Is this an existing installation, or just a hypothetical? What sensors or devices do you actually have available or planned? As Littleinch said - have the pump control to DP2? What is DP1 and that 3-way actually controlling to/doing?
Unless I am not understanding the application.....
Your flow through DP2 needs to be greater than or equal to DP1. With a constant flow requirement through DP2, I would NOT control the pump. Make it constant volume and put a circuit setter (or similar device) in the bypass line that matches the pressure drop of DP1. The pump won't know or care whether the flow goes through DP1 or through the bypass line. Pressure drop will be the same either way. 3-way valve can operate on temperature.
Fully in agreement with what Bronyraur said.If constant flow is to be maintained across dp2,both flow resistance and available pressure head need to remain constant.This means a valve with a fixed setting right after DP2 and the pump running at constant speed.What is the purpose of the 3 way mixing valve?The 3 way valve operation may change system head and may result in flow variation through DP2 all other parameters remaining the same.Is this for an energy recovery loop?
Ummm, DP means differential pressure. You want to control the pump to a constant “flow” at “DP2?” No. Control the pump speed to maintain the differential pressure (like, "DP") at “DP2.” The 3-way valve will maintain minimum flow at what you call “DP1” to keep the chillers happy. I tried, but not sure if I hit it…
Use constant speed pump sized for the worst flow pressure drop through coil and chiller. At the bypass leg of the 3 way valve put in balancing valve to create same pressure drop as through the cooling (when all flow is through the cooling coil) but with all the flow through the bypass. Now if actually there are lots of cooling coil with 3 way valves served by the chiller you would need to add additional balancing valves at the downstream side of each 3 way valve. The balancing contractor would then have to set this valve so design flows through all the coils are maintained. Pressure drop through this balancing valve on the worst case run must be included in the pump sizing.