I think you mis-understand the function of a PID, it's primary functions is to reach it's set point as quickly as possible without much overshoot (some like it without any), maintain that set-point, if there is a disturbance then it will react to correct it to maintain the control as close as possible to the set-point. The PID is not working correctly if it cannot reach the required value, the reasons are the PID algorithm is not doing it's job, the controlling components i.e. motor/valve or what ever is not capable of reaching set-point.
here is a scenario, You give the PID a set-point of 100, it reaches 94, in practice the PID will ramp up the output to 100%, if it fails to reach 100 then your hardware is not up to the job, for example a pump driven by an inverter is set for 0-60hz and your PID output gives 0-10v the inverter is set to 0-60hz for the 0-10v you require a flow of 100 galls per minute, the PID will ramp to 100% but can only achieve 94, therefore increasing the set-point will not do anything. I strongly suggest you look at the motor / PID as there must be something wrong. First of all, it appears you are simulating this well at least as far as HMI etc. have you actually got a physical motor and flow/speed with feedback ?.
Here is the manual for using the PID instructions:
https://dl.mitsubishielectric.com/dl/fa/document/manual/plc/sh080040/sh080040s.pdf
These are the functions
PID control data setting S(P).PIDINIT PIDINIT(P)
PID operation S(P).PIDCONT PIDCONT(P)
PID control status monitor PID57(P)
Specified loop No. operation stop S(P).PIDSTOP PIDSTOP(P)
Specified loop No. operation start S(P).PIDRUN PIDRUN(P)
Specified loop No. parameter change S(P).PIDPRMW PIDPRMW(P)
Note: the PID function uses something like 30 + memory areas i.e. "D" words & "M" bits, not all need to be set only initially to set up the modes & parameters.
This is quite complex & not for the faint hearted.