Using Simulink/Matlab to Solve Ordinary Differential Equations

“One Word: Simulink.”

Using Simulink/Matlab to Solve Ordinary Differential Equations Jake Blanchard University of Wisconsin 2009

Introduction Matlab offers several approaches for solving initial value ordinary differential equations  Runge-Kutta solutions are common (ode45, ode15s, etc.)  Simulink is a Matlab add-on that allows one to simulate a variety of engineering systems  We can use Simulink to solve any initial value ODE 

Process 

Simulink offers a variety of components that are assembled graphically to provide a full system simulation

http://www.engin.umich.edu/class/ctms/simulink/model/model.htm

An Example 

Consider a model for a damped, forced oscillator 2

d x dx  3  4 x  5 cos( 2 t ) 2 dt dt x(0)  0 dx (0)  0 dt

Preparation

2

d x dx  5 cos( 2 t )  3  4 x 2 dt dt

The Simulink Model 2 Clock

t->2t

cos 2t->cos2t)

5 5cos(2t)

1 s

1 s

d2x/dt 2->dx/dt

dx/dt ->x

3 dx /dt ->3dx/dt

Scope

4 x->4x

The Simulink Model

2

d x dx  5 cos( 2 t )  3  4 x 2 dt dt

The Simulink Model d 2x dx  5 sin( 2 t )  3  4x 2 dt dt d 2x dt 2

dx dt

x

3

dx dt

4x

Initial Conditions The ICs are set in the integrator blocks  Right click the block and open “Integrator Parameters”  This sets value of output variable from the integrator block 

Demo