as you may have already experienced PID controller will not provide accurate control if not TUNED correctly. otherwise, the output will not follow or overshot.

there are three PID tuning methods

heuristic tuning, rule-based tuning, and model-based tuning. Each method has its pros and cons.

start with Zeigler-Nichols Method

Dear Mahmoud Ghahremani

Thank you for your answer.

Ziegler-Nichols is the method I am working on.

Best

There is different method like pso, heuristic tuninig... However the simple one is Ziegler-Nichols and you can use auto tune option in matlab to check if pid is the good option for you

Dear Kareem Albadri

Thank you for your answer.

Best

Ziegler-Nichols

for systems with delay

https://stackoverflow.com/questions/26508261/tuning-pid-in-systems-with-delay

Please look at the following paper

http://www.ie.tec.ac.cr/einteriano/analisis/clase/13.1.Zomorrodi_Shahrokhi_PID_Tunning_Comparison.pdf

Hamid Keshmiri Neghab, First things first, do you have the mathematical model for the MISO system?

Dear Yew-Chung Chak

I have the state-space model of the system which is identified by the ARX method.

Hi Hamid Keshmiri Neghab,

Thanks for your update. With a state-space model, there should be various control design tool that you can explore to design and tune the control gains until the the desired system performance is obtained.

Hello Hamid Keshmiri Neghab ,

You have asked a very good question, usually the tuning process is not mentioned a lot in the literature pushing it under the carpet by mentioning " trial and error " although this is true somehow but this requires a lot of experience from the practitioner. I would suggest two solutions depending on my previous work, you can start with placing the poles that would ensure the stability of the system by pole placement to determine the gains and thus u = -kx (state feedback control) and by this you would gain some intuition about the values of the gains when you want to use the PID later on. Another method is to use Model free controller (intelligent PID), when using this method, you can start with any reasonable choice of PID controller gains and then you are left to tune only one parameter (alpha). This controller is simple and sometimes resolve the problem of having to tune manually the PID controller.

Please refer to this article for more information : Conference Paper Passive Fault-Tolerant Control of a Fixed-Wing UAV Based on ...

Dear Ali Srour

Thank you for your complete answer.

Analiticil adjusts with routh hurwirtz methods and zigler Nicholas two methods are the most known. Also adjusted with experimentally and with Simulations trying near values...

I suggest to Follow #relaxc and #relaxctuner http://relaxc.appedge.com/

free tool to tune #relaxc and to make a PID well-balanced.

We need more information, what is the model or what is the purpose of the output? It is not an easy question because is too general and maybe we should need a robust controller.

İf your system is Nonlinear Surely. ..Also you can check the automatic control textbooks för easy solutions

There are methods of adjusting controller gains (PID or even non-linear) using algorithms for optimizing the parameters of your system (static error, speed...). Among these algorithms are PSO, GWO, WCA ...