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Lecture Series – 8
Solving Differential equations
using SIMULINK
Shameer Koya
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
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
 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
 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
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
  

&
 Assume that u(t) = 0, that is, there is no input.
8
2
2
5 9
d x dx
x
dt dt
  
 Set the initial conditions of the integrator
9
Ouput
10
11
Thanks
Questions ??

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Mat lab solving equations simulink

  • 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