Need some help with solving diff.equ with matlab/simulink

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SUMMARY

The discussion focuses on solving the differential equation x'[t] + x[t] = a + Sin[b*t] using MATLAB/Simulink, with specific parameters a=1, b=1, and initial condition x(0)=2. The user provides the solution x(t) = 1/2 e^-t (-cos(t) e^t + sin(t) e^t + 2 e^t + 3) and the transfer function G(s) = (a/s + b/(b^2 + s^2))/(s + 1). The main issue raised is the correct application of the initial value in the context of the transfer function, which the user ultimately resolves.

PREREQUISITES
  • Understanding of differential equations, specifically first-order linear equations.
  • Familiarity with MATLAB and Simulink for solving differential equations.
  • Knowledge of Laplace transforms and their application in control systems.
  • Basic understanding of transfer functions and their significance in system analysis.
NEXT STEPS
  • Explore MATLAB's built-in functions for solving differential equations, such as ode45.
  • Learn about the implementation of transfer functions in Simulink.
  • Study the concept of initial conditions in the context of Laplace transforms.
  • Investigate the graphical representation of solutions to differential equations in MATLAB.
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Students and professionals in engineering, particularly those studying control systems or using MATLAB for mathematical modeling and simulation of dynamic systems.

rularn
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Hi!

Homework Statement


I have this x'[t] + x[t] = a + Sin[b*t] diff.equ that I would like to solve with matlab/simulink.
Let set a=1, b=1 and
x(0)=2

Homework Equations


I know that x(t) = 1/2 e^-t (-cos(t) e^t+sin(t) e^t+2 e^t+3) and what it look like (see pic). I aslo got the transfer equ G(s) from Laplace and it should be:

G(s) = (a/s+b/(b^2+s^2))/(s+1),


The Attempt at a Solution



The only thing I don't get right is the initial value as you can see at the pic. It also shows what it should look like. What do I do wrong?

It should be easier to use the transfer equ G(s), but I don't get that right either. Any suggestions?

http://img205.imageshack.us/img205/821/reglerth3.jpg


Thank you!
 
Last edited by a moderator:
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Ah don't worry guys, I fixed it
 

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