How to design a PID controller for a second order system

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Thread Starter

freshman

Could anybody help me to set the parameters for a PID controller which will be applied on a second order system (G(s)=1/(s*s+1.88e3s+12.96e6)). I am not so sure how to set the PID paprameters such like Kc, Ki, Kp.

Thank you!

helen
 
D

Daniel Chartier

Hello, Helen;
The following link will take you to a FAQ page referring to Ziegler & Nichols' ultimate cycle technique, which is easy to implement if you have manual control of the process for a test. This is an empirical design, not as mathematical as some would like, but it adapts well to real processes. If you have derived the system equation from the process, you should find it easy to play with the controls and get the oscillation you need to determine the control parameters.

http://ourworld.compuserve.com/homepages/ACTGMBH/zn.htm

Hope this helps,
Daniel Chartier
 
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R.M.Ghodasara

Dear freshman,

First of all u have to find time response parameters likes natural frequency, geta and setelling time from your second order T.F. After that u have to use lead compensation as a PID controller to satisfy your required specification. In second case u can use Zieglore-Nicholes or Cohen-Coon controller-tuning method to satisfy your specification.

From
R.M.Ghodasara.
INDIA
 
J

J.P.Schoeffer

In your T.F., the process gain is G(s=0)=772e-9 (-122dB) (?)

PI controller can be implemented: Kp(1+Tis/Tis) with: Kp=10 (proportional gain) Ti=9.1e-7 (integral time constant)

But: problem of saturation at the output of the controller...
 
Hi, Daniel Chartier,

Thank you very much! It is really a good reference for me!

Have a nice day!

Helen.
 
hi,friend!

Thank you very much!

While, may I know how did you get the settings of these parameters?

Thank you.
Helen
 
Dear R.M.Ghodasara.

Thank you for the kindly reply, I am trying the steps and try to find some way to solve the problem.

Regards,
Helen
 
J

J.P.Schoeffer

Hello,

Sorry for my poor English.
I am astonished by the weak value of your process gain (?). Consequently, you will have problems of saturation with the values proposed (with other values, response time will be important).

Because of this process gain, there is no stability problem, therefore no D controller (PI only).
If you want any informations about the calculation of Kp and Ti, you can reach me ([email protected]).
 
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