Sreekanth,

This would tend to be the outcome if the plant in question actually requires non-minimum phase zeros in the closed loop for the specified control condition..

-Sanjay 

The comment from Mr. Masaoud is true. In addition, the negative gain cause direct action to the controller, meanwhile the positive gain forces the reverse acting to contoller. Since Your controller is PI, if the e is not zero.. the integral part is so sensitive which wiĺl effect to the controller action.

The significant of negative gain... was answer by real example given by Mr. Masaud. Hope this aswer your question. :)

KI may be negative when the error e is positive for most of the time, then crosses zero and setlles with a small negative value. This is our experience.

Thank you Masoud, Sanjoy, Aripriharta and Krishnarayalu.  

@Sanjoy, Sir you mentioned that this situation occurs when system requires right hand side zeros in the closed loop system. This RHS zeros effect the bandwidth of the system (we can see in boost converter control problem). So, is system with negative coefficients in PI controller less stable? 

Dear Sreekanth,

As said by @Masoud it depends on the system and how you are calculating error. PI needs to minimize the error by giving required control signals to the system. So, I would say that mainly system and error calculation defines the negative and positive value of the gain.

Thank you Sachin sir.

Hi Sreekanth,

(Sorry to be replying rather late ! This is specific to the question you directed to me.)

There will be a tendency of negative gains to affect stability no doubt ! You would perhaps recall that I mentioned systems that "requires non-minimum phase zeros". Obviously the requirement would include a presumption that stability is not too adversely affected by such gains ! Or stated differently, there is enough stability margin to contain such fallout.

Cheers !

-Sanjay

Thank you Sanjoy sir for your detailed explanation. Yes, I  agree with you regarding the stability presumption. 

It depends on the influence of the input on the output.

For the system: dx/dt = -x +u , a positive value of u would increase x and a negative value of u would decrease x.

If the control error e is positive, that means x is under the setpoint, in this case we want to increase x with u that should be positive, that's why u=p*e should be positive and P should thereby be positive. Analogically for a negative control error.

For the system: dx/dt = -x -u , a positive value of u would decrease x and a negative value of u would increase x.

If the control error e is positive, that means x is under the setpoint, in this case we want to increase x with u that should be negative that's why u=p*e should be negative and P should thereby be negative. Analogically for a negative control error.