Artificial Stability

Austin published the following recently:

Load an airplane in Plane-Maker.
Go to the EXPERT menu, ARTIFICIAL STABILITY screen.

This is where you can enter control-system constants to make your plane feel stable even though, in reality, it isn't. This is especially common in fighter jets and helicopters... fighters are most manueverable if unstable, and helos just have nothing to naturally MAKE them stable! So we design control systems to MAKE THEM SEEM STABLE. These control systems typically do this by ADDING SOME INPUT IN ADDITION TO YOUR STICK INPUT to make the plane do what you want.

A common case of this in the civilain world is the yaw damper... your feet still move the rudders, there's no doubt about that, but the yaw-damper system ADDS SOME ADDITIONAL RUDDER DEFLECTION FOR YOU TO DAMP OUT THE ROTATION RATES OF THE PLANE. How much rudder does it add? Well, that is a decision made be the controls-system engineer... in this case known as: "YOU".

Let's imagine a yaw damper. The goal is to add some rudder deflection to whatever the pilot hammers in with his feet to stop aircraft rotation... this is seen in high-end Mooneys and most jets. So ask yourself this: How much rudder do you WANT to add to stop rotation? FULL rudder? Just 1/10 of the max rudder deflection? Obviously, if the plane is only wagging it's little booty a LITTLE BIT, you only want to add a LITTLE rudder to stop it. But, if the plane is shakin' dat thang at a high rate, then you better put in a LOT of rudder to put a stop to it NOW. So how do we decide how much rudder to put in? Well, there are plenty of ways, but in X-Plane, we say that we enter some fraction of the rudder input PER DEGREE PER SECOND OF ROTATION RATE.

So, imagine the plane is wagging it's little tail (from turbulence, varying crosswind, the pilot stepping on the rudder, WHATEVER) at 90 degrees per second. (Now let's THINK about that for a second!!!!! HOLD YOUR HAND IN FRONT OF YOUR FACE AND PRETEND IT IS AN AIRPLANE. NOW ROTATE YOUR HAND THRU 90 DEGREES OF HEADING CHANGE IN 1 SECOND. THAT IS 90 DEGREES PER SECOND.) As you see, it is a moderate rotation rate, but not a really huge rotation rate. However, when you are in the real airplane, 90 degrees per second of tail-wagging will feel like a LOT. (kicking the rudders a bit in a Cessna 172, for example, will shake it's little booty at about 35 degrees per second). So, lets say that 90 degrees per second is so much rotation rate that we are willing for the control-system to put in FULL RUDDER to oppose it. That means that if the plane is rotating at 90 degrees per second, we want to put in FULL rudder to oppose that motion, and at 45 degrees per second we want to put in HALF rudder to oppose that motion, and at a measly 9 degrees per second we want to only put in 1/10 rudder to oppose that motion. At the 35 degree-per-second tail-wag of a 172, the control system would put in as much as about 35% rudder deflection to oppose tail-wagging and yaw-stabilize the plane. This does not sound like an unreasonable constant.

So what do you enter in Plane-Maker to make it happen? Well, for the "heading: target sideslip" you might just enter "0" (the plane always tries to stabilize at 0 sideslip) and for "fraction deflection per degree difference" simply enter "0" (the system is not trying to achieve a desired sideslip, only DAMP OUT the tail-wagging by opposing ROTATION RATES) and for "fraction deflection per degree per second" enter "0.0111". Why 0.0111? Well, take that 0.0111 and multiply it by 90 (the rotation rate that we would apply FULL rudder at) and you get 1.00.. or, translated: "FULL rudder deflection". Put another way, if you want full rudder at 90 degrees per second yaw rate, simply take 1.0/max yaw rate and you will get 1/90 or 0.011. This is a reasonable yaw-damper constant. Try entering it for the 172, save the plane in Plane-Maker, load it again in X-Plane, and pop the rudders left and right: you should see the plane damps out faster, as would a real one if such a yaw damper were installed in reality.

Now, maybe you want even MORE stabilization... try entering 0.1 in the "fraction deflection per degree per second". Now THINK about what that means. That means that if the plane is rotating thru 10 degrees per second, the rudder will move fully to oppose it. (10 degrees per second times 0.1 control per degree per second = 1.00, which is FULL DEFLECTION.) Move your hand at a rotation rate of 10 degrees per second. This means it should take 9 seconds to move your hand thru 90 degrees. That is a SLOW rotation rate. Yes, with a constant of 0.1, even this SLOW rotation rate will be opposed by FULL rudder. YIKES!!!!!!!!! If you just BREATHE on this airplane now it will kick FULL rudder to oppose it! Yikes! This is scary, because IF YOU TAKE THIS THING INTO TURBULENCE I GUARANTEE THE AIR WILL KICK YOU AROUND AT WELL OVER 10 DEGREES PER SECOND ROATION RATES, SO I GUARANTEE YOU WILL SEE =>FULL<= RUDDER DEFLECTION FIRST ONE WAY, AND THEN THE OTHER, AS THE PLANE WAY OVER-REACTS TO EACH ANGULAR ROTATION INDUCED BY THE TURBULENCE BY KICKING FULL RUDDER TRYING TO OPPOSE THAT ROTATION! So, as you can see, a constant of 0.1 is really pretty high.

