For α = 4.5%

(1)

Chapter 5

(2)

t (s) 5 10 15 20 -2 t (s) 5 10 15 20 -10 t (s) 5 10 15 20 || " V|| 2 (V 2 ) #10-5 0 2 4 6 8 t (s) 5 10 15 20 I || 0.42 0.43 0.44 0.45

Figure 5.1: ∆V and I vs t at U = 0.1 m s

−1

, ω = 1571 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-5 0 2 4 6 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-5 0 2 4 6 ! (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6 8

(3)

t (s) 5 10 15 20 " V || (V) #10-4 -5 0 5 t (s) 5 10 15 20 " V ? (V) #10-4 -5 0 5 10 t (s) 5 10 15 20 || " V|| 2 (V 2 ) #10-7 0 1 2 3 4 t (s) 5 10 15 20 I || 0.419 0.4195 0.42 0.4205 0.421

Figure 5.3: ∆V and I vs t at U = 0.1 m s

−1

, ω = 3142 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-4 0 0.5 1 1.5 2 ! M (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 2 4 6

Figure 5.4: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 3142 rad s

−1

and

(4)

t (s) 0 5 10 15 20 -2 t (s) 0 5 10 15 20 -0.02 t (s) 0 5 10 15 20 || " V|| 2 (V 2 ) #10-4 0 1 2 3 4 t (s) 0 5 10 15 20 I || 0.402 0.404 0.406 0.408

Figure 5.5: ∆V and I vs t at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-4 0 0.5 1 1.5 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-4 0 1 2 3 ! (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 0.5 1 1.5

(5)

Figure 5.7: ∆V and I vs t at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-4 0 2 4 6 ! M (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 1 2 3

Figure 5.8: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and

(6)

t (s) 0 5 10 15 20 -3 t (s) 0 5 10 15 20 -0.03 t (s) 0 5 10 15 20 || " V|| 2 (V 2 ) #10-3 0 0.5 1 t (s) 0 5 10 15 20 I || 0.372 0.374 0.376 0.378

Figure 5.9: ∆V and I vs t at U = 0.1 m s

−1

, ω = 7854 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-5 0 2 4 6 8 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-4 0 2 4 6 ! (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 2 4 6

(7)

t (s) 0 5 10 15 20 " V || (V) #10-3 -3 -2 -1 0 1 t (s) 0 5 10 15 20 " V ? (V) -0.04 -0.02 0 0.02 t (s) 0 5 10 15 20 || " V|| 2 (V 2 ) #10-3 0 0.5 1 1.5 t (s) 0 5 10 15 20 I || 0.356 0.358 0.36 0.362 0.364

Figure 5.11: ∆V and I vs t at U = 0.1 m s

−1

, ω = 9425 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-5 0 1 2 3 4 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-4 0 2 4 6 ! M (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 2 4 6

Figure 5.12: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 9425 rad s

−1

and

(8)

t (s) 5 10 15 20 -3 t (s) 5 10 15 20 -0.04 t (s) 5 10 15 20 || " V|| 2 (V 2 ) #10-3 0 0.5 1 1.5 t (s) 5 10 15 20 I || 0.342 0.344 0.346 0.348 0.35

Figure 5.13: ∆V and I vs t at U = 0.1 m s

−1

, ω = 10 996 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-5 0 1 2 3 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-4 0 2 4 6 8 ! (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 2 4 6 8

(9)

t (s) 0 5 10 15 " V || (V) #10-3 -4 -2 0 2 t (s) 0 5 10 15 " V ? (V) -0.06 -0.04 -0.02 0 0.02 t (s) 0 5 10 15 || " V|| 2 (V 2 ) #10-3 0 0.5 1 1.5 2 t (s) 0 5 10 15 I || 0.325 0.33 0.335 0.34

Figure 5.15: ∆V and I vs t at U = 0.1 m s

−1

, ω = 12 566 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-5 0 1 2 3 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-4 0 2 4 6 8 ! M (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -6 0 0.5 1

Figure 5.16: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 12 566 rad s

−1

(10)

t (s) 5.5 6 6.5 7 7.5 8 -2 t (s) 5.5 6 6.5 7 7.5 8 -10 t (s) 5.5 6 6.5 7 7.5 8 || " V|| 2 (V 2 ) #10-5 0 2 4 6 8 t (s) 5.5 6 6.5 7 7.5 8 I || 0.42 0.43 0.44 0.45

