Spring mass damper system shows position of mass only to be on positive side

Hi,

I have been out of touch with simulink and wanted to restart with a simple spring mass damper system. Here is the model I used:

Here is the script that contains inputs and plot commands:

sim_Time=150;
k=.5;
b=.2;
m=4.5;
F=2;
sim('MassSpringDamper_Trial.slx');
plot(Position.data)
legend('Position of mass')
hold all
plot(Force.data)
legend('Position of mass','Force')

And I got the output, close and not exactly, what I would like to see:

There are two things that concern me:

1. Why are the 'Position of mass' plot values always on the positive side? The spring mass system vibrates between both the negative and positive limits from its neutral position, doesn't it?
2. The step input force is set with an initial value 0 and final value 'F'. So I was thinking the 'Position of mass' to have a non zero value right from time t = 0. But almost till t=8, I see the 'Position of mass' to be zero.

Can someone explain the reason(s) pl.? Thanks already!

Answer 1

[Paul]

The transfer function from Force to Position has dc gain of 2. The input F has a value of 2, so the steady state of the output should be 4, as shown.

However, the rest of the results look suspect. The period if the oscilations should be ~18 secs. Note that

plot(Position.Data)

is just plotting points vs an index. Shouldn't that command either be

plot(Position)

or

plot(Position.Time,Position.Data)

Let's see what one of those plots look like.

Also, what is the value of the Step Time parameter in the Force block?

[Udhaya K]

Thanks for helping me, Paul.

//The transfer function from Force to Position has dc gain of 2//

I am sorry I don't understand this. Where is this gain of 2 coming from and why should that determine the neutral position of oscillation?

And, I changed the script to plot(Position.Time,Position.Data) and that correct the positiion of mass to change from time t=0 itselft + Period of vibration is nearly 19 s. This is an encouraging result to me :)

Force parameter:

[Paul]

The transfer function reperesented by the block diagram is:

>> H=tf(1/m,[1 b/m k/m])

H =
 
           0.2222
  ------------------------
  s^2 + 0.04444 s + 0.1111

H is the transfer function of a stable system. The ratio 0.2222/.11111 = 2 is the dc gain (i.e., H evaluated at s = 0) and the steady state output to a step input, F, is yss = F*2. To check your results (assuming you have the Control System Toolbox) try:

[y,t] = step(H,sim_Time);
plot(t,2*y)
hold on
plot(Position.Time,Position.Data)

The updated script is still plotting

plot(Force.data) % should be plot(Force) or plot(Force.Time,Force.Data)

The position plot looks correct but a bit jagged (i.e., with clear vertices), I don't see that using the default solver parameters or the default parameters in the ToWorkspace blocks. Did you change those?

[Udhaya K]

Thanks a lot for explaining the details, Paul. But, no offense meant, I have a poor understanding on transfer functions and hence couldn't follow your reply. Is it possible by changing any parameter in the model that I get the neutral displacement as 0 without changing the amplitudes and frequency?

//The position plot looks correct but a bit jagged (i.e., with clear vertices), I don't see that using the default solver parameters or the default parameters in the ToWorkspace blocks. Did you change those?//

Honestly speaking, I don't even know that there are possibilitiesto change the parameters. Here is what it looks like when I double-clicked it:

Thank you so much again for helping me!

[Paul]

One way to obtain oscilations around 0 position is to set F to 0 and set the Initial Condtion on the integrator (from xdot to x) to a non-zero value.