Fuzzy logic applicationsAircraft landing control

Uva Wellassa University of Sri Lanka

Group Members…

Samarathunga S.M.B.P.B.

Karunarathna R.M.C.P.

Thennakoon H.M.D.J.

Somasiri K.G.H.A.

There are many areas of uncertainty or fuzziness in real world systems and an efficient way of dealing with this fuzziness is by the mechanism of fuzzy logic.

Owing to its ease of implementation and robustness, fuzzy logic control (FLC) is increasingly growing in popularity among control engineers.

Fuzzy logic relates to the way of people think and talk, in other words, their use of natural language.

What is fuzzy logic?

Difference between fuzzy and crisp sets

Fuzzy Logic applications

Power system stability controllers. Temperature controller. Anti lock break system(ABS). Hybrid modelling. Fuzzy controlled washing machine. Air Condition machine.

Aircraft Landing Control Problem

We will conduct a simulation of the final descent and landing approach of an aircraft.

The desired downward velocity is proportional to the square of the height. Thus, at higher altitudes, a large downward velocity is desired.

As the height (altitude) diminishes, the desired downward velocity gets smaller and smaller.

In the limit, as the height becomes vanishingly small, the downward velocity also goes to zero.

In this way, the aircraft will descend from altitude promptly but will touch down very gently to avoid damage.

The two state variables for this simulation will be the height above ground “h” , and the vertical velocity of the aircraft “v”.

The control output will be a force that, when applied to the aircraft, will alter its height, , and velocity, . The differential control equations are loosely derived as follows.

Mass moving with velocity has momentum

If no external forces are applied, the mass will continue in the same direction at the same velocity, . If a force f is applied over a time interval t, a change in velocity given by below equation.

If we let and we obtain

or the change in velocity is proportional to the applied force.Then, we get

Membership value for heightHeight (ft.)

0 100 200 300 400 500 600 700 800 900 1000

Large (L) 0 0 0 0 0 0 0.2 0.4 0.6 0.8 1

Medium (M) 0 0 0 0 0.2 0.4 0.6 0.8 1 0.8 0.6

Small (S) 0.4 0.6 0.8 1 0.8 0.6 0.4 0.2 0 0 0

Near Zero (NZ)

1 0.8 0.6 0.4 0.2 0 0 0 0 0 0

Membership value

Membership value for velocity

Height (ft.)

-30

-25 -20 -15 -10 -5 0 5 10 15 20 25 30

Up large (UL)

0 0 0 0 0 0 0 0 0 0.5 1 1 1

Up small (US)

0 0 0 0 0 0 0 0.5 1 0.5 0 0 0

Zero (Z) 0 0 0 0 0 0.5 1 0.5 0 0 0 0 0

Down small (DS)

0 0 0 0.5 1 0.5 0 0 0 0 0 0 0

Down large (DL)

1 1 1 0.5 0 0 0 0 0 0 0 0 0Membership value

Membership values for control forceHeight (ft.)

-30

-25 -20 -15 -10 -5 0 5 10 15 20 25 30

Up large (UL)

0 0 0 0 0 0 0 0 0 0.5 1 1 1

Up small (US)

0 0 0 0 0 0 0 0.5 1 0.5 0 0 0

Zero (Z) 0 0 0 0 0 0.5 1 0.5 0 0 0 0 0

Down small (DS)

0 0 0 0.5 1 0.5 0 0 0 0 0 0 0

Down large (DL)

1 1 1 0.5 0 0 0 0 0 0 0 0 0Membership value

Fuzzy associative memories (FAM) table

Velocity

Height DL DS Zero US ULL Z DS DL DL DL

M US Z DS DL DL

S UL US Z DS DL

NZ UL UL Z DS DS

Cycle 0 Cycle 1 Cycle 2 Cycle 3

Height (ft) 1000.0 ? ? ?

Velocity ( -20 ? ? ?

Control force - ? ? ?

Let’s calculate 1st cycle Let,

Initial height Initial velocity

When at above condition Height fires L at 1.0 & M at 0.6 and Velocity fires only DL at 1.0.

Height Velocity Output

L (1.0) AND DL (1.0) Z (1.0)

M (0.6) AND DL (1.0) US (0.6)

We can use defuzzify using centroid method and get This output force calculate under initial conditions.

Then calculate the output of the next cycle.

Height fires at and at

Velocity fires at and at

Height Velocity Output

L (0.96) AND DS (0.58) DS (0.58)

L (0.96) AND DL (0.42) Z (0.42)

M (0.64) AND DS (0.58) Z (0.58)

M (0.64) AND DL (0.42) US (0.42)

We can calculate by centroid method it is

For next cycle

Then calculate the output of the next cycle.

Height fires at and at

Velocity fires at and at

Height Velocity Output

L (0.93) AND DL (0.43) Z (0.43)

L (0.93) AND DS (0.57) DS (0.57)

M (0.67) AND DL (0.43) US (0.43)

M (0.67) AND DS (0.57) Z (0.57)

We can find the value of by using centroid method it is .

Likewise we can calculate the

And

Summary of the cycle results

Cycle 0 Cycle 1 Cycle 2 Cycle 3

Height (ft) 1000.0 980.0 965.8 951.1

Velocity ( -20 -14.2 -14.7 -15.1

Control force 5.8 -0.5 -0.4 0.3

Summary of the cycle results

Cycle 0 Cycle 1 Cycle 2 Cycle 3

Height (ft) 1000.0 980.0 965.8 951.1

Velocity ( -20 -14.2 -14.7 -15.1

Control force 5.8 -0.5 -0.4 0.3

References…

Ross, T.J., 2010, FUZZY LOGIC WITH ENGINEERING APPLICATIONS, 3rd edition, John Wiley & Sons, Ltd..

Sisil Kumarawadu, 2010, CONTROL SYSTEMS Theory and Implementations, Narosa Publishing House.