How to find step response of a non linear system

I am reading a paper "Design of PID-P Controller for Non-Linear System using PSO " by Rajim Gupta, P.K.Padhy. In that paper, the authors have simulated a step response of a nonlinear system with a PID controller. My question is, how can one simulate the step response of a nonlinear system with a PID controller using MATLAB? Further, how to find time response specifications such as rise time,. settling time, etc., for the same?

[KALYAN ACHARJYA]

The following link is helpful

http://www.ece.uvic.ca/~agullive/trans/B_p1-38.pdf

[Rakesh Jain]

No please, the above link deals with linear systems only. I want to simulate the step response of a non linear system, which is not given in the aforementioned link

[Birdman]

What does your system look like? The equations? Probably a linearization process will take place.

[Rakesh Jain]

The system is as follows: y dot = 0.5y^2 -y + x. It is given on Pg. 3 at http://ieeexplore.ieee.org/document/6780184/ I need to simulate a closed loop response with PID controller with Kp = 2, Ki=0.6 and Kd=0.5

Answer 1

[Birdman]

Run the attached model. Let me know the results.

[Rakesh Jain]

Thanks a lot, but I am not able to run this file. I am getting the following error. "Model 'nonLinear_PID' was created with a newer version (9.0) of simulink. Can you please export the file to the version MATLAB R2016a and re-attach the file.

[Birdman]

There you go.

[Rakesh Jain]

I am sorry but I am still getting the following error "matlab has encountered an internal problem and needs to close". What I did was, initially I saved the contents of the above file as .mdl and then tried to open it via simulink. But I am getting the error mentioned above. Is it possible for you to attach it in some other manner

[Birdman]

I am attaching it as a zip file. Just extract the file within, which is slx and then open.

[Rakesh Jain]

Thanks a lot for your help. I really had no idea how to start doing it. Finally, thanks to you, I have been able to do it. The output response is attached herein.

[Birdman]

You are welcome. :)

[Rakesh Jain]

One final question. What does the variable x_y mean in the simulink model?

[Birdman]

It represents x-y operation in the equation.