Compensator Design in system control

[jhonvaljon]

Hello, in my final project for System Control i have been stuck for some time on this following task

What i cannot figure out is how to make all these condition work at the same time.

When I tried designing a PD controller in sisotool or MATLAB for the i and ii part it worked but i couldn't meet the other 2 requirements.
Adding a pole at origin will ruin my system response and trying to go for a pole/zero cancellation will greatly mess my settling time. And i didn't even reach the iv part.
I have tried lots of possible PI or PD combinations and PID ones but something is always lacking.

How do you guys propose i work? What i am missing out? How can sisotool in simulink help me meet the 3rd and 4th requirement without messing up my first two?

Any help is appreciated. Thank you.

My images are here because they didn't seem to upload well: https://imgur.com/0SDfsKm
https://imgur.com/1mvsBps

 

[berkeman]

Hello, in my final project for System Control i have been stuck for some time on this following task

What i cannot figure out is how to make all these condition work at the same time.

When I tried designing a PD controller in sisotool or MATLAB for the i and ii part it worked but i couldn't meet the other 2 requirements.
Adding a pole at origin will ruin my system response and trying to go for a pole/zero cancellation will greatly mess my settling time. And i didn't even reach the iv part.
I have tried lots of possible PI or PD combinations and PID ones but something is always lacking.

How do you guys propose i work? What i am missing out? How can sisotool in simulink help me meet the 3rd and 4th requirement without messing up my first two?

Any help is appreciated. Thank you.

Welcome to the PF.

Your image did not seem to Upload correctly. Is it in PDF or JPG format? Or are you linking to it somewhere?

 

[jhonvaljon]

Welcome to the PF.

Your image did not seem to Upload correctly. Is it in PDF or JPG format? Or are you linking to it somewhere?

I don't know why it didn't upload correctly so i linked to imgur correctly.

 

[donpacino]

What type of controllers have you learned about?
Can you show us part 1 of the problem so we can see more than just an equation?

 

[jhonvaljon]

What type of controllers have you learned about?
Can you show us part 1 of the problem so we can see more than just an equation?

I know PID, and lag , lead and lag lead.

part 1 is only drawing the response or the uncompensated system for step input, ramp input and getting some properties like settling time and Overshoot, it is not very important.

 

[donpacino]

Is part 1 the same system as part 2. If it is then it could be important information for us... Is this an angle controller, speed controller, etc

As far as solving for parts 3 and 4, you need to keep them in mind when designing for 1 and 2. You have a type 1 system, by adding a PI (D) controller you'll make it a type 2. For a ramp input you should be have a error of zero for speed, with a constant error for acceleration. Is that ok given what your system is? You aren't solving for one part after another, you need to solve all at once.

To design for 4, you either need to add a saturation to your design, making it non-linear outside of a certain range, or you need to ensure that your PID values * your error will never exceed 2.

Why don't you try looking at some of the frequency plots the MATLAB tools provide, they may be able to help (hint hint)

 

[jhonvaljon]

Is part 1 the same system as part 2. If it is then it could be important information for us... Is this an angle controller, speed controller, etc

As far as solving for parts 3 and 4, you need to keep them in mind when designing for 1 and 2. You have a type 1 system, by adding a PI (D) controller you'll make it a type 2. For a ramp input you should be have a error of zero for speed, with a constant error for acceleration. Is that ok given what your system is?

To design for 4, you either need to add a saturation to your design, making it non-linear outside of a certain range, or you need to ensure that your PID values * your error will never exceed 2.

Why don't you try looking at some of the frequency plots the MATLAB tools provide, they may be able to help (hint hint)

This is an angle controllers. And yes Part 1 is the same as Part 2. In part 2 we have to design Gc which is 1 in part 1.
I agree about what you said in making the system a type 2 thus the Error for ramp is 0 , i tried that but the problem is that adding a pole at origin messed up my whole response (i and ii conditions) and trying the pole zero cancellation also didn't help.

Concerning frequency plot i am not very familiar with them or how will they help me design my compensator.

 

[donpacino]

This is an angle controllers. And yes Part 1 is the same as Part 2. In part 2 we have to design Gc which is 1 in part 1.
I agree about what you said in making the system a type 2 thus the Error for ramp is 0 , i tried that but the problem is that adding a pole at origin messed up my whole response (i and ii conditions) and trying the pole zero cancellation also didn't help.

Concerning frequency plot i am not very familiar with them or how will they help me design my compensator.

