Understanding Transfer Functions in ODEs

Click For Summary
SUMMARY

The discussion centers on deriving the transfer function from a second-order ordinary differential equation (ODE) represented as A*Y = M*X'' + (B+C)*X' + D*X. By applying the Laplace transform, the user correctly formulates the transfer function TF(s) = X(s)/Y(s) as A*Y(s) = M*s^2*X(s) + (B+C)*s*X(s) + D*X(s). The transfer function is accurately derived, confirming the user's approach to the design project.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with Laplace transforms
  • Knowledge of transfer functions in control systems
  • Basic concepts of system dynamics
NEXT STEPS
  • Study the derivation of transfer functions from various types of ODEs
  • Learn about the stability analysis of systems using transfer functions
  • Explore the application of Laplace transforms in engineering problems
  • Investigate the use of MATLAB for simulating transfer functions
USEFUL FOR

Students in engineering, particularly those focusing on control systems, as well as professionals involved in system dynamics and analysis of ODEs.

incognitor
Messages
4
Reaction score
0
Hi,

I am undertaking an undergrad design project and want to ensure I'm doing this correctly,

I have derived the ODE as shown below;

A*Y = M*X'' + (B+C)*X' + D*X
Where A,M,B,C,D are constants.

By taking the Laplace transform, I get;
A*Y(s) = M*s^2*X(s) + (B+C)*s*X(s) + D*X(s)

Therefore,
My transfer function becomes;

TF(s) = X(s)/Y(s) = the image of the transfer function below;
http://imageshack.us/a/img37/8820/95533304.jpg


Am I correct here?
 
Last edited by a moderator:
Physics news on Phys.org
Anyone?
 

Similar threads

Undergrad Uniform convergence of family of functions with continuous index
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Lipschitz continuity of vector-valued function
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Assistance in checking transfer function
  • · Replies 1 ·
Replies
1
Views
2K
Process Control (transfer function) problem
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Proving that convexity implies second order derivative being positive
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Find f(z) given f(x, y) = u(x, y) + iv(x,y)
  • · Replies 8 ·
Replies
8
Views
1K
Undergrad How to manipulate functions that are not explicitly given?
  • · Replies 16 ·
Replies
16
Views
3K
Graduate ODE -> Transfer Function Assistance
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Determination of error in interpolating polynomial
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Finding the derivative of a characteristic function
  • · Replies 5 ·
Replies
5
Views
3K