Chiller Controls

Generally speaking you have two types of controls, those for safety, to protect the system components, and those for controlling the system, that turn components on and off or regulate to match load...Most chilled water systems like this one regulate themselves to meet the load required....as the heat load demand increases the compressor loads up, this requires more water circulation, both chilled and condenser water....these are usually regulated by either pressure or temperature...

https://www.controleng.com/single-article/control-sequences-for-chilled-water-systems/2eb1feb85d57006c05373f54d9a37eeb.html

The pump running contact can be used to inhibit the integral term of the controller.

If the pressure is low because the pump is not running, then the valve or speed setpoint controller output will try to go to max. If you then start the pump, then you'll get a big slug of water through the open valve, or full speed pump. The controller won't 'wind up' if it doesn't try to respond to an invalid process condition, such as pump stopped.

The differential pressure sensor is another method to determine if the pump is running. If the pump is stopped, and your sensor is not fooled by a check valve between the pump and the sensor, the pressure at suction & discharge will be very close. So you can inhibit the controller by using the pump differential pressure switch, if that is something you have.

You don't really need to establish a sequence, so much as to make sure your valve ramps and speeds allowed don't cause large amounts of water to move quickly, breaking pipe supports and cracking equipment casings.