Algae control comes down to controlling nitrates and phosphates. If you have a problem with algae it is because these two nutrients are out of control. Do not think that just because your test kits read zero or low values that you do not have a problem. In many cases the algae is removing the nutrients and growing. This is why there is a problem.
Here are possible sources of nitrates and phosphates -
Feeding, especially flake food and not rinsing frozen foods before feeding.
Using tap water to mix salt. Always use RO/DI water for this.
"Dirt traps" and "nitrate factories" in the system.
Low quality carbon can leach nutrients.
Low quality salt can sometimes add nutrients. This is unusual today.
Livestock load on the system
Here are possible ways to remove nitrates and phosphates -
Water changes. Change 1/2 the water and you reduce the nutrients by 1/2.
Skimming. Remove the waste products before the biological filtration need to break then down.
Nitrate and phosphate removal products.
Deep sand beds.
Each of these has advantages and disadvantages. Most people that control algae will use many of the above methods.
There are also other items that can effect algae growth rates.
Good clean up crew.
Other livestock that eats algae.
Low general water quality, especially when the readings are off.
Lighting, sometimes you can reduce it, especially in FO or FOWLR systems.
Old light bulbs. Colors change as they age and this can be a factor.
Water flow. More flow will often help keep algae down.
Manual removal. Very important, especially when there is a big problem.
End of lecture.
By all means please post the information requested by @PSU4ME so we can give more specific. When posting test results, please post actual values. Statements like "all parameters are fine" do nit convey any information. What seems ok to you might indicate a problem to someone else.
As for the corals, please tell us what species you are trying to keep. Some have very specific demands and requirements. Other species can be difficult with any system or setup or care.