Dutch Roll

Dutch roll is one of the aircraft lateral-mode that consists of out-of-phase rolling and yawing motion of the aircraft. It is a result of "imbalance" between roll and yaw damping characteristics of the aircraft (i.e the aircraft is more stable in the lateral sense rather than in directional sense). Hence, dutch roll alleviation can be achieved by using yaw-damper that feeds back the yaw rate (from the yaw rate gyro) to the Stability Augmentation System to improve the directional damping characteristics of the aircraft.

This video shows Dutch Roll excitation by using a doublet rudder input.
Panel shown is Cessna 172, however the aerodynamic model used is a generic jet aircraft flying at 30,000 ft and at the speed of around M0.74.

Apology

After the whole series of event the past week, I learned one thing, not only from the events around me but also from my own experience. That one thing is to apologize.

I watched Grey's anatomy last night and one thing that didn't really catch my attention until today when I experience it myself is Bailey's words to Derek (after facing his first lawsuit as he becomes the interim chief of surgery), "One thing that I know would help a lawsuit, and that's what Dr. Weber would do, he would walk into the room and apologize to that woman. Everyone needs to feel appreciated." (not a direct quotation).

I was walking to another staff's office as I passed his office this morning. I found him staring at the monitor with his door open. Well, I thought to myself, "Perhaps this is the time." And so I walked in to his office this morning and cornered him. Although I heard strain in his voice, but he said "I received your e-mail and I do apologize. It turns to be a very nasty weekend for me until Wednesday. Let's meet on Thursday or Friday.." Although he made an excuse that he has sent an email to everyone but apparently had missed me in the list, but it doesn't matter to me. It feels good to be appreciated. And I learned today that an apology goes a very long way.

So, let's meet on Thursday or Friday. I hope we are going to make it this time.

An apology is the superglue of life. It can repair just about anything. ~Lynn Johnston

And as I forgive seventy times seven times, I, too, realized that I have been forgiven and given many more chances. So, let's remember that all of us, son of man, are given the power to forgive each other, too.

Skiing over the reference ellipsoid

It was a fun weekend, learning how to ski and actually did it yourself... except for the falling part, I pretty enjoyed it. But now all my body is aching and my left ankle still hurts. *sighs*

Nevertheless, the pain is good enough to get rid of my pain this past few days. He is a great man, a great person to talk, too. I tried to understand his not replying to e-mail, but I really can't appreciate him for not coming to an appointment that he had agreed upon and he had been reminded about the day before.

Fine... I will give you another chance.

In any case, update on the project FDE. I implemented the reference ellipsoid into the model and by now it would be able to pick up the curvature and eccentricity of the earth. :) However, I just realized that this particular set of aerodynamic coefficient is very sensitive... either to altitude (when I start to tweak the altitude for density correction), or to CL_a, because it starts to behave very differently for CL_a = 0.2481 something which is accurate up to 10^-3 and for the so-called "true" CL_a.

Next thing I will need to do is to find a way how to implement look up table for the aerodynamic coefficient. :) Oh I so want to see the stall buffet!

Heading Hold

One note before I go to bed and call this very long day a day...
I realized that the Heading Hold mode in the previous architecture does not work very well because it allows roll angle to shoot. I have revised the architecture on the heading hold to be an outer loop of an inner loop made of roll angle hold (attitude reference system, then). The error signal that comes from the heading error is fed through a PID controller before being treated as a reference bank angle to track. The PID controller needs to be limited to maximum bank angle allowed and an anti wind-up is necessary. The wind-up mode that I chose to use is the clamp mode. In this mode, the controller output will be clamped to the saturation point provided

• The controller output reaches the saturation point, AND
• The integrator input is of the same sign with the output.

The controller will start to work properly again when the integrator starts to change sign.

The performance looks to be satisfactory. Although some tuning needs to be made in order to make the heading rate reasonable.


Some additional projects to be done:

• Yaw damper and the dutch roll mode video... it could make a nice article, I guess. It's almost very hard to understand what is dutch roll mode until you see it in this simulation.

Autopilot and SAS

It's amazing how Simulink can enhance your work. My life has been centered around MATLAB and I start to feel helpless without my MATLAB.

Anyway, I finished converting my M-file into Simulink model and today I have enhanced the aircraft with proper yaw damper and add heading hold feature to the autopilot. Moreover, the phugoid suppresant which consists of a PI controller from pitch attitude error and a pitch rate gyro feedback has been implemented correctly now. Here is the architecture of the Autopilot and Stability Augmentation System (SAS) at the moment.

I love this Simulink. I can just add a washout circuit (which is defined very well in the frequency domain) to the yaw damper very easily!