frictionless cart would behave.

The cart has no input force applied, so all horizontal movements would be due purely to the centrifugal+normal force of the pendulum, being driven by gravity.

The initial conditions of the system would be that the initial cart speed/position = 0, the initial angular rate of pendulum = 0, and the initial positional angle of the pendulum = 0.01 radians, and just let to fall


Homework Equations





The Attempt at a Solution



After solving through all the kinematic laws, and trying to simulate the system, what I am seeing is that without friction, the pendulum continues to swing perpetually back and forth, always reaching the initial height at a angle symmetrical to the starting angle.

Does this sound feasible?
 
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  • #2
It would help if you provide an image of the system you have in mind. The images from a google search 'inverted pendulum' suggest that while the pendulum is falling, the cart will be accelerated in one direction and while the pendulum is rising, the cart is accelerating in the opposite direction.

If that interpretation is correct, the appearance of the motion of the pendulum will depend on the observer. If you are sitting on the cart, I believe the pendulum will appear to swing in a circle but from the lab frame, it would make a distorted shape (I can't imagine it right away, but it should not be hard to find mathematically)
 

1. What is an inverted pendulum attached to a cart?

An inverted pendulum attached to a cart is a classic control system problem often studied in engineering and physics. It involves a cart on a frictionless surface with a pendulum attached to the cart's top, which can move freely in only one dimension. The goal is to control the movement of the cart and pendulum in order to keep the pendulum upright.

2. How does the inverted pendulum system work?

The inverted pendulum system works by using a control algorithm to continuously adjust the position and velocity of the cart in order to maintain the pendulum in an upright position. This is typically done using sensors, actuators, and feedback loops to measure and adjust the system's variables.

3. What are the applications of an inverted pendulum attached to a cart?

The inverted pendulum system has various applications, including robotics, self-balancing vehicles, and control system development. It is also commonly used as a teaching tool to demonstrate concepts in control theory and feedback control systems.

4. What is the significance of having a frictionless surface for the cart in an inverted pendulum system?

A frictionless surface is significant in an inverted pendulum system as it allows for easier control of the cart's movement without external forces affecting its motion. This simplifies the system and allows for a more accurate study of the control algorithm's effectiveness in maintaining the pendulum's balance.

5. Are there any real-world examples of an inverted pendulum attached to a cart?

Yes, there are several real-world examples of an inverted pendulum attached to a cart. One example is the Segway, a self-balancing electric vehicle that uses an inverted pendulum system to maintain balance. Another example is the Furuta pendulum, a research tool used to study control systems and dynamics.

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