Inverted Pendulum Simulation

In summary, the conversation discusses the process of building a single axis inverted pendulum using a PID system. The focus is on creating a program to simulate the tipping motion and the effects of moving the base to counter it. The main challenge is determining the correct mathematical model, including large angle motion, and deciding whether to use Newton's Second Law or the Lagrange formulation. The importance of defining variables and developing equations of motion for both the pendulum and the cart is emphasized.
  • #1
collinpetty
1
0
Hello,

I am attempting to build a single axis inverted pendulum using a PID system to keep the rod balanced. I am interested in writing a program to simulate the rod tipping over and the effects of moving the base (pivot point) left or right to counter the tipping effect. I can't quite figure out the math to model a rod of uniform density that is standing on end falling over. I remember learning formulas for pendulums in physics class but it was for pendulums that swing less than 15 or so degrees (assuming that for values close to 0 sin(x)=x). Also, I'm not sure I know how to model a scenario where the base of the rod that is tipping over is pushed quickly back "under" the rod (beneath and actually slightly past the center of mass of the rod). Any and all help would be appreciated.

Collin
 
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  • #2
Before you can worry about making a simulation, you need to get the correct mathematical model, including large angle motion, as you noted. You will need to settle upon an approach to the problem, either by using Newton's Second Law, or by using the Lagrange formulation, if you are familiar with that method. You need to give some thought to what you will include in your model. Will you model only the motion of the pendulum itself, or do you also need to model the motion of the cart (slider, or whatever you want to call it) that carries the pivot point? For a complete system model, you will need to include both, which means that you will need to develop equations of motion for both the pendulum and the cart, so that there will be 2 degrees of freedom. Begin by carefully defining your variables, drawing free body diagrams if you are going to use Newton's second law, and then put together the equations of motion. Good luck.
 
  • #3
,

Thank you for reaching out with your question about building a single axis inverted pendulum and simulating its behavior. This is an interesting and challenging project that requires a solid understanding of physics and mathematics. Let me provide some insights and guidance that may help you in your simulation.

Firstly, it is important to understand the physical principles behind an inverted pendulum. The inverted pendulum system consists of a rod with a pivot point at the base and a mass at the top. The goal of the system is to maintain the mass in an upright position, even when the base is moved or disturbed. This is achieved through the use of a control system, such as a PID system, which adjusts the base position to keep the rod balanced.

To accurately simulate the behavior of an inverted pendulum, you will need to consider several factors. These include the length and mass of the rod, the position and mass of the pivot point, and the force applied to the base. You will also need to consider the effects of gravity, which will act on the mass at the top of the rod.

In terms of the math involved, you will need to use equations of motion and rotational dynamics to model the behavior of the system. The equations for a pendulum with small oscillations can be used as a starting point, but you will need to make adjustments for a larger range of motion and the added complexity of a moving base.

To model the scenario where the base of the rod is quickly pushed back under the rod, you will need to incorporate a sudden change in the base position and apply the appropriate forces to the system. This will require careful calculations and consideration of the system's dynamics.

I would recommend consulting with a physics or engineering textbook or seeking guidance from a mentor or instructor to help you with the mathematical modeling of your inverted pendulum simulation. With a solid understanding of the physical principles and the use of accurate equations, you should be able to build a realistic simulation of the system.

Best of luck with your project! Keep exploring and experimenting, and don't hesitate to ask for help when needed. Science is all about learning and collaboration, and I'm sure you will be able to successfully simulate your inverted pendulum with some dedication and effort.
 

What is an inverted pendulum simulation?

An inverted pendulum simulation is a virtual model of a pendulum that is balanced in an inverted position, with its center of mass above its point of support. This type of simulation is commonly used in control theory and robotics to study the dynamics and stability of a system.

Why is an inverted pendulum simulation important?

An inverted pendulum simulation allows researchers and engineers to study the behavior of a pendulum in a controlled and repeatable environment. This can help in the design and analysis of control systems for real-world applications, such as balancing robots or stabilizing structures.

What are the main challenges in creating an accurate inverted pendulum simulation?

The main challenges in creating an accurate inverted pendulum simulation include accurately modeling the dynamics of the system, accounting for external forces such as friction and air resistance, and implementing realistic control strategies. Additionally, the simulation must be able to handle nonlinearities and uncertainties in the system.

What are some real-world applications of inverted pendulum simulations?

Inverted pendulum simulations have various real-world applications, including robotics, aerospace engineering, and control systems design. They can also be used in educational settings to teach principles of control theory and stability.

What are some common control strategies used in inverted pendulum simulations?

Some common control strategies used in inverted pendulum simulations include proportional-derivative (PD) control, state feedback control, and optimal control. These strategies aim to stabilize the pendulum and keep it balanced in the inverted position by adjusting the control input based on the system's current state.

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