Camad:
If you know the type, brand or make of your gas compressor, then identify it and let us know. I believe, from your sketch, that it is a centrifugal type; but then, your use of non-standard instrument symbols is also another amateur mistake in communicating engineering data.
However, if it is a dynamic (centrifugal) type - as opposed from a positive displacement (reciprocating) type, the flow rate the machine displaces depends on the “Head” or resistance that opposes the flow. This is clearly explained and described in all compressor textbooks and in our Forums. This topic has been discussed in our Forums for many years now and the related threads can be read by using our Search Engine.
Are you a student? Your query is so elementary and basic that I wonder if you have had the normal, required academic courses to get a degree in engineering. Of course, a gas compressor will continue to compress gas while it is rotating - even a centrifugal device.
The reason why your pressures (you fail to identify which specific pressures you mean) and your flow rates are varying is probably due to the manner in which your instrument controls are functioning. Your sketch, as I stated, does not use normal, standard instrument symbology and there are what appears to be pressure signals being sent to a throttle valve in the suction side of a centrifugal (?) compressor, upstream of the suction scrubber. What a “signal selector” really is and really does is anyone’s guess. Your diagram does not show any surge controller - if indeed, it is a centrifugal type.
I highly recommend you resort to studying the instructions found for all industrial compressors (both centrifugal and reciprocating) which are routinely supplied with all manufactured compressors. These instructions cover all operational, maintenance, and safety issues specifically related to the machine and should clearly explain the reasons and the methodology of the instrumentation furnished on the machine. Additionally, you should read and study as many compressor textbooks as you may have available to you. Amazon books is a good source on the internet.