Well as long as you have an integrator in your controller, you'll add a pole to your system so you won't need to add another.
Why are you doing pole cancellation? what pole are you trying to cancel?
Look at a bode plot, or just look at a plot of the poles and zeros. There is a VERY dominant pole, that will essentially govern how your system responds. Everything else is only minor effect. So you can almost remove the zero and 2 of the poles while designing your system, and then add them in later to test your solution to simplify any mathematics.

 

[jhonvaljon]

Well as long as you have an integrator in your controller, you'll add a pole to your system so you won't need to add another.
Why are you doing pole cancellation? what pole are you trying to cancel?
Look at a bode plot, or just look at a plot of the poles and zeros. There is a VERY dominant pole, that will essentially govern how your system responds. Everything else is only minor effect. So you can almost remove the zero and 2 of the poles while designing your system, and then add them in later to test your solution to simplify any mathematics.

I don't have an integrator in my system, i added it in hopes of fixing my ss error.
As i said above, i am doing pole cancelation to remove the effect that the pole at origin was causing. (It made the system unstable)

 

[jhonvaljon]

How can you guide me to solve my problem?
Should i keep trying to add Pd and PI ? As this has not been working. There is always one patt that keeps getting messed up.

 

[donpacino]

Well a PI (proportional integral) controller has an integrator, which is the integrator I was talking about. ;) You'll need the I, just a PD controller will not work.

I would start by designing a PI controller to meet the overshoot and settling time you need with the step input. with a GP of 0.00375/[s*(s+0.0085)] That should get you in the ballpark. You might need to add the zero as it is not quite an order of magnitude smaller (its close).

Once you do that take a look at your u(t). How close is it to 2, if it is close you need to make your system less aggressive. if you can't make your system less aggressive and still meet your settling time/overshoot requirements, then you'll need to add saturation which will make your system non-linear (which is fine).

double check your input to part C. because the error will go to zero eventually. If it does not, you need to increase the effect of your integrator. You may also want to add anti windup or similar controls to your integrator.

ou should be checking parts 1 2 and 4 at the same time. Have a graph showing your y(t), u(t) and r(t) for both a step and ramp input. Write a MATLAB function, or use built in tools, to calculate settling time and overshoot on the fly.

Once you get this done and you have good PI values, redo it with while adding in the other poles. Your controller should still mostly work, you might need to tweak it a bit. You might need at add a LITTLE bit of derivative control, but not much.

 

[jhonvaljon]

Well a PI (proportional integral) controller has an integrator, which is the integrator I was talking about. ;) You'll need the I, just a PD controller will not work.

I would start by designing a PI controller to meet the overshoot and settling time you need with the step input. with a GP of 0.00375/[s*(s+0.0085)] That should get you in the ballpark. You might need to add the zero as it is not quite an order of magnitude smaller (its close).

Once you do that take a look at your u(t). How close is it to 2, if it is close you need to make your system less aggressive. if you can't make your system less aggressive and still meet your settling time/overshoot requirements, then you'll need to add saturation which will make your system non-linear (which is fine).

double check your input to part C. because the error will go to zero eventually. If it does not, you need to increase the effect of your integrator. You may also want to add anti windup or similar controls to your integrator.

ou should be checking parts 1 2 and 4 at the same time. Have a graph showing your y(t), u(t) and r(t) for both a step and ramp input. Write a MATLAB function, or use built in tools, to calculate settling time and overshoot on the fly.

Once you get this done and you have good PI values, redo it with while adding in the other poles. Your controller should still mostly work, you might need to tweak it a bit. You might need at add a LITTLE bit of derivative control, but not much.

Ok i will try to do it and get back at you.
And btw we have not taken saturation and anti windup.

 

[jhonvaljon]

Well a PI (proportional integral) controller has an integrator, which is the integrator I was talking about. ;) You'll need the I, just a PD controller will not work.

I would start by designing a PI controller to meet the overshoot and settling time you need with the step input. with a GP of 0.00375/[s*(s+0.0085)] That should get you in the ballpark. You might need to add the zero as it is not quite an order of magnitude smaller (its close).

isn't the Gp you proposed existing in my TF ? Also, again trying to meet my PO and TS needs, i placed a zero at -0.021, but now adding anything else ruins my system.

 

[donpacino]

isn't the Gp you proposed existing in my TF ? Also, again trying to meet my PO and TS needs, i placed a zero at -0.021, but now adding anything else ruins my system.

Yeah. really I just meant remove the high frequency poles to simplify the design, then add them in later. It can help you get a better understanding of what works for the system.

Once your zero is in place, try increasing your integral gain.