Generator and Capacitors

I'm thinking that you should check your voltage regulator. If it is not paralleled with another bus, it should be set in "non-droop" mode.

https://en.wikipedia.org/wiki/Voltage_droop

Caps are not a good idea if you have a lot of electronic power systems and a high impedance source like a generator. You are just asking for resonance problems. All of your servo amplifiers, VFDs (if any) and power supplies have capacitors in them already. Solve your problem at the generator as suggested.

Some points...

1. Standard instrumentation for speed has a sluggish response. Your 40 rpm (2.7%) dip may be much less than you really have.
2. Standard performance for a diesel mechanical governor would be 4% fall from no- load to full load, steady state, and 10% dip on sudden full load from no-load.
3. The 4% speed fall steady-state is necessary for controlled load-up and load sharing in parallel with a Grid or other generators. A generator on its own can operate with much less than 4% which can speed response.
4. It is not clear if it is the minimum frequency reached causing trouble. If that is so, then increasing speed setting 5% should not cause trouble for any loads, but will raise the inertia 10% and directly raise bottom frequency by 5%.
5. The governor/fuel pump usually has limits on rate of fuel increase and maximum fuel, which can be adjusted. e.g. there is usually a mechanical stop on the fuel rack for injection pump stroke.
6. Ratings are often given as the absolute maximums - Continuous duty engines used to be rated for 10% overload for 1 hour in 12.
7. No comment has mentioned the voltage dips - here again the panel meter does not respond quickly. A direct-on-line started motor takes 6 times full-load current [and 1-2 times rated kW] & standard design requires 80% minimum volts during start. The commonest mistake in sizing diesel generators is to just look at kW (horsepower) and not amps. While generator makers have done a lot to improve overload performance, 3 x rated load at 80% volts is good & whatever the excitation, speed dip proportionally reduces volts.
8. Voltage regulators typically have 3% voltage fall at 100% amps for stable parallel running - this can be reduced on a solo unit. As for frequency, it is probably OK to increase volts setting to 105% nominal - reducing the dip minimum.
9. The loads you give sound like inverter drive speed controls - these rectify the AC to DC - so they do not care about frequency, but are directly affected by volts. The compressor may be direct on line, but if it is normally running at rated speed & not started each time pressure drops then it will not be a big kW/amp step.
10. There may be adjustments possible on the drives to limit sudden kW/amps demands, current limits, ramp rates etc.

I suggest discussing your problem with the genset and drive suppliers - they may be able to help with measurements & adjustments to reduce your frequency/volts fluctuations.