Converting a nonlinear eqn of motion to a state-space model

In summary, the conversation discusses converting a system with two configuration variables, q1 and q2, and inputs tau1 and tau2, to a state-space equation with state-variables x1 = q1_dot, x2 = q1_2dot, x3 = q2_dot, x4 = q2_2dot. The question is about how to decouple the variables q1 and q2 in the equations of motion in order to create a state-space equation. The speaker mentions not having found an example of applying state-space techniques to a non-linear problem.
  • #1
Sean L
1
0

Homework Statement


upload_2019-2-7_0-3-21.png

equations above are descriptive of a system with two configuration variables, q1 and q2. inputs are tau1 and tau2. d and c values are given.
the question is about conversion of above equations to a state-space equation where the state-variables are x1 = q1_dot, x2 = q1_2dot, x3 = q2_dot, x4 = q2_2dot.

Homework Equations



The Attempt at a Solution


Since variables q1 and q2 are coupled in the equations of motion, so I haven't been able to come up with a way to decouple them and makes a state-state equation. Any insights on this would very much be appreciated.
 

Attachments

  • upload_2019-2-7_0-3-21.png
    upload_2019-2-7_0-3-21.png
    4.3 KB · Views: 761
Physics news on Phys.org
  • #2
What are g1 and g2?
 
  • #3
Sean L said:

Homework Statement


View attachment 238367
equations above are descriptive of a system with two configuration variables, q1 and q2. inputs are tau1 and tau2. d and c values are given.
the question is about conversion of above equations to a state-space equation where the state-variables are x1 = q1_dot, x2 = q1_2dot, x3 = q2_dot, x4 = q2_2dot.

Homework Equations



The Attempt at a Solution


Since variables q1 and q2 are coupled in the equations of motion, so I haven't been able to come up with a way to decouple them and makes a state-state equation. Any insights on this would very much be appreciated.
I've taken an entire semester of state space techniques and have yet to find an example of applying the technique to a non-linear problem.
 

1. What is a state-space model?

A state-space model is a mathematical representation of a system that describes its internal state variables and how they change over time. It is commonly used in control theory and allows for the analysis and design of complex systems.

2. Why is it necessary to convert a nonlinear equation of motion to a state-space model?

Converting a nonlinear equation of motion to a state-space model allows for the use of powerful tools and techniques from control theory, such as the state-space representation and state feedback control. It also simplifies the analysis and design process for complex systems.

3. What are the steps involved in converting a nonlinear equation of motion to a state-space model?

The first step is to identify the state variables of the system, which are the minimum set of variables that can fully describe the system's behavior. Next, the nonlinear equations of motion are rewritten in terms of the state variables. Finally, the state equations and output equations are derived, which form the state-space model.

4. Are there any limitations to converting a nonlinear equation of motion to a state-space model?

Yes, there are some limitations. The state-space model assumes that the system is linear and time-invariant, which may not always be the case. Additionally, if the system is highly nonlinear, the state-space model may not accurately represent its behavior.

5. Can a state-space model be used for any type of system?

Yes, a state-space model can be used for a wide range of systems, including mechanical, electrical, and biological systems. However, it is most commonly used for systems that can be described by a set of differential equations.

Similar threads

Engineering First order non linear to state space equations
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Engineering Converting a series connected transfer function to the state space model
    • Engineering and Comp Sci Homework Help
Replies
1
Views
843
Express the system in state space form
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Finding the state space model of a nonlinear system
    • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
Linearizing a system of equations?
    • Engineering and Comp Sci Homework Help
Replies
5
Views
2K
State-space modeling of a control system
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Engineering Control Systems: How would you find the State Equations for this simple circuit?
    • Engineering and Comp Sci Homework Help
Replies
1
Views
2K
State Space Model of an RL Circuit
    • Introductory Physics Homework Help
Replies
1
Views
3K
State-Space model of spring-mass system
    • Engineering and Comp Sci Homework Help
Replies
4
Views
4K
Equation of Motion of a Inverse Pendulum on a Cart
    • Engineering and Comp Sci Homework Help
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top