JoeWong,
I agree that if you put in independent control loops in series you are asking for a dynamics disaster.
Multiple valve in series work just fine if you send the same control signal to each of them. If the system wants 43% of valve travel, it sends a 43% (10.88 ma) signal and all the valves obediently open the same amount. There is no instability. The only trick is to check the impedance of each valve and the loop impedance limit of the controller. It may be necessary to add a signal repeater and another power supply in the loop.
However for this application the discussion of multiple valves is moot. AND, regarding the discussion of an orifice: THe orifice MUST be installed downstream of the control valve, and orifices, being a fixed restriction, are optimized for only one flowrate. Not a good idea unless the valve only operates on-off.
Boiler feedwater at this range of pressure is handled well by a single cage-type globe valve with multistage cages. Shouldn't need more than 2 stages. The cages have many small (~3mm) holes that break the flow into small jets. Multistage cages have multiple concentric cages and the holes are offset to cause tortuous flow. The directional and velocity changes also cause pressure reduction, so a 2-layer cage actually has 5 pressure reductions for a single fluid path. Flow is inward through the cage so that any cavitation bubbles implode in the free volume inside the cage instead of against a surface where they can cause damage. Cavitation may be "contained" instead of being eliminated, but the whole point is to avoid cavitation damage. 4500 kPa is not extremely high pressure.
Example: Valtek Cav-Control or Channelstream trims.
You referenced uncondensible or dissolved gas: Boiler feedwater is diligently purified before it is introduced into the system and additives and deaerators scrub any gases that leak into the system. Any bubbles in feedwater are steam that comes from the flashing of the water itself.