Determining Response of Overdamped System

[donpacino]

 

[NascentOxygen]

OP's system needs precisely 50% swing in the wrong direction, then no overshoot upon settling. Experimenting with a few values, it looks like a zero around 1.8 will achieve that.

BUT is there any parameter you can now vary to get the other two faster settling plots to fit OP's graph? I think not.

I do think you are trying to solve a problem different from the OP and his professor: he doesn't know about zeros, he proposes a realisation having no zeros, and I think it can be demonstrated using the simple RLC series circuit with different initial inductor current.

 

[donpacino]

OP's system needs precisely 50% swing in the wrong direction, then no overshoot upon settling. Experimenting with a few values, it looks like a zero around 1.8 will achieve that.

BUT is there a parameter you can vary to get the other two faster settling plots to fit OP's graph? I think not.

I do think you are trying to solve a problem different from the OP and his professor: he doesn't know about zeros, and he proposes a realisation having no zeros, and I think it can be demonstrated using the simple RLC series circuit with different initial inductor current.

I can agree with that statement. The problem is there was no circuit in the initial problem. I made an assumption that the answer had to be mathematical in nature.

just as a note (even though this is spelling out a potential answer which is frowned upon)
if you use the following MATLAB code, you will get answers that more or less mimic the results above. (exaggerated results )

% sys1: no zeros
% sys2: dominant zero in right half plane
% sys3: dominant zero in left half plane

sys1 = tf( [ 1 ] , [1 8 13] )
sys2 = tf( [-1 1] , [1 8 13] )
sys2 = tf( [ 1 1] , [1 8 13] )

step(sys1, sys2, sys3)

 

[NascentOxygen]

It's remarkable how closely you've been able to match the original plots. I don't think you stand any chance of being able to implement this using a passive circuit---a single zero with a changeable sign would seem to rule this out.

On the other hand, were this asked in a control subject, your answer would probably be the one that the instructor wanted. So well done.

 

[Ivan Antunovic]

Hello donpacino,I have worked in the ferquency domain for the transfer functions for DC motors, asynchrouns motors,RC filters etc,but poles and zeroes are not analysed so much,it focuses more on the control. I think this is covered at the next semester in a subject called 'Automatic regulation'.

And sorry for the late answer I am really busy with the finals.

My professor doesn't want from me to think as mathematician , he wants me to think with my own head and think as a engineer and a physicist,he wants from me to describe him a problem and give him solution without equations actually by logical thinking.

 

[donpacino]

And sorry for the late answer I am really busy with the finals.

no worries

My professor doesn't want from me to think as mathematician , he wants me to think with my own head and think as a engineer and a physicist,he wants from me to describe him a problem and give him solution without equations actually by logical thinking.

engineers and physicists have to think about the mathematical concepts. I am an engineer as well. I've had to use the type of analysis I've mentioned at my job. math is simply a tool for engineers and physicists.

If you haven't discussed poles and zeros yet then most likely the answer is initial conditions, like you already mentioned. the green would simply be initial conditions of zero (or close to it)

 

[Ivan Antunovic]

no worriesengineers and physicists have to think about the mathematical concepts. I am an engineer as well. I've had to use the type of analysis I've mentioned at my job. math is simply a tool for engineers and physicists.

I agree 100% with you ,math is our tool.Do you work as Control engineer, I guess you are using a lot of MatLAB at your work?