Creating a block for a term like (4s+1) in simulink?

Hello! In an exam I wrote a few weeks ago, we were given a block diagram to model in simulink, and one of the blocks was (4s + 1), where s is the Laplace variable. Naturally, I attempted to use the Transfer Fcn bloc, but this threw an error, because 'The given transfer function is an improper transfer function. The order of the transfer function numerator must be less than or equal to the denominator'. Any help with this? Thanks

Answer 1

[Aquatris]

I suggest you try to understand why 4*s+1 cannot be simulated. Although there are workarounds. hint: what does s do to a time domain signal?

One way to implement those things is with a low pass filter that has a high enough frequency to make it proper. High enough is a frequency where you do not care about the dynamics anymore. This way you do not change the dynamics of the 4*s+1 in the frequency range you desire.

So in example, you want to implement (4s+1), assume you only care about simulating the dynamics that is less than 50 rad/s. Keep in mind that there will be slight changes to phase and magnitude when you introduce a low pass filter , but if you select the low pass frequency high enough, that difference becomes negligible. Then you can pick for instance a 400 rad/s low pass filter to make the transfer function proper ;

s = tf('s');

sys = 4*s+1;
sysModified = sys/(s/50+1); % with 50 rad/s LP
sysModified2 = sys/(s/400+1);% with 400 rad/s LP

% notice the orange line (4*s+1 with 400 rad/s LP) is almost identical to the blue line (4*s+1)
% for frequencies less than 50 rad/s
bode(sys,sysModified,sysModified2)
legend('4s+1','4s+1 with LP 50 rad/s','4s+1 with LP 400 rad/s','Location','SouthWest')

[Valerie]

Thank you so much, this worked out!