Figure 5.17: ∆V and I vs t at U = 1 m s

−1

, ω = 1571 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-5 0 2 4 6 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-5 0 2 4 6 ! (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 2 4 6

(11)

t (s) 3.5 4 4.5 5 5.5 " V || (V) #10-4 -5 0 5 10 t (s) 3.5 4 4.5 5 5.5 " V ? (V) #10-4 -5 0 5 10 t (s) 3.5 4 4.5 5 5.5 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 3.5 4 4.5 5 5.5 I || 0.419 0.4195 0.42 0.4205 0.421

Figure 5.19: ∆V and I vs t at U = 1 m s

−1

, ω = 3142 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-4 0 0.5 1 1.5 ! M (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 2 4 6

Figure 5.20: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 3142 rad s

−1

and

(12)

t (s) 3 3.5 4 4.5 5 5.5 -2 t (s) 3 3.5 4 4.5 5 5.5 -0.02 t (s) 3 3.5 4 4.5 5 5.5 || " V|| 2 (V 2 ) #10-4 0 1 2 3 4 t (s) 3 3.5 4 4.5 5 5.5 I || 0.402 0.404 0.406 0.408

Figure 5.21: ∆V and I vs t at U = 1 m s

−1

, ω = 4712 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-4 0 1 2 3 ! (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 1 2 3 4

(13)

t (s) 5 5.5 6 6.5 7 7.5 " V || (V) #10-4 -5 0 5 10 t (s) 5 5.5 6 6.5 7 7.5 " V ? (V) #10-4 -5 0 5 10 t (s) 5 5.5 6 6.5 7 7.5 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 5 5.5 6 6.5 7 7.5 I || 0.3904 0.3906 0.3908 0.391

Figure 5.23: ∆V and I vs t at U = 1 m s

−1

, ω = 6283 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-5 0 2 4 6 8 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-4 0 1 2 3 4 ! M (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 0.5 1 1.5

Figure 5.24: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 6283 rad s

−1

and

(14)

t (s) 2.5 3 3.5 4 4.5 5 -3 t (s) 2.5 3 3.5 4 4.5 5 -0.04 t (s) 2.5 3 3.5 4 4.5 5 || " V|| 2 (V 2 ) #10-3 0 0.5 1 t (s) 2.5 3 3.5 4 4.5 5 I || 0.372 0.374 0.376 0.378

Figure 5.25: ∆V and I vs t at U = 1 m s

−1

, ω = 7854 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-5 0 2 4 6 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-4 0 2 4 6 ! (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 1 2 3

(15)

t (s) 2.5 3 3.5 4 4.5 5 " V || (V) #10-3 -3 -2 -1 0 1 t (s) 2.5 3 3.5 4 4.5 5 " V ? (V) -0.04 -0.02 0 0.02 t (s) 2.5 3 3.5 4 4.5 5 || " V|| 2 (V 2 ) #10-3 0 0.5 1 1.5 t (s) 2.5 3 3.5 4 4.5 5 I || 0.356 0.358 0.36 0.362 0.364

Figure 5.27: ∆V and I vs t at U = 1 m s

−1

, ω = 9425 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-5 0 1 2 3 4 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-4 0 2 4 6 ! M (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 1 2 3 4

Figure 5.28: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 9425 rad s

−1

and

(16)

t (s) 3 3.5 4 4.5 5 5.5 -3 t (s) 3 3.5 4 4.5 5 5.5 -0.04 t (s) 3 3.5 4 4.5 5 5.5 || " V|| 2 (V 2 ) #10-3 0 0.5 1 1.5 t (s) 3 3.5 4 4.5 5 5.5 I || 0.342 0.344 0.346 0.348 0.35

Figure 5.29: ∆V and I vs t at U = 1 m s

−1

, ω = 10 996 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-5 0 0.5 1 1.5 2 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-4 0 2 4 6 ! (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 2 4 6

(17)

t (s) 3.5 4 4.5 5 5.5 6 " V || (V) #10-3 -4 -2 0 2 t (s) 3.5 4 4.5 5 5.5 6 " V ? (V) -0.06 -0.04 -0.02 0 0.02 t (s) 3.5 4 4.5 5 5.5 6 || " V|| 2 (V 2 ) #10-3 0 0.5 1 1.5 2 t (s) 3.5 4 4.5 5 5.5 6 I || 0.325 0.33 0.335 0.34