Now, to give you an idea of how bad it can get, I have actually seen a plane where someone entered a constant of 3.0... THIRTY TIMES HIGHER than this hypothetical case. Think about what this means: For a rotation rate of 1/3 degree per second (in other words, it takes 270 seconds (4.5 minutes) to move thru 90 degrees of heading, an EXTREMELY LOW ROTATION RATE, the system would put in FULL OPPOSITE RUDDER! HOLY COW! That means that the plane has even the tiniest, slowest-imaginable HINT of rotation in a given direction, THE RUDDER SLAMS HARD OVER TO THE STOP TO COUNTER IT. Needless to say, any time this plane entered even the slightest hint of turbulence, the rudder would slam from one stop to the other in a wildly exaggerated effort to counter the turbulence.. ugh! If you must kill a fly buzzing around you in a china-shop, don't go after it with a chainsaw... the results won't be pretty. This particular plane handled OK if there was no turbulence: Since nothing ever came along to ROTATE the plane, the flight controls never had to move to OPPOSE THAT ROTATION... but, as soon as the slightest imperfection came along to move the plane (in this case turbulence, though it coudl easily be the pilot kicking a flight conrol, a bird-strike, an engine-failure, a bumpy landing, flying into changing winds.. ANYTHING. One thing that you can ONLY learn by actually getting your pilots license and getting your butt in the sky is that it is a VERY IMPERFECT WORLD UP THERE.. The plane is constantly barraged by all manner of imperfections, perturbations, and external winds and forces... and, much like with a BOAT, this must be EXPECTED and anticipated in the design.

Now let's apply what we have learned to PITCH stability: Say your plane is not very stable in pitch and you want to lock it down a bit. (First of all, in X-Plane 8.30 RC-2 and later you can slide the "control addition" sliders in the "Joystick" screen second tab to the right a bit to add some aritifical stability to help stabilize the plane a bit.. this simply engages a system that I designed for you to help stabilize the plane). But let's say you DON'T want to use my sytem to stabilize the plane, but really design your own to mimic the one actually installed in the real plane! Well, enter maybe 20 degress for the target angles of attack (enough to stall the plane) enter 0.1 for the fraction deflection per degree difference (if the angle of attack is 10 degrees off, then the plane applies full elevator to capture the desired angle of attack.. a very agressive but not insane constant) and enter 0.05 for the "fraction deflection per degree per second" (If the nose is coming up at 20 degrees per second, then the system will apply full elevator to stop it). These are some pretty agressive constants (a lot of elevator is brought in to counteract a small amount of motion) but I have my reasons: 1: The plane needs to have lower rates in pitch than in yaw. Why? Because if you yaw a plane a bit, not that much will change: the vertical stabilizer, which is being broadcast to the air, is small! But, if you PITCH the plane a bit, then the WHOLE WING AND HORIZONTAL STAB is shown to the air... the effect will be a lot greater than in yaw where only the vertical stab is offset, because the wing is so much bigger!!!! So, we got a lot more effect for each degree of angle of attack than we do of sideslip, so we need lower pitch rates than yaw rates to keep within comfortable (safe) G-loads, so we enter HIGHER constants in pitch than yaw to really work hard to counter those pitch rates. Also, there is another reason we can enter higher constants than you think: 2: I cheat. X-Plane will AUTOMATICALLY REDUCE THE CONSTANTS as you speed up, because it knwo that at hi speed it better enter smaller control deflections to keep from busting anything! So the constants you enter here are only fully applied down near the stall where control authority is mushy... the controls relax and phase out as the indicated airspeed (air pressure on the controls) builds up.

Now, are you ready to see this schieze in practice? Open up my VTOL in Plane-Maker ("File" menu, "Open Aircraft", "Austin's Designs : Austin's Personal VTOL" and look in the "Expert" menu : "Artificial Stability" screen. Notice that I have only LOW-SPEED constants here, designed to phase out rotation rates to make the thing easy to fly. Look at the rotations I shoot for with full-scale stick deflections in hover: Max of 30 degrees pitch, 45 degrees roll, and 45 degrees PER SECOND ROTATION RATE in yaw. And now you know what the 0.02 and 0.01 do as well. Now get into X-Plane and load up this little bird (it starts off with thrust vector at 90 degrees, straight up). Add power and raise up off the ground and work on your hovering. Slide left and right. Fore and aft. Up and down. Do it with small control deflections. Now, see that little switch on the panel called "ART STAB"? Turn it OFF to fly WITHOUT stability augmentation. VIVA LA DIFFERENCE!