gain scheduling or alternate approach?

Dear all,

I'm designing an aircraft controller for a semester project. Strictly control, as the identification part has already been done. My problem is the following: the identification phase produced in excess of 100 state-space models, for varying flight and loading conditions.

I've been going over books and doing internet searches, but apparently (as a single source states) the way to do it is to design controllers for every single model! Now, this strikes me as highly innefficient, and I'm positive there should be something else to do. Well, I got the impression that adaptive controllers could be the best option, but on the other hand (as my control knowledge reached optimal but never got to adaptive - control, I mean) I'm afraid it might be overkill, as designing a control law for a single model is something tractable even to the traditional methods.

Does anyone have any suggestion that could lead me into the right approach?

Thanks in advance,

Renato Serodio

Reply to
Renato Serodio
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Do you truly have 100 different state-space models, each with a different structure, or can you reduce it down to a few or one model with varying parameters?

Certainly if you have 100 different models and each one is correct and you always know which one to use and you can transition from one to the other without nasty bumps then it's a way to finish the semester (sometimes I think those projects are there to teach you when to quit thinking and when to start doing).

My preference would be to find a as few models as I could with parameters that depended on some easily measurable state, then do gain scheduling. The idea of doing linear interpolation on up to 100 points doesn't phase me, as long as I know that I won't mess up my states in the transitions.

Reply to
Tim Wescott

Renato,

How many variables do you have to control? From my limited understanding of aircraft they are pitch, roll, yaw, as well as thrust. So my very simple minded, process control, mind would say:

1 - Put all the models into a simulator.

2 - Add a simple PID loop for every degree of freedom. (There certainly aren't 100 or no pilot could every hope to fly a plane.)

3 - Connect the controller to the key variable of interest and then tune each loop empirically.

I bet you get better success than any more analytic approach. Once you done the above three steps you will probably gain in understanding sufficiently to make continuous, incremental improvements by way of adding process understanding to your control system based on what you observe to be the small number of actually significant components of your model. You can make these improvements until your time runs out and then hand in whatever you have. It will be something that works.

The alternative is to beat your head against a wall of incomprehensible complexity and end up with nothing but a severe headache. You won't get any marks for that.

In my humble opinion.

Walter.

Reply to
Walter Driedger

There are a lot of cross-coupling terms, but I'm too ignorant to imagine where 100 could arise from. But there's more than roll, pitch, yaw ans thrust. There's also air speed, which affects lift and which is affected by pitch. Airspeed, pitch, and roll all affect lift. Etc.

Jerry

Reply to
Jerry Avins

Gain-scheduling *is* a form of Adaptive Control (the most predictable and reliable) - and may be the most appropriate in this application; since, AIR, gain-scheduling *is* used in aircraft control systems. OTOH, if you want to be at the cutting edge of aircraft control-system design: someone told me last year that aircraft control-system designers (not my own area of expertise - so you may want to check) are now looking seriously at Model-Predictive Control (MPC) - which has been in use in the process industries for 2-decades. The fact that you already have all the necessary models should help.

Kelvin B. Hales Kelvin Hales Associates Limited Consulting Control Engineers Web:

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Reply to
Kelvin Hales

The problem is that as the aircraft speed (and weight, if you're modeling that) change the aircraft characteristics as a plant change, usually enough that you can't design a controller that's acceptable, or even stable, over the entire operating envelope of the aircraft. To cope with this you either need to make a controller that only operates during cruise, you need to make a controller that changes it's characteristics with some measurable aircraft parameter, or you need to make a fully adaptable controller that's always modifying it's internal plant model to adaptively tune the controller.

I think the 100 models he's talking about are 100 different plant models as the speed and loading change (perhaps 10 steps in each?), not a model with 100 states.

Reply to
Tim Wescott

If you search the AIAA website for "gain scheduling", you'll see a lot of hits.

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What I have seen done recently is to reduce the number of multivariable controls that have to be designed by grouping the models that don't have significant variation and then designing ONE robust control for that group. The resulting group'ed controllers still have to be scheduled with your scheduling variable.

For example, in the approach to landing task for a VTOL aircraft, as you slow from 120 to 60 knots, your point model eigenvalues will change and the control effectiveness of the flight controls surfaces change. Thus is is extremely diffcult to design ONE control that will handle this entire range. Better to schedule on velocity and design several controllers over this range. But then each of these point designs are made to be robust to other variables that you might have normally schedule, but are not treating more as disturbances.

If your case, if you don't have significant changes if the eigenvalues of your state space models, then you might be able to get away with a single robust design. But you'll have to spend a lot of time examining the various input to output transfer functions to make sure a significant sensitivity doesn't change when going from model to model.

Actually, designing 100 state space controllers isn't a huge problem once you have your algorithm setup. You can automate it easily. The tough part is then 1) reducing the order of these models so that all the model order reductions are the same size and then 2) selecting the appropriate scheduling variables for all 100 models and then 3) implementing all of this while keeping track of everything; 4) validating that the whole thing actually works over the range of interest.

Reply to
g9u5dd43

Dear all,

many thanks for your prompt answers. In fact, I've got 5 weight distributions, each with 280 flight conditions (involving altitude, mach number and flap position). These 5 times 280 is the number of plants that have been identified. My apologies if the word model misled some of you. The number of states in each plant is 4 (for longitudinal motion), and I have two inputs. In addition, three states are observed - available at output. Indeed, each plant for itself is not even a challenge - anything from root-locus to PID will do a >good< job.

Now, that a single controller wouldn't suit all flight conditions is taken for sure. That gain scheduling would have to be used was also clear from the outset. What keeps boggling my mind is how to deal with this number of plants. On my asking him, my supervisor commented on me having to use 'some kind of automatic procedure' to calculate control laws. Now, a script that calculates damping and frequency and adjusts gain to match requirements is not a problem - what happens is that there are handling qualities requirements to be taken into account, and that I'm afraid a standard design might require a bit more hand-work to make it comply throughout the 5x280 plants.

After reading your answers, for which I am very thankful, I believe the problem is now whether to 'interpolate' the plants and use adaptive control (which I'll have to learn), or to select 'groups' and design controllers for these. This last options seems to be followed in industry also. It must be noticed, though, that a proper engineer has a certain 'feel' which I lack - hence my difficulty in picking groups.

Anyway, both methods seem to waste quite a bit of the information in the

5x280 plants. It might be my own inexperience talking, but isn't there another way that makes the job of the guy who identified the model completely worthwhile?

I await your answers eagerly!

Yours faithfully,

Renato Serodio

Reply to
Renato Serodio

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