Figure 5.31: ∆V and I vs t at U = 1 m s

−1

, ω = 12 566 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-5 0 1 2 3 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-4 0 2 4 6 8 ! M (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 2 4 6 8

Figure 5.32: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 12 566 rad s

−1

and

(18)

t (s) 200 400 600 800 1000 1200 -2 t (s) 200 400 600 800 1000 1200 -2 t (s) 200 400 600 800 1000 1200 || " V|| 2 (V 2 ) #10-7 0 1 2 3 t (s) 200 400 600 800 1000 1200 I || 0.4222 0.4224 0.4226 0.4228

Figure 5.33: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 3142 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-4 0 0.5 1 1.5 2 ! (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 2 4 6

(19)

t (s) 200 400 600 800 1000 1200 " V || (V) #10-4 -4 -2 0 2 4 t (s) 200 400 600 800 1000 1200 " V ? (V) #10-4 -5 0 5 10 t (s) 200 400 600 800 1000 1200 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 200 400 600 800 1000 1200 I || 0.3926 0.3928 0.393 0.3932

Figure 5.35: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-4 0 2 4 6 ! M (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 1 2 3

Figure 5.36: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

(20)

t (s) 20 40 60 80 100 120 -2 t (s) 20 40 60 80 100 120 -2 t (s) 20 40 60 80 100 120 || " V|| 2 (V 2 ) #10-7 0 1 2 3 t (s) 20 40 60 80 100 120 I || 0.4212 0.4213 0.4214 0.4215

Figure 5.37: ∆V and I vs t at U = 10

−2

m s

−1

, ω = 3142 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 2 4 6 8 10 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 2 4 6 8 10 " V ? (V) #10-4 0 0.5 1 1.5 2 ! (rad/s) 0 2 4 6 8 10 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 2 4 6

(21)

t (s) 20 40 60 80 100 120 " V || (V) #10-4 -4 -2 0 2 4 t (s) 20 40 60 80 100 120 " V ? (V) #10-4 -5 0 5 10 t (s) 20 40 60 80 100 120 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 20 40 60 80 100 120 I || 0.3923 0.3924 0.3925 0.3926

Figure 5.39: ∆V and I vs t at U = 10

−2

m s

−1

, ω = 6283 rad s

−1

and α = 4.5 %.

Figure 5.40: FFT spectral density of ∆V vs ω

M

at U = 10

−2

m s

−1

, ω = 6283 rad s

−1

(22)

t (s) 10 20 30 40 50 -2 t (s) 10 20 30 40 50 -2 t (s) 10 20 30 40 50 || " V|| 2 (V 2 ) #10-7 0 1 2 3 t (s) 10 20 30 40 50 I || 0.421 0.4211 0.4212 0.4213 0.4214

Figure 5.41: ∆V and I vs t at U = 3 × 10

−2

m s

−1

, ω = 3142 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 10 20 30 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 10 20 30 " V ? (V) #10-4 0 0.5 1 1.5 2 ! (rad/s) 0 10 20 30 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 2 4 6

(23)

t (s) 10 20 30 40 50 " V || (V) #10-4 -4 -2 0 2 4 t (s) 10 20 30 40 50 " V ? (V) #10-4 -5 0 5 10 t (s) 10 20 30 40 50 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 10 20 30 40 50 I || 0.3919 0.392 0.3921 0.3922 0.3923

Figure 5.43: ∆V and I vs t at U = 3 × 10

−2

m s

−1

, ω = 6283 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 10 20 30 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 10 20 30 " V ? (V) #10-4 0 2 4 6 ! M (rad/s) 0 10 20 30 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 1 2 3

Figure 5.44: FFT spectral density of ∆V vs ω

M

at U = 3 × 10

−2

m s

−1

, ω = 6283 rad s

−1

(24)

t (s) 5 10 15 20 -5 t (s) 5 10 15 20 -5 t (s) 5 10 15 20 || " V|| 2 (V 2 ) #10-7 0 1 2 3 4 t (s) 5 10 15 20 I || 0.419 0.4195 0.42 0.4205 0.421

Figure 5.45: ∆V and I vs t at U = 0.1 m s

−1

, ω = 3142 rad s

−1

and α = 4.5 %.

(25)

Figure 5.47: ∆V and I vs t at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and α = 4.5 %.

