How to prevent current and voltage fluctuations for loads connected in parallel to the same power supply?
It is possible that your power supply is unable to hold the voltage under a higher load, I don't know because you have not specified neither the power supply current/power rating, nor the power of any of the devices connected to it.
 Additionally, a picture can help a lot, as it will help us see what you can't see as being problematic with your setup.
 Once you give more details (picture and schematic if possible), I will be able to help.  

Without knowing more about the setup I would suggest this:
1. Connect each device to the power supply with a separate cable! Don't use the same cable for multiple devices!
2. Your audio amplifier and the h-bridge controlling the actuator could use a larger electrolytic capacitor on each (2200-4700F).
3. Your cable/wire could be too thin and dropping too much voltage under load.
4. You might also need an additional capacitor on the power supply (2200uF-4700uF).