Question

Use Simulink to show the time responses of the following system from t-0 to 5 with a step function input: . 1 x12x1-2x2 +x2 + f ä2--x1 + 2x2-3x2 + 2x3 i3-3 +2x2-3x3 (a) Show the time responses graphically using the Euler method and 4th-order RK Method. (b) Compare the results at t-5 between the Euler method and 4th-order RK Method

Answer 1

The Matlab schematic is given as

.-3 22-33 1 x3. x3 -3 x2..--x1.+x1 +2x2-3x2+2x3 x2. x2 x1.. x1-2x1+f+x2-2x2. x1 x1 x1 in

Note here F is the unit step.

Assuming all the initial condition for each state to be zero. The response using Euler solver is given as follows

x1e

50 150 200 0.5 2.5 3.5 4 4.5 Offset 0

x2e

x3e

Assuming all the initial condition for each state to be zero. The response using RK4 solver is given as follows

x1rk4

x2rk4

x3rk4

Results are almost the same for both Runge Kutta and Euler method although computation needed in Runge-Kutta is much higher.

In every case, the solver sample time is 0.01 sec.