There is no derivative in the PI controller.

If you are talking about PI, you should take care of the equation as there are two equations.

m = 100/p (e + 1/I * integration of error)   --> (1)

m = Kp (e + Ki * integration of error) --> (2)

Apparently p, Kp have inverse relation, I ,Ki has inverse relation. So you can think that different reference say different and conflicting things.

You can find the details in http://en.wikipedia.org/wiki/PID_controller

It depends on the plant. But in general for a PID controller, I would say that the P term decreases the rise time and the steady-state error; whereas the D term tends to increase damping. Although both have the potential to result in excessive noise amplification or an unstable closed-loop system if not used in moderation. 

When you increase P, the system acts more quickly towards the target, but you can improve the risk of an uncontrolled overshoot. Increasing I you'll maintain the response over the historic system reactions over time. It can improve overshoot also.

Hello

İncreasing P generally increases control signal, Integral effect will make slower the system and derivative will increase the speed. But D term can cause something called derivative kick if a sudden change appears in ref. 

But the effect of these terms is changable because of nonlinearity. You can see this effects if you work with fuzzy PIDs.

First, you assume that your system is "good enough" so that simple P, PD, PI, or PID controllers can control it.

P control gives the plant a signal, which is proportional to the position tracking error. If the error is positive, the control signal is such that will force it to move in the negative direction (and vice-versa). If "everything is alright" the idea is that the motion would stop at zero error when the signal is zero.

However, things have inertia and even if the control signal is zero, the system keeps moving due to inertia until the error is large enough such that the proportional signal moves it back towards zero, yet this may continue until everything quiets down.

To prevent this from happening, you must supply a signal which opposes the velocity effect and this is the derivative component D.

PD seem therefore to be sufficient. However, the plant accumulates errors due to friction, and other parasite terms, which cannot be eliminated when the signal stops and therefore, we introduce the integral I signal which integrates the error signal. The integral of a constant keeps increasing until the constant error vanishes.

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Here is a way of tuning a PID controller, from first principles ... 

https://www.researchgate.net/publication/299569076_Optimal_Design_of_Digital_Anticipatory_Servomechanisms_with_Good_Noise_Immunity

Conference Paper Optimal Design of Digital Anticipatory Servomechanisms with ...

The following table can summarized the effects of independent P, I, and D Tuning 📷