Hi, I have to design a 'phase-lead compensator' for these design specs:

• Ts < 4 secs
• PO < 16%
• Here's the system: https://app.box.com/s/7xvaociom7rjq39uzq15
  
• Here's G(s): https://app.box.com/s/9egxf68k0n91hf0h892l

To be honest I'm really not sure where to start. I think I've got to plot the 'root locus' but whether this is of the open-loop or closed-loop I'm not sure. Any input would be appreciated....

 

Assume a second order response approximation of the actual response.
The required PO then leads to the damping factor \(\zeta \).
The settling time needs to be stated as being within a certain percentage (5%,2%, ??) of the final value. This leads to a value of \(\omega_n \) given the required damping factor \(\zeta \).
Knowing damping factor and \(\omega_n \) then allows you to place a target dominant complex pole pair on the root locus plane. Presumably the uncompensated root locus doesn't include the target pole pair. Lead compensation design then requires you to "force" the root locus to intersect the target dominant pole pair.
There is a wealth of guidance on the Web on how to do this. You should show some effort on your part to indicate you are at least familiar with the process.

 

Yes I should have said that the Ts is +/- 5%.

• I used this schematic to find theta1 & theta2 (point A is at -5.0 on real axis i.e. sigma= -K/Ts) Ts = 4 & K = Ts * 5: https://app.box.com/s/0i97d7xkonsia9psr7it
• I then used this schematic to find the pole & zero: https://app.box.com/s/cln8ji2w57g044pzubg1
• From the above process I found; Z = -2.69 & P = -10.37
• Would this make my compensator be: (s+Z)/(s+P) = (s+2.69)/(s+10.37)?

 

Hi, I have to design a 'phase-lead compensator' for these design specs:

• Ts < 4 secs
• PO < 16%
• Here's the system: https://app.box.com/s/7xvaociom7rjq39uzq15
  
• Here's G(s): https://app.box.com/s/9egxf68k0n91hf0h892l

To be honest I'm really not sure where to start. I think I've got to plot the 'root locus' but whether this is of the open-loop or closed-loop I'm not sure. Any input would be appreciated....

Other than the specifications given, one might also expect to have a steady state error specification. Could be important in the aircraft control.

You also asked...

"Would this make my compensator be: (s+Z)/(s+P) = (s+2.69)/(s+10.37)?"

I don't think this will work. Even if you achieved the overshoot limit, you would be way off in the settling time.