PID controller in simulink

Hi everyone! I am working on PID controller. I am having a model in simulink which I have uploaded at http://tinypic.com/view.php?pic=15cyg2&s=6. The gains of PID are: kp=1,Kd=1,ki=1.Saturation block has limits equal to -30 & +30. The state-space model has A=[0 1 0 0; 0 3.5 -106.5 0.37;0 0 0 1;0 0.21 -6.3 1.59]; B=[0 0;48.06 46664; 0 0; 340.18 47.7]; C=[1 0 1 0]; D=[0 0] and initial condition equal to 0. The system should converge at 20 as input is 20. But the problem is firstly its not converging and secondly the input of PID which is error signal appears as it is; as output with no modification. Need urgent help?

[Azzi Abdelmalek]

What is the constant you are using? and what method are you usinng to set PID prameters for unstable systems

[Beenish Mazhar]

Its just the input;as in my system two inputs are required for complete system modelling. Actually I am following a paper in which gains are already mentioned so I am not following any method to set PID parameters. I am varying them on hit and trial basis. Is there any such method to set the parameters.

[Gul Rukh Khan]

Yes, Ziegler Nochols method is used dear.

[Gul Rukh Khan]

Dear Azizi brother, I have one question, I want to Tune my Simulink Model with PID, but I tried a lot to tune but failed badly. If you kind send your email address, I will send the model, and after Tuned kindly send back to me on this email: [e-mail] Please, just send me an email with your good name AZIZI and obliged. with Many Thanks

Gul Rukh Khan

Answer 1

[Beenish Mazhar]

The problem can be sorted out if we use Ziegler-Nichols Tuning of PID controller.

[Walter Roberson]

Azzi commented "the answer expected was the value of PID parameters Kp Ti and Td"

Answer 2

[Ryan G]

I looked at the root locus with the PID and I don't believe this will be enough to adequately stabilize this system. Just for kicks I tried utilizing looptune to stabilize the system and was successful in finding a 4th order TF that would do it. Since I know nothing of your system other than the SS matrices it may or may not make any sense.

If you replace the PID with a Transfer fcn block this should stabilize the system:

num = [-1.19566835199456 0.150677296783384 -4.87470249290078 -5.9378741332245 -3.64167152790914e-05];

den = [1 32.4776016633891 994.732763803663 6558.83645377611 0.0401083722778298];

The resulting controller doesn't do a particularly good job but your system may not be easy to stabilize anyway.

What is the 2nd input and why don't you use it?

[Beenish Mazhar]

Its the requirement of my system.I have kept it zero to make the problem simple initially later on I will give it some value other than zero.

[Ryan G]

The reason I ask is both inputs are coupled. So if you have a controller on both inputs it is easier to stabilize. As I mentioned previously, it's difficult to determine what makes sense not knowing anything about the system. I would suggest taking a look at slTunable if you have access to the robust control toolbox.

This will allow you to add an arbitrary compensator and have MATLAB automatically place the poles and find the gains based on requirements. However, if the system cannot meet the requirements or cannot be stabilized (which seems to be the case for just PID here) then it won't work.

I would figure out how you want to implement both inputs and tune them together.

[Beenish Mazhar]

ok sir I will work on it. Thank you for your guidance.

Answer 3

[Azzi Abdelmalek]

eig(A) shows that your system is unstable (positive real(poles)in your system)

 eig(A)

 ans =

        0          
   2.5582 + 2.3191i
   2.5582 - 2.3191i
  -0.0264

and if your output is not converging that means your PID parametes are not quite choosen

[Beenish Mazhar]

If I only use the PID controller with the same gains as mentioned above; & give its output as feedback it converges at the desired value. But when I use the space state block with it its not converging. The matrices mentioned above actually represent a physical system so I can't modify them. But how can I change my gain parameters in such a way that they completely suit my system. I even tried by varying the gains but no useful result. any guidance?

[Azzi Abdelmalek]

when you don't use SS model means you are using a system with transfer function H(p)=1. you did'nt tell about unstability of your system.

[Beenish Mazhar]

Sir I was just trying to verify the function of PID so that's why I was using it alone; but if my system is unstable; then what strategy should I choose with the gains of PID so that the system should converge. One thing more sir which I forgot to mention; as my system is unstable so that's why I am using PID controller which would make it to converge otherwise according to me there is no need to use it.

[Azzi Abdelmalek]

We don't use PID to make systems stable, (ofcourse they can do it) . PID are mainly used to control the output, make it below a certain reference in presence of any dsturbance. Now the problem is to find adequat PID parameters, because the ones you gave did'nt work, If I find something I will post it

[Azzi Abdelmalek]

I guess, since your system is 4rth order and unstable, it's difficult to be stabilized with a PID, maybe you should look for another controller