Figure 5.48: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and

(26)

t (s) 4 5 6 7 8 9 -5 t (s) 4 5 6 7 8 9 -5 t (s) 4 5 6 7 8 9 || " V|| 2 (V 2 ) #10-7 0 1 2 3 4 t (s) 4 5 6 7 8 9 I || 0.4185 0.419 0.4195 0.42 0.4205

Figure 5.49: ∆V and I vs t at U = 0.25 m s

−1

, ω = 3142 rad s

−1

and α = 4.5 %.

(27)

t (s) 4 5 6 7 8 9 " V || (V) #10-4 -5 0 5 t (s) 4 5 6 7 8 9 " V ? (V) #10-4 -5 0 5 10 t (s) 4 5 6 7 8 9 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 4 5 6 7 8 9 I || 0.3902 0.3904 0.3906 0.3908

Figure 5.51: ∆V and I vs t at U = 0.25 m s

−1

, ω = 6283 rad s

−1

and α = 4.5 %.

Figure 5.52: FFT spectral density of ∆V vs ω

M

at U = 0.25 m s

−1

, ω = 6283 rad s

−1

(28)

t (s) 4 5 6 7 8 -5 t (s) 4 5 6 7 8 -5 t (s) 4 5 6 7 8 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 4 5 6 7 8 I || 0.417 0.418 0.419 0.42

Figure 5.53: ∆V and I vs t at U = 0.5 m s

−1

, ω = 3142 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 100 200 300 400 500 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 100 200 300 400 500 " V ? (V) #10-4 0 0.5 1 1.5 2 ! (rad/s) 0 100 200 300 400 500 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5 2

(29)

t (s) 3 4 5 6 7 " V || (V) #10-4 -5 0 5 t (s) 3 4 5 6 7 " V ? (V) #10-4 -5 0 5 10 t (s) 3 4 5 6 7 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 3 4 5 6 7 I || 0.39 0.3902 0.3904 0.3906

Figure 5.55: ∆V and I vs t at U = 0.5 m s

−1

, ω = 6283 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 100 200 300 400 500 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 100 200 300 400 500 " V ? (V) #10-4 0 1 2 3 4 ! M (rad/s) 0 100 200 300 400 500 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 1 2 3

Figure 5.56: FFT spectral density of ∆V vs ω

M

at U = 0.5 m s

−1

, ω = 6283 rad s

−1

and

(30)

t (s) 3.5 4 4.5 5 5.5 6 -5 t (s) 3.5 4 4.5 5 5.5 6 -5 t (s) 3.5 4 4.5 5 5.5 6 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 3.5 4 4.5 5 5.5 6 I || 0.4175 0.418 0.4185 0.419 0.4195

Figure 5.57: ∆V and I vs t at U = 0.75 m s

−1

, ω = 3142 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 200 400 600 " V ? (V) #10-4 0 0.5 1 1.5 2 ! (rad/s) 0 200 400 600 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 1 2 3

(31)

t (s) 3 4 5 6 7 " V || (V) #10-4 -5 0 5 10 t (s) 3 4 5 6 7 " V ? (V) #10-4 -5 0 5 10 t (s) 3 4 5 6 7 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 3 4 5 6 7 I || 0.3898 0.39 0.3902 0.3904

Figure 5.59: ∆V and I vs t at U = 0.75 m s

−1

, ω = 6283 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 200 400 600 " V ? (V) #10-4 0 1 2 3 4 ! M (rad/s) 0 200 400 600 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 0.5 1 1.5 2

Figure 5.60: FFT spectral density of ∆V vs ω

M

at U = 0.75 m s

−1

, ω = 6283 rad s

−1

(32)

t (s) 3.5 4 4.5 5 5.5 -5 t (s) 3.5 4 4.5 5 5.5 -5 t (s) 3.5 4 4.5 5 5.5 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 3.5 4 4.5 5 5.5 I || 0.419 0.4195 0.42 0.4205 0.421

Figure 5.61: ∆V and I vs t at U = 1 m s

−1

, ω = 3142 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-4 0 0.5 1 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-4 0 0.5 1 1.5 ! (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 2 4 6

(33)

t (s) 5 5.5 6 6.5 7 7.5 " V || (V) #10-4 -5 0 5 10 t (s) 5 5.5 6 6.5 7 7.5 " V ? (V) #10-4 -5 0 5 10 t (s) 5 5.5 6 6.5 7 7.5 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 5 5.5 6 6.5 7 7.5 I || 0.3904 0.3906 0.3908 0.391

Figure 5.63: ∆V and I vs t at U = 1 m s

−1

, ω = 6283 rad s

−1

and α = 4.5 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-5 0 2 4 6 8 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-4 0 1 2 3 4 ! M (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 0.5 1 1.5

