what are the checks required if the Control valve have Hunting Issue ?

Assuming a pneumatic actuator and positioner, the cause can be either a malfunctioning positioner/valve/actuator or a mistuned loop is providing a control signal that is 'hunting'.

If the valve tracks the input signal with precision and the loop hunts, then the tuning is too agressive.
If the valve stutters or fails to respond with the input signal, then look at the positioner, linkage, valve and the actuator

- dirty/wet air can cause stiction in those positioners with a spool valve so that the spool valve jerks instead of moving smoothly. Or piezo valves will stick in the pfft-pfft-pfft type Siemens positioners.
- check the positioner linkage to the valve stem. Loose, sloppy, disconnected or missing linkage is a prime cause of hunting.
- check the movement of the stem through the packing gland. If the packing gland is too tight, the stiction will cause the stem movement jump in steps, rather than move smoothly. A positioner helps over come stiction, but there are limits.
- smart positioners can be misconfigured or configured for a different valve response than the one its installed on. Re-initializing/re-tuning the positioner can eliminate that as cause.
- oversized valve (typical valve is line size with a high Cv) where the slightest valve movement overshoots the error and it's a constant hunt for the sweet spot.
- positioner overshoot combined with agressive loop tuning can drive the loop in oscillation, a form of hunting.
- I've heard that leaky diaphragm can cause hunting, but I haven't seen it.
- insufficient actuator resolution
I once ran into an electric actuated gas valve on an oven where the electric actuator could only resolve about about 25 discrete steps over its 90 degree travel - about every 0.7mA the actuator would move a step. That was nowhere near enough resolution to position the valve where it needed to be for straightline control and the valve constantly hunted up and down trying to hit the sweet spot, which it couldn't find. Horrible little actuator. Not a likely scenario on a Fisher or Masoneilon valve, but it happened.
what should i need to check in the Masonielan and fisher valves , if Copntrol valve have hunting problem ? please share your valuable thoughts.
The trick is to determine whether the problem is with the valve or is a tuning problem. Step one is to put the controller in the manual mode, then you start making small changes in the output (1/2%) in either direction. Document each change and continue in the same direction until you see a clear process response, continue to make 1/2% steps in the same direction until you see the second process response. Then start to make 1/2% steps in the opposite direction until you see a clear process response, you will have a good picture of how the valve tracks the controller output. If there was more than 1/2% output change between the first process response and the second process response (same direction) the valve exhibits high friction that is influencing your process control. If there is more than 1/2% output change between the second process response and the third process response (change in direction) the valve has hysteresis, slack. Either will cause process control issues and cannot be corrected by retuning the controller. The only option is to repair or replace the valve. There are valve testers that will analyze your valves for performance issues but the process must be down to use them. Benchmark by Black Diamond Engineering is one, Flowscan by Fisher Valve Co. is another.