Why would you need the system model for a heuristic method?

Is there any method to calculate the PID parameters for this model

Hi Sai,

First, you need to find the transfer function of this unknown second order system. To find the transfer function assuming you have only the step response of the system, please check the attached figure. You need to measure the rise and peak time from the figure and substitute in the equations as in the attached figure. Once you get the transfer function, you can go through the normal procedure for PID tuning. You need to apply P control action then increase the gain until you get the ultimate gain (you can do it by Simulink) after that you can select the other parameters according to the required control action from Zeigler method.

I hope this to help you.

Regards

Sai Gm - heve you shown to us really the OPEN LOOP step response (and not the closed-loop)?

@Mohammad Thanks.

now i can get the transfer function for my model, after tuning controller parameters how can i get the desired overshoot and settling time. I don't want to use trail and error method. Is there any method to calculate controller parameters and with these parameters  can i get my desired overshoot and settling time in the output

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@ Lutz ya it is the open loop step response. 

After applying a P controller, the closed loop transfer function becomes: C(s)/R(s)=K_p*(W_n)^2/[S^2+2*zeta*(W_n)^2+(1+K_p)*(W_n)^2]. Where K_p is the gain. If you like to have special performance for this system based on the closed loop step response, you need to apply a step input and hence, R(s)=1/S. The system response becomes: C(s)=K_p*(W_n)^2/S*[S^2+2*zeta*(W_n)^2+(1+K_p)*(W_n)^2]. Then you need to find the time-response of this system. From the response, you can select the criteria for the performance. For example, if need to adjust the rise time to a certain value (say 0.5s). Set the time response to 1 and apply the time in this equation to 0.5. Then you can get K_p (probably not linear equation) satisfying the rise time=0.5s.

in order to find the find the transfer function, you can also use "ident" in matlab.

then go to: http://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method

and using the provided table, calculate the desired PID coefficients.

using Ziegler nichlos I can calculate the values but the values are not desirable when disturbance in the system are higher

Z-N is a tuning method for PID to give an acceptable result, but it is not optimal for all conditions and applications. It does not guarantee the disturbance rejection.

One of the most practical and easy methods that I usually take in these problems is trial and error! It may seem an obvious answer, but it saves so much time!

You will easily figure out a trend a change to variation in any of the variables of your system. Then, you can select the gains such that it has the shape of the response that you desire! 

And that is exactly what a heuristic method implies. Oh the other hand, I agree with others in this thread that model identification could effectively address the OP's problem.