This issue is called as PI tunning. Parameters depend on transfer function of the plant to be controlled. As sometimes is difficult to know what is the transfer function, an heuristic method to tunning the PI is used such as Ziegler-Nichols. You can find more info in internet about this method.

Other possibility is making a stability analysis but it can be tricky, requires time and you should know the transfer function of your system.

As Mr. Javier above mentions, searching for PI tuning is the best way to find useful references. Stability analysis is tricky and requires knowledge of the tf of the system. If you know it, you can try using the Control Systems Toolbox in Matlab to make a PI controller according to specific criteria (like steady error, overshoot etc.) Check the official page by mathworks, and you can also fine examples in Youtube about root locus analysis. If you like you can also check out this publication, chapter 12-13

http://www.mathworks.com/products/control/

Book An Introduction to Control Theory Applications with Matlab

Identify what is the input (manipulated variable) and the output (controlled variable). You can build an empirical model, e.g., linear First-Order plus Dead-time (FOPDT) model to mathematically relate the input-output dynamic behavior, which you could then use to find the parameter values of your PI controller. There are lots of tuning methods available for PI controllers, Ziegler-Nichols is just one among many. Type on the Google scholar "PID tuning" and you can get a lot of info about tuning PI and PID controllers. If the system of interest is nonlinear, then the tuning problem will be harder, as the PI parameter values will need some adjustment depending on the operating condition under which your system is running. The simplest but often quite effective method would be the gain scheduling. Of course, if linear approximation is fairly good, you could also use Matlab Control System Tuning, but of course this assumes very little knowledge of the users.

The ATV method from Astrom is quite simple and good first approach to tune a PID controller. You run a relay experiment where you move +/- a choosen "a" value on the input, you observe the "h" amplitude and period of the output. From this you get the Ku and Tu parameters through simple formulas, and from them you get the Kp, Ti and Td if you want, using Ziegler Nichols or alternative tables. If your system is linear enough and up to 2nd order + small delay this is quite good. If dynamic of your system is more complex than 1 or 2nd order + small delay you should get the Transfer function and made a frequency design, checking the bode plot for example.

There are two methods adaptive cahngeable PI gain parametres by Neural networkks or Constant parameteres between acceptable gain parameters

You can use cascaded control structure. One PI controller for outer loop and another PI/PID controller for inner loop. Tune the inner loop controller in such a way that the inner loop dynamics is reasonably faster than the outer loop. Then the loop interaction will be minimum. Moreover any disturbance occurring in inner/outer loop will be rejected within that respective loop only and hence performance will be improved in both step point tracking and disturbance rejection.

For your reference you may see the attached image for cascade control 

One of the effective method is Ziegler-Nicholes tuning and Modern Engineering Books will be good for this search.

You may approach this problem by simulating the controller with various combinations of P and I simultaneously and watching the output for the key response parameters of interest. This could be maximum overshoot (which should be low), rise time (which should be low), and the most important, (settling time) which should be low. The  combinations of P and I that give the optimum output response would be the those you can use for the design of the controller.

Without a plant model, I would just set the I term (K_i) to zero and adjust the P term (K_p)  until I get a nice looking transient response and not too much jitter in the steady-state response (which may happen if a large K_p gain is used). Then start increasing K_i until the steady-state tracking error decreases at an acceptable rate.

Hi Fang

One f the simplest way to this is using matlab sisotool toolbox (design & Tuning).

How ever it depend on your system.

This link may help you:

http://ctms.engin.umich.edu/CTMS/index.php?example=AircraftPitch§ion=ControlPID

http://heera.engr.siu.edu/staff1/pour/courses/ece456/Lectures/LW11-SISOTool.pdf

rise time, steady state error, overshoot and settling time, these four parameters will tell u that how to change the parameters of the controller.

the I controller actually is nothing but a regulator , on the other hand P controller changes the effect of instability; usually.relation of P and I controller can be described in terms of mathematics ,which i assume u already know.

as per my experience, please go for some desired values for the aforementioned parameters (while choosing values u might have to do trade-offs) and then do choose the PI values.

Ziegler-Nichols works well if you have a lot of uncertainty about the plant model and you would like to tune the fb loop just looking at the input output behavior of the system. Note that it does not work well for many plants but is ok for plants wilth slow dynamis.

If you have a precise plant model, one approach would to select the ratio KI/Kp small so as to have kind of a pole zero cancellation ( the PI controller introduces a pole at zero in the forward path; which is good for steady error but bad for transients) and to tune the transient response by tuning Kp. This is classically done with the root locus method for linear plants of any order.

You may also chose to use frequency response approach where you design the controller based on Bode plots.

If your plant is not very problematic (low damped uncertain pole and zeros, time delays etc) just use the sisotool of Matlab.