Figure 5.64: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 6283 rad s

−1

and

(34)

(35)

Chapter 6

(36)

t (s) 0 100 200 300 400 2.1 t (s) 0 100 200 300 400 2.5 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 t (s) 0 100 200 300 400 I || 0.4065 0.4066 0.4067 0.4068

Figure 6.1: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-6 0 1 2 3 4 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-5 0 0.5 1 1.5 ! (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6 8

(37)

t (s) 0 100 200 300 400 " V || (V) #10-4 2.2 2.3 2.4 2.5 t (s) 0 100 200 300 400 " V ? (V) #10-4 2.5 3 3.5 4 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1.4 1.6 1.8 2 2.2 t (s) 0 100 200 300 400 I || 0.393 0.3931 0.3932 0.3933

Figure 6.3: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-5 0 0.5 1 1.5 2 ! M (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5

Figure 6.4: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and

(38)

t (s) 0 100 200 300 400 2.3 t (s) 0 100 200 300 400 3 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1.5 2 2.5 3 t (s) 0 100 200 300 400 I || 0.3782 0.3783 0.3784 0.3785

Figure 6.5: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 7854 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-5 0 1 2 3 ! (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5 2

(39)

t (s) 0 100 200 300 400 " V || (V) #10-4 2.5 2.6 2.7 2.8 t (s) 0 100 200 300 400 " V ? (V) #10-4 3.5 4 4.5 5 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 2 2.5 3 3.5 t (s) 0 100 200 300 400 I || 0.3682 0.3683 0.3684 0.3685

Figure 6.7: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 9425 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-6 0 0.5 1 1.5 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-5 0 1 2 3 ! M (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5 2

Figure 6.8: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 9425 rad s

−1

and

(40)

t (s) 0 100 200 300 400 2.6 t (s) 0 100 200 300 400 3.5 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 2 2.5 3 3.5 t (s) 0 100 200 300 400 I || 0.3529 0.353 0.3531 0.3532 0.3533

Figure 6.9: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 10 996 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-6 0 0.5 1 1.5 2 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-5 0 1 2 3 ! (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 1 2 3

(41)

t (s) 0 100 200 300 400 " V || (V) #10-4 2.65 2.7 2.75 2.8 2.85 t (s) 0 100 200 300 400 " V ? (V) #10-4 4 4.5 5 5.5 6 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 2 2.5 3 3.5 4 t (s) 0 100 200 300 400 I || 0.3401 0.3402 0.3403 0.3404

Figure 6.11: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 12 566 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-6 0 0.5 1 1.5 2 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-5 0 1 2 3 ! M (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 1 2 3

Figure 6.12: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 12 566 rad s

−1

(42)

t (s) 2 4 6 8 10 12 1.8 t (s) 2 4 6 8 10 12 2 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 t (s) 2 4 6 8 10 12 I || 0.4064 0.4065 0.4066 0.4067

Figure 6.13: ∆V and I vs t at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-6 0 1 2 3 4 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-5 0 0.5 1 1.5 ! (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6 8

(43)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2 2.2 2.4 2.6 2.8 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2.5 3 3.5 4 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 1.4 1.6 1.8 2 2.2 t (s) 2 4 6 8 10 12 I || 0.3929 0.393 0.3931 0.3932

Figure 6.15: ∆V and I vs t at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-5 0 0.5 1 1.5 2 ! M (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5

Figure 6.16: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and

(44)

t (s) 4 6 8 10 12 14 2 t (s) 4 6 8 10 12 14 3 t (s) 4 6 8 10 12 14 || " V|| 2 (V 2 ) #10-7 1.5 2 2.5 3 t (s) 4 6 8 10 12 14 I || 0.3783 0.3784 0.3785 0.3786

Figure 6.17: ∆V and I vs t at U = 0.1 m s

−1

, ω = 7854 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-6 0 0.5 1 1.5 2 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-5 0 0.5 1 1.5 2 ! (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5

(45)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2.2 2.4 2.6 2.8 3 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 3.5 4 4.5 5 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 2 2.5 3 t (s) 2 4 6 8 10 12 I || 0.366 0.3661 0.3662 0.3663

Figure 6.19: ∆V and I vs t at U = 0.1 m s

−1

, ω = 9425 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-6 0 0.5 1 1.5 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-5 0 1 2 3 ! M (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5 2

