This document discusses using Simulink to solve differential equations. It explains that differential equations can be solved in Simulink by setting up the right-hand side of the equation and connecting it to the input of an integrator block. It provides an example of solving the differential equation dx/dt = -x + 1 with an initial condition of 0. It also discusses how to handle higher order differential equations and set initial conditions for the integrator blocks.

1. 11
Lecture Series – 8
Solving Differential equations
using SIMULINK
Shameer Koya

2. Solve the differential equation
 Note: The input is 1 after t> 0
 Input - step function - stepping time is not
t=1 but t=0
 Initial Condition is 0
2
2 1, 0.
(0) 0.
dx
x t
dt
x
   


3. 3
Solution
 The equation is where
 Instead of differentiation, we do the reverse
operation, integration, to solve the equations
 In SIMULINK means integration
 Input to the integrator is and output x
 set up the right hand side and connect the everything
to the input of the integrator.
2 1Dx x  
d
D
dt

1
s
dx
Dx
dt


4. 4

5.  Another issue that we have
not considered is initial
condition.
 As you know every
differential equation should
have initial conditions given.
 The default value in
SIMULINK is zero.
 To change that click the
integrator.
5
Double-click
Initial condition

6.  If you want to see both the input and output at the same time, use Mux
(multiplexer) block, which you can find under Signals and Systems
block library
6

7. Higher order differential equation
 Second order equation
 To set up the right-hand side two integrators are needed
 The input to the first integrator is the second derivative
and its output is
 second integrator producing x(t) at its output
7
2
2
5 9
d x dx
x
dt dt
  
d x
dt
2
2
dx
dt
(0) 2
(0) 2
dx
x
dt
x
  

&

8.  Assume that u(t) = 0, that is, there is no input.
8
2
2
5 9
d x dx
x
dt dt
  

9.  Set the initial conditions of the integrator
9

10. Ouput
10

11. 11
Thanks
Questions ??