HART; PID Loop via PC & HART modem
Adding the HART Modem will get the process value into the computer. Depending on what you choose to use as a controller and an actuator you could make this work, but it won't be an industrial standard process control loop in terms of reliability or perhaps performance, as Windows is not a real-time operating system (but it may be good enough). 

One approach is to make a controller with your favorite software such as MATLAB/Simulink, LabView, raw coding in C (for the intrepid and/or old-school). 

You'll have to figure out how to control the valves from your PC (not shown in your block diagram). And if you get the BSOD on the PC make sure that there is no undue ill effects on people or property. 

Personally, I think you'd be better off buying a process controller with a serial interface (and a suitable output) and use the PC as a supervisory system rather than putting it into the process control loop.