Figure 6.20: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 9425 rad s

−1

and

(46)

t (s) 2 4 6 8 10 12 2.4 t (s) 2 4 6 8 10 12 3.5 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 2 2.5 3 3.5 t (s) 2 4 6 8 10 12 I || 0.3528 0.3529 0.353 0.3531 0.3532

Figure 6.21: ∆V and I vs t at U = 0.1 m s

−1

, ω = 10 996 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-6 0 0.5 1 1.5 2 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-5 0 1 2 3 ! (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 1 2 3

(47)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2.4 2.6 2.8 3 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 4 4.5 5 5.5 6 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 2 2.5 3 3.5 4 t (s) 2 4 6 8 10 12 I || 0.34 0.3401 0.3402 0.3403 0.3404

Figure 6.23: ∆V and I vs t at U = 0.1 m s

−1

, ω = 12 566 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 20 40 60 80 100 " V ? (V) #10-5 0 1 2 3 ! M (rad/s) 0 20 40 60 80 100 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 1 2 3

Figure 6.24: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 12 566 rad s

−1

(48)

t (s) 1 1.5 2 2.5 3 3.5 -6 t (s) 1 1.5 2 2.5 3 3.5 -6 t (s) 1 1.5 2 2.5 3 3.5 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 3 t (s) 1 1.5 2 2.5 3 3.5 I || 0.414 0.4141 0.4141 0.4142 0.4142

Figure 6.25: ∆V and I vs t at U = 1 m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

(49)

t (s) 1.5 2 2.5 3 3.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 1.5 2 2.5 3 3.5 " V ? (V) #10-4 -5 -4 -3 -2 -1 t (s) 1.5 2 2.5 3 3.5 || " V|| 2 (V 2 ) #10-7 1.5 2 2.5 3 t (s) 1.5 2 2.5 3 3.5 I || 0.3998 0.3999 0.4 0.4001

Figure 6.27: ∆V and I vs t at U = 1 m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-6 0 0.5 1 1.5 2 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-5 0 0.5 1 1.5 2 ! M (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6

Figure 6.28: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 6283 rad s

−1

and

(50)

t (s) 1.5 2 2.5 3 3.5 -6 t (s) 1.5 2 2.5 3 3.5 -6 t (s) 1.5 2 2.5 3 3.5 || " V|| 2 (V 2 ) #10-7 1.5 2 2.5 3 t (s) 1.5 2 2.5 3 3.5 I || 0.3855 0.3856 0.3857 0.3858 0.3859

Figure 6.29: ∆V and I vs t at U = 1 m s

−1

, ω = 7854 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-5 0 0.5 1 1.5 2 ! (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5

(51)

t (s) 1.5 2 2.5 3 3.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 1.5 2 2.5 3 3.5 " V ? (V) #10-4 -6 -5 -4 -3 -2 t (s) 1.5 2 2.5 3 3.5 || " V|| 2 (V 2 ) #10-7 1.5 2 2.5 3 3.5 t (s) 1.5 2 2.5 3 3.5 I || 0.3716 0.3717 0.3718 0.3719 0.372

Figure 6.31: ∆V and I vs t at U = 1 m s

−1

, ω = 9425 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-5 0 1 2 3 ! M (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5

Figure 6.32: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 9425 rad s

−1

and

(52)

t (s) 1.5 2 2.5 3 3.5 4 -5 t (s) 1.5 2 2.5 3 3.5 4 -6 t (s) 1.5 2 2.5 3 3.5 4 || " V|| 2 (V 2 ) #10-7 2 2.5 3 3.5 t (s) 1.5 2 2.5 3 3.5 4 I || 0.358 0.3581 0.3582 0.3583

Figure 6.33: ∆V and I vs t at U = 1 m s

−1

, ω = 10 996 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-5 0 1 2 3 ! (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5 2

(53)

t (s) 2.5 3 3.5 4 4.5 " V || (V) #10-4 -5 -4 -3 -2 -1 t (s) 2.5 3 3.5 4 4.5 " V ? (V) #10-4 -6 -5 -4 -3 -2 t (s) 2.5 3 3.5 4 4.5 || " V|| 2 (V 2 ) #10-7 2 2.5 3 3.5 4 t (s) 2.5 3 3.5 4 4.5 I || 0.3446 0.3447 0.3448 0.3449 0.345

Figure 6.35: ∆V and I vs t at U = 1 m s

−1

, ω = 12 566 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-5 0 1 2 3 ! M (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5 2

