State Space representation of an inverted Pendulum

In summary, the conversation is about creating state space representations and someone is asking for clarification on how to get the matrix A from their equations. They have provided their attempt at a solution and have also included a link to the desired solution. The desired solution is presented as a 4x4 matrix.
  • #1
shreddinglicks
212
6

Homework Statement


I am trying to learn how to create state space representations. I am using this link to study.

http://www2.ensc.sfu.ca/people/faculty/saif/ctm/examples/pend/invpen.html

Could someone explain how to get the matrix A from my equations?

Homework Equations

The Attempt at a Solution


I have when changing variables:

x'1 = x = x2
x'2 = x'' = (I/(mL)+L)x'4 - gx3
x'3 = phi' = x4
x'4 = phi'' = ((M/ml)+(1/L))x'2 + (b/(ml))x2 - (F/(ml))

How do I get matrix A from this? I have the desired solution attached which is also in the link above.
 

Attachments

  • Capturec.PNG
    Capturec.PNG
    6.2 KB · Views: 272
Physics news on Phys.org
  • #2
I am trying to understand how to get there.The desired solution is:A = [0 1 0 0] [0 0 -g/L (I+mL)/(mlL)][0 0 0 1] [0 0 (M+mL)/(mlL) -b/(ml)]
 

1. What is a state space representation?

A state space representation is a mathematical model that describes the behavior of a system over time. It is a set of equations that relate the state variables (such as position, velocity, and acceleration) of a system to its inputs and outputs.

2. How is an inverted pendulum represented in state space?

An inverted pendulum can be represented in state space by defining its state variables as the angle of the pendulum and its angular velocity. The inputs to the system would be the force applied to the pendulum, and the output would be the position of the pendulum.

3. What are the advantages of using state space representation for an inverted pendulum?

Using state space representation allows for a more comprehensive understanding of the behavior of an inverted pendulum. It also allows for the use of control theory techniques to design controllers for stabilizing the pendulum. Additionally, state space representation can handle nonlinear systems and external disturbances, which are common in real-world applications.

4. What are the limitations of state space representation for an inverted pendulum?

One limitation of state space representation is that it can be computationally expensive for complex systems. It also requires accurate modeling of the system, which can be challenging for systems with a high degree of complexity or uncertainty. Additionally, state space representation may not provide intuitive insights into the physical behavior of the system.

5. How is state space representation used in the control of an inverted pendulum?

State space representation is used in the design of controllers for an inverted pendulum through the use of control theory techniques such as pole placement and optimal control. The state variables and inputs of the system are manipulated to achieve stability and desired performance of the pendulum.

Similar threads

I Representation of Spin 1/2 quantum state
    • Quantum Physics
2
Replies
61
Views
1K
State-space description, nonlinear system, inverted pendulum
    • Calculus and Beyond Homework Help
Replies
1
Views
3K
Inverted Pendulum on a Cart -- Nonlinear State Space equations
    • Programming and Computer Science
Replies
1
Views
2K
I Understanding Spin States in 2D Vector Spaces
    • Quantum Physics
Replies
6
Views
1K
I Fundamental representation and adjoint representation
    • Quantum Physics
Replies
27
Views
940
State space controllers - find equations from differentials
    • Advanced Physics Homework Help
Replies
12
Views
1K
B Tensor product of operators and ladder operators
    • Quantum Physics
Replies
2
Views
1K
Solution to Coupled Second Order ODE's
    • Calculus and Beyond Homework Help
Replies
4
Views
6K
Find the basis of a vector subspace of R^2,2
    • Calculus and Beyond Homework Help
Replies
9
Views
2K
A Ballentine on the "multicomponent state function"
    • Quantum Physics
Replies
1
Views
858

Hot Threads

Recent Insights

Back
Top