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Equations Related To Linearization-Feedback Linearization-Handout, Exercises of Signal Processing and Analysis

Jaypee University of Engineering & TechnologySignal Processing and Analysis

Prof. Kashmira Yashwant provided this handout at Jaypee University of Engineering and Technology for Feedback Linearization course. It includes: Equations, Related, Linearization, Rotation, Subsystem, Acceleration, Rotors, Thrust, Generated

Typology: Exercises

2011/2012

Uploaded on 07/17/2012

gaggan
gaggan 🇮🇳

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SystemEquations:
Rotationsubsystemofactualplantis:
12 11r
aa bu



(1)
34 22r
aa bu



(2)
533
abu



 (3)
44
u
p
b
 (4)
Wherepisthetotalaccelerationwithrespecttofreefall,soitdependsonthetotalthrustgeneratedby
allrotors.
22
124
)(ub
(5)
22
213
)(ub
(6)
2222
31234
()ud

 (7)
2222
41234
()bu

(8)
1234r

 (9)
Allothersymbolsareinaccordancewiththethesiswearefollowing.
Insertingvaluesfrom(5)‐(9)into(1)‐(4)andintroducingnewvariablesto,weget:
22
121 34 42121
)(()aa bb v




(10)
2
32
31 2442 213
(())aa bbv
  



(11)
2222
53 1 2 4 33
()bdav



 (12)
2222
41234 4
()vbpb


 (13)
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Download Equations Related To Linearization-Feedback Linearization-Handout and more Exercises Signal Processing and Analysis in PDF only on Docsity!

System Equations:

Rotation subsystem of actual plant is:

1 2 r 1 1

   a   a   b u

3 4 r 2 2

   a   a   b u

5 3 3

   ab u

4 4

p   bu (4)

Where p is the total acceleration with respect to free fall, so it depends on the total thrust generated by

all rotors.

2 2

1 2 4

ub (   ) (5)

2 2

2 1 3

ub (   ) (6)

2 2 2 2

3 1 2 3 4

ud (         ) (7)

2 2 2 2

4 1 2 3 4

ub (       ) (8)

r 1 2 3 4

All other symbols are in accordance with the thesis we are following.

Inserting values from (5)‐(9) into (1)‐(4) and introducing new variables to , we get:

2 2

1 2 1 2 3 4 1 2 4 1

   a   a (       )  b b (   ) v

2

3

2

3 4 1 2 4 2 1 3 2

   a   a (      )  b b (   ) v

2 2 2 2

5 3 1 2 3 4 3

   ab d (       ) v

2 2 2 2

4 1 2 3 4 4

p ^  bb (        )  v (13)

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