Figure 6.36: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 12 566 rad s

−1

and

(54)

t (s) 0 100 200 300 400 2.1 t (s) 0 100 200 300 400 2.5 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 t (s) 0 100 200 300 400 I || 0.4065 0.4066 0.4067 0.4068

Figure 6.37: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-6 0 1 2 3 4 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-5 0 0.5 1 1.5 ! (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6 8

(55)

t (s) 0 100 200 300 400 " V || (V) #10-4 2.2 2.3 2.4 2.5 t (s) 0 100 200 300 400 " V ? (V) #10-4 2.5 3 3.5 4 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1.4 1.6 1.8 2 2.2 t (s) 0 100 200 300 400 I || 0.393 0.3931 0.3932 0.3933

Figure 6.39: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-5 0 0.5 1 1.5 2 ! M (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5

Figure 6.40: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

(56)

t (s) 0 20 40 60 80 2.1 t (s) 0 20 40 60 80 2.5 t (s) 0 20 40 60 80 || " V|| 2 (V 2 ) #10-7 1.1 1.2 1.3 1.4 1.5 t (s) 0 20 40 60 80 I || 0.4065 0.4066 0.4067 0.4068

Figure 6.41: ∆V and I vs t at U = 10

−2

m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

(57)

t (s) 0 20 40 60 80 100 " V || (V) #10-4 2.2 2.3 2.4 2.5 t (s) 0 20 40 60 80 100 " V ? (V) #10-4 2.5 3 3.5 4 t (s) 0 20 40 60 80 100 || " V|| 2 (V 2 ) #10-7 1.4 1.6 1.8 2 2.2 t (s) 0 20 40 60 80 100 I || 0.3929 0.393 0.3931 0.3932

Figure 6.43: ∆V and I vs t at U = 10

−2

m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

Figure 6.44: FFT spectral density of ∆V vs ω

M

at U = 10

−2

m s

−1

, ω = 6283 rad s

−1

(58)

t (s) 0 10 20 30 2 t (s) 0 10 20 30 2 t (s) 0 10 20 30 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 t (s) 0 10 20 30 I || 0.4064 0.4065 0.4066 0.4067

Figure 6.45: ∆V and I vs t at U = 3 × 10

−2

m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 10 20 30 " V || (V) #10-6 0 1 2 3 4 !_M (rad/s) 0 10 20 30 " V ? (V) #10-5 0 0.5 1 1.5 ! (rad/s) 0 10 20 30 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6 8

(59)

t (s) 0 10 20 30 " V || (V) #10-4 2.2 2.3 2.4 2.5 2.6 t (s) 0 10 20 30 " V ? (V) #10-4 2.5 3 3.5 4 t (s) 0 10 20 30 || " V|| 2 (V 2 ) #10-7 1.4 1.6 1.8 2 2.2 t (s) 0 10 20 30 I || 0.3929 0.393 0.3931 0.3932

Figure 6.47: ∆V and I vs t at U = 3 × 10

−2

m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 10 20 30 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 10 20 30 " V ? (V) #10-5 0 0.5 1 1.5 2 ! M (rad/s) 0 10 20 30 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5

Figure 6.48: FFT spectral density of ∆V vs ω

M

at U = 3 × 10

−2

m s

−1

, ω = 6283 rad s

−1

(60)

t (s) 2 4 6 8 10 12 1.8 t (s) 2 4 6 8 10 12 2 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 t (s) 2 4 6 8 10 12 I || 0.4064 0.4065 0.4066 0.4067

Figure 6.49: ∆V and I vs t at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

(61)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2 2.2 2.4 2.6 2.8 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2.5 3 3.5 4 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 1.4 1.6 1.8 2 2.2 t (s) 2 4 6 8 10 12 I || 0.3929 0.393 0.3931 0.3932

Figure 6.51: ∆V and I vs t at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

Figure 6.52: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and

(62)

t (s) 0 2 4 6 8 1 t (s) 0 2 4 6 8 2 t (s) 0 2 4 6 8 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 1.8 t (s) 0 2 4 6 8 I || 0.4065 0.4066 0.4067 0.4068

Figure 6.53: ∆V and I vs t at U = 0.25 m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

(63)

t (s) 0 2 4 6 8 " V || (V) #10-4 1.5 2 2.5 3 3.5 t (s) 0 2 4 6 8 " V ? (V) #10-4 2.5 3 3.5 4 4.5 t (s) 0 2 4 6 8 || " V|| 2 (V 2 ) #10-7 1.4 1.6 1.8 2 2.2 t (s) 0 2 4 6 8 I || 0.3929 0.393 0.3931 0.3932

