How is your medium composition and which type of product do you have?

I used LB medium and added 2.2 g glucose /h. We expressed a protein (MetAP).

Usually, pH tends to  decrease in a fermentation becuase some of the products are acidic.  However, in this case, pH rises. This indicates that the cells were not able to utilize the carbon source or it may be at high concentration to inhibit and kill the E. coli. For this reason a lot of basic compound are produced from the decomposition of the cells.   

at the first, be sure about its pH sensor. in addition, in parallel, run a similar condition of fed-batch in the erlenmeyer flask-scale using shaker incubator.

Check whether the biomass production after each aliquot of  medium addition is as per you expectation. I presume that there is no contamination in the system. It is only showing a very significant lag which is slowing the growth. 

Could be due to the malfunctioning pH sensor. What is the pH of the feed, above 7 or below 7? If the feed pH > 7, so that would cause the acid being added to regulate the bioreactor medium at pH 7, of course, assuming low microbial activity producing CO2 or/and other acidic products. If feed pH < 7, yet more acid was added to the bioreactor - well, this is unusual. Better redo the experiment, as quite often that an unusual event is due to human errors, or could be a slim case of something extraordinary, yet to be discovered!

same situation happened with bacterial batch type fermentation in lab. finally i put the culture  in refrigerator for a 20 days in 1% nutritive solution and this tip worked well. 

Typically, if you have complex medium ingredients, they are composed of protein/peptides. LB, as example, is made from yeast extract and trypton. When cells use these nutrients, they cleave off ammonia from the contained amino acids, as they have a much greater demand for the carbon then for the nitrogen contained therein. Ammonia is released. In consequence, ammonia attracts a proton to form ammonium in aqueous solution - that is simple chemistry, which causes the pH increase.

If possible you could always check your other fermentation productions instead of the protein by using a GC or HPLC, normally the pH increase was due to the production of ethanol. If the biomass decreased, then the pH shouldn't change.

In case you have implemented a pH-stat control strategy, please note that a significant addition of isopropyl-β-D-thiogalactopyranoside (IPTG), which is acidic, may be able to decrease the pH of the fermenter broth, say, to around 6. In such circumstances, the pH-stat controlling system may eventually first add basic solution to increase the pH, and that may possibly cause a pH overshoot, particularly for a relatively slow stirring rate. If that occurs, the pH-stat system may then start to add acid solution. Eventually, pH may decrease to about 7, and if closely match the set-point, addition of acid solution may decrease and eventually stop. This being the case, it should be noticed that only if the addition of the acid solution continues steadily without addition of basic solution, while the pH remains nearly neutral, it can be safely concluded that basic compounds are predominantly generated, this leading to a steadily inherent tendency for the basicity of the broth to increase. 

For answers to a somewhat related question, please see: https://www.researchgate.net/post/Why_are_my_Fermenter_pH_measurements_not_accurate_and_why_is_there_a_delay_in_readings_almost_5_minute_to_complete

I have to second the comment made by professor Wittmann. In a defined medium, like M9, you see a pH decrease due to a combination of acid production (mainly acetic acid) and consumption of ammonia as a nitrogen source, which removes a basic component from the medium. In a complex medium like LB, however, cells will utilise amino acids as a carbon source, leading to a net release of ammonia to the medium. This results in an increase in medium pH as long as amino acids are used as a carbon source.

In the initial period of fermentation, as large amounts of organic acids are produced by acid forming bacteria, the pH inside the digester can decrease to below 5. This inhibits or even stops the fermentation process.  However, as the digestion process continues, concentration of NH4 increases due to digestion of nitrogen, which can increase the pH value to above 8. In your case, you could think of lowering the pH by adding acid rich materials like foodwaste

Please check your bioreactor system, is it control system well functioned or not?. pH probe calibration from beginning, buffer system (acid and alkali) controller. Please check carefully.

Please check your pH-stat strategy again, by using the data obtained from a batch fermentation by using the same medium and pH controlling agents. Depletion of carbon souce may lead to pH shoot up. Good luck

during the product , it may increase or decrease

which kind of fermentation/broth are you testing?

Another vote for pH increase due to use of amino acids in LB as a nitrogen source. pH was initially falling because of glucose fermentation into acetic acid and when it was exhausted pH went up. It makes sense. Also cell lysis after hard induction by IPTG is likely

I agree with Prof Wittman.

I think Profs. Whiittman & Gustavsson explained clearly and nicely the mechanism of pH shift in relation tof media composition, during the course of fementtion. As you mentiond the other group doing the same is not experiencing the pH shift as yours. Please check if all the conditions were same as yours: the purpose of the fed-batch culture, the culture strategy, medium composition, inoculum size and its age, how long to continue the fed-batch culture,  etc. and Accordingly,  you better design your culture medium and a strategy to control pH f\to continue the culture as planned. Basic informations of the bacteria and culture medium medium should come from batch culture. Good luck.

During fermentation, pH usually decreases but it increases after a period. This is due to microorganisms consumed the nutrients and produced organic acids released into the medium, thus pH decreased. After the period, microorganisms face the lack of nutrients and begin to consume the organic acids as the nutrients sources, thus pH increased.