In a plane equipped with a reciprocating engine that drives a propeller, the pilot can adjust throttle, mixture, and prop pitch. Ignition timing is another input, although I expect this is usually managed by the engine itself via a distributor or ECU (depending on the age of the aircraft).
So for a jet engine, are there fundamental control inputs (either pilot-managed or computer-managed) other than fuel fuel rate?
I don’t have an answer but if I had to guess I would say that there is probably some mechanical adjustments to control airflow (carburetor) and nozzle (thrust) effects either for intake or exhaust.
Other adjustments might include fuel preheating adjustments or fuel location (exactly where the raw fuel is added)
From a pilot point of view it’s just a single lever per engine that controls the amount of fuel going to the combustion chamber. That’s all that’s required to control the engine thrust. The thrust lever generally doesn’t provide direct control of fuel to the engine though. It sends an input to the fuel control unit and that sends the fuel to the engine. There are safeguards in place to prevent too much fuel being sent at once. In modern jet engines it doesn’t matter how quickly you move the thrust levers, the fuel control unit or similar device will ensure that fuel is metered at a rate that the engine can handle. Ignition is used for starting only. Because the fire in a jet is always burning you don’t need to have an active ignition source once the engine is running. There are no controls for air other than what I’ve described below.
In terms of what else is going on, a jet engine can gulp too much air through the intake at times and so there are valves that automatically open to bleed this excess air (“bleed air”) away so it doesn’t hinder the compression process.
Bleed air is also taken for other purposes such as airconditioning/pressurisation and anti-ice systems. The valves for the extra services may be pilot controlled. On my type there is a bleed air switch for each engine on the air supply panel, turning this switch on takes air from the engine and makes it available to the aircon and pressurisation systems. There is also a switch for each engine on the ice protection panel that operates a valve to supply engine air to the engine anti-ice system, but these aren’t controls for the engine so much as other services the engine can provide.
Compared to a reciprocating engine, turbine engines are very simple, and don’t require as much “engine handling”. This is a good thing because jet engines make the aeroplane a lot faster and it’s best if your brain isn’t consumed with leaning mixtures, applying carb heat, or adjusting rpm. Much better to have a single “go” lever so that you can be doing more important stuff like mentally staying a few steps ahead of the aeroplane.
Of course supersonic aeroplanes and jets with afterburners are a bit more complicated, but a basic jet engine is simple.
You might find the wiki (and further Googling) for FADEC (Full Authority Digital Engine Control) interesting. It lists some of the parameters and settings the engine management computer adjusts for both turbine and piston powered aircraft.
Google Books has a large preview of the F-86 operating manual. From it, I only see the throttle as the pilot-actuated engine control, although there are supplemental switches to activate various emergency fuel systems. And the master switch to turn the engine on.
This link is to a message board post purporting to describe the monitored parameters of the Engine Electronic Controller (EEC) for the Rolls Royce Trent 500 turbofan. As Richard Pearse pointed out, it looks to basically control fuel flow and bleed air valves, although the post notes that the EEC also controls the position of variable stator vanes (the “VSVs” in the message board link.). My guess is that these VSVs direct airflow within the turbine. The .pdf is to an analysis of why one of those VSVs broke within the engine of a 777.