Figure 6.55: ∆V and I vs t at U = 0.25 m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 50 100 150 200 250 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 50 100 150 200 250 " V ? (V) #10-5 0 0.5 1 1.5 2 ! M (rad/s) 0 50 100 150 200 250 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1

Figure 6.56: FFT spectral density of ∆V vs ω

M

at U = 0.25 m s

−1

, ω = 6283 rad s

−1

(64)

t (s) 1 2 3 4 5 -4 t (s) 1 2 3 4 5 -4 t (s) 1 2 3 4 5 || " V|| 2 (V 2 ) #10-7 0.5 1 1.5 2 t (s) 1 2 3 4 5 I || 0.414 0.4141 0.4142 0.4143

Figure 6.57: ∆V and I vs t at U = 0.5 m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

(65)

t (s) 1 2 3 4 5 " V || (V) #10-4 -4 -3 -2 -1 t (s) 1 2 3 4 5 " V ? (V) #10-4 -5 -4 -3 -2 t (s) 1 2 3 4 5 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 1 2 3 4 5 I || 0.3998 0.3999 0.4 0.4001

Figure 6.59: ∆V and I vs t at U = 0.5 m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 100 200 300 400 500 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 100 200 300 400 500 " V ? (V) #10-5 0 0.5 1 1.5 2 ! M (rad/s) 0 100 200 300 400 500 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1

Figure 6.60: FFT spectral density of ∆V vs ω

M

at U = 0.5 m s

−1

, ω = 6283 rad s

−1

and

(66)

t (s) 1.5 2 2.5 3 3.5 4 -6 t (s) 1.5 2 2.5 3 3.5 4 -4 t (s) 1.5 2 2.5 3 3.5 4 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 1.5 2 2.5 3 3.5 4 I || 0.414 0.4141 0.4142 0.4143

Figure 6.61: ∆V and I vs t at U = 0.75 m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 200 400 600 800 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 200 400 600 800 " V ? (V) #10-5 0 0.5 1 1.5 ! (rad/s) 0 200 400 600 800 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6

(67)

t (s) 1.5 2 2.5 3 3.5 4 " V || (V) #10-4 -6 -4 -2 0 t (s) 1.5 2 2.5 3 3.5 4 " V ? (V) #10-4 -5 -4 -3 -2 -1 t (s) 1.5 2 2.5 3 3.5 4 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 1.5 2 2.5 3 3.5 4 I || 0.3998 0.3999 0.4 0.4001

Figure 6.63: ∆V and I vs t at U = 0.75 m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 200 400 600 800 " V || (V) #10-6 0 1 2 3 !_M (rad/s) 0 200 400 600 800 " V ? (V) #10-5 0 0.5 1 1.5 2 ! M (rad/s) 0 200 400 600 800 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6 8

Figure 6.64: FFT spectral density of ∆V vs ω

M

at U = 0.75 m s

−1

, ω = 6283 rad s

−1

(68)

t (s) 1 1.5 2 2.5 3 3.5 -6 t (s) 1 1.5 2 2.5 3 3.5 -6 t (s) 1 1.5 2 2.5 3 3.5 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 3 t (s) 1 1.5 2 2.5 3 3.5 I || 0.414 0.4141 0.4141 0.4142 0.4142

Figure 6.65: ∆V and I vs t at U = 1 m s

−1

, ω = 4712 rad s

−1

and α = 0.06 %.

(69)

t (s) 1.5 2 2.5 3 3.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 1.5 2 2.5 3 3.5 " V ? (V) #10-4 -5 -4 -3 -2 -1 t (s) 1.5 2 2.5 3 3.5 || " V|| 2 (V 2 ) #10-7 1.5 2 2.5 3 t (s) 1.5 2 2.5 3 3.5 I || 0.3998 0.3999 0.4 0.4001

Figure 6.67: ∆V and I vs t at U = 1 m s

−1

, ω = 6283 rad s

−1

and α = 0.06 %.

!_M (rad/s) 0 200 400 600 800 1000 " V || (V) #10-6 0 0.5 1 1.5 2 !_M (rad/s) 0 200 400 600 800 1000 " V ? (V) #10-5 0 0.5 1 1.5 2 ! M (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6

Figure 6.68: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 6283 rad s

−1

and

(70)