Converting a simple mass-spring system to state-space model, how?

In summary, the conversation is about a simple homework problem that involves converting a system to a state-space model. The system is represented by the equation m*x" + k*x = f(t), with m = 5 and k = 1. The person asking for help is struggling because they have not put in enough effort. They mention their attempt at solving the problem, which involves creating state variables and matrices for the state-space model.
  • #1
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Homework Statement



Hi guys/girls

Professor gave this very simple homework where I need to convert the system below to a state-space model.
Mass_spring.png

The system itself is represented by the equation
Code: 
m*x" + k*x = f(t)
Where m = 5 and k = 1. Note that, " (doublequote) is a second-order derivative.
Unfortunately I don't have the background to solve it because I slacked too much :redface:

Homework Equations


State-space model that we use is below:
ddfd74546a0e35f9ec054af2ecd3f2fa.png

d0ac09f5cde2ce822ecc3e369692d04b.png


Any help&explanation would be appreciated, thank you.

EDIT: Ok, I've just read the rules and apparently I'm not allowed to as for solutions without an attempt to solve it. Since I can't even attempt, may I ask a good place/source to start?
 
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  • #2
attempt:

Code: 
5y" + 0y' + y = u

since my diff. eq. is second order, I should have 2 state variables:
Code: 
x1 = y
x2 = y'
so the state space model's matrixes become
Code: 
A = [ 0 1 ]   B = [ 0 ]
    [ 1 0 ]       [ 1 ]

C = [ 1 0 ]   D = [ 0 ]

does it look ok?
 
  • #3
Dude,

A = [0 1]
[(-k/m 0]

-k/m = -1/5 lol!
 

FAQ: Converting a simple mass-spring system to state-space model, how?

1. What is a mass-spring system?

A mass-spring system is a physical system consisting of a mass connected to a spring. The mass is free to move along a horizontal or vertical axis, and the spring provides a restoring force that is proportional to the displacement of the mass from its equilibrium position.

2. Why would someone want to convert a simple mass-spring system to a state-space model?

Converting a mass-spring system to a state-space model allows for more accurate and detailed analysis of the system's behavior. State-space models are also easier to manipulate mathematically and can be used to design control systems for the physical system.

3. What is a state-space model?

A state-space model is a mathematical representation of a physical system that describes the system's behavior over time using a set of differential equations. It consists of a set of state variables that represent the system's internal states and a set of input and output variables that describe the system's inputs and outputs.

4. How do you convert a simple mass-spring system to a state-space model?

To convert a mass-spring system to a state-space model, you first need to determine the state variables, which can be the position and velocity of the mass. Then, you can write the differential equations that describe the system's behavior using these state variables. Finally, you can rearrange the equations to put them in the standard state-space form.

5. What are the benefits of using a state-space model for a mass-spring system?

State-space models allow for more detailed analysis and control of the system's behavior compared to simple mass-spring models. They also make it easier to incorporate additional variables and inputs into the system, such as external forces or nonlinearities. Additionally, state-space models are widely used in engineering and can be easily implemented in simulations and control systems.

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