I want to maintain pressure and flow rate of the fluid in the system. The system is as shown in the figure attached. When I reduce the flow control valve opening, the flow flow reduces as admired. But back pressure also increase. When I increase flow control valve opening, the flow rate increase but backpressure reduces. Similarly pump speed alters flow and pressure. So, the pressure and flow rate are interacting. They are coupled. How do I control the pump speed and flow control valve opening to obtain desired combinations of flow and pressure? How do I decouple them? How do I set PID tuning parameters for Pump and Flow control valve? The flow control valve I am using is the butterfly valve.

 

There are numerous issues you've not mentioned.
(1) Is the engine constant speed?
(2) Why are you using a butterfly valve?
(3) What is the pipe size and nominal flow rate?
(4) You've not mentioned temperature control when that is the main function of the coolant loop.

Process design is as important as automation.