For α = 0.22%

(1)

Chapter 7

(2)

t (s) 100 150 200 250 300 350 " V || (V) #10-4 2 2.2 2.4 2.6 t (s) 100 150 200 250 300 350 " V ? (V) #10-4 2 2.5 3 3.5 t (s) 100 150 200 250 300 350 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 t (s) 100 150 200 250 300 350 I || 0.4111 0.4112 0.4113 0.4114

Figure 7.1: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-5 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

Figure 7.2: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and

(3)

t (s) 100 150 200 250 300 350 " V || (V) #10-4 2.2 2.4 2.6 2.8 t (s) 100 150 200 250 300 350 " V ? (V) #10-4 2.5 3 3.5 4 4.5 t (s) 100 150 200 250 300 350 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 100 150 200 250 300 350 I || 0.3986 0.3987 0.3988 0.3989

Figure 7.3: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-5 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 4 ! 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 7.4: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and

(4)

t (s) 100 150 200 250 300 350 " V || (V) #10-4 2.2 2.4 2.6 2.8 t (s) 100 150 200 250 300 350 " V ? (V) #10-4 2 3 4 5 t (s) 100 150 200 250 300 350 || " V|| 2 (V 2 ) #10-7 1.5 2 2.5 3 t (s) 100 150 200 250 300 350 I || 0.3834 0.3834 0.3835 0.3835 0.3836

Figure 7.5: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 7854 rad s

−1

and α = 0.22 %.

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

Figure 7.6: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 7854 rad s

−1

and

(5)

t (s) 100 150 200 250 300 350 " V || (V) #10-4 2.5 2.6 2.7 2.8 2.9 t (s) 100 150 200 250 300 350 " V ? (V) #10-4 3 4 5 6 t (s) 100 150 200 250 300 350 || " V|| 2 (V 2 ) #10-7 1.5 2 2.5 3 3.5 t (s) 100 150 200 250 300 350 I || 0.3707 0.3707 0.3707 0.3708 0.3708

Figure 7.7: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 9425 rad s

−1

and α = 0.22 %.

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

Figure 7.8: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 9425 rad s

−1

and

(6)

t (s) 100 150 200 250 300 350 " V || (V) #10-4 2.4 2.6 2.8 3 t (s) 100 150 200 250 300 350 " V ? (V) #10-4 3 4 5 6 t (s) 100 150 200 250 300 350 || " V|| 2 (V 2 ) #10-7 1 2 3 4 t (s) 100 150 200 250 300 350 I || 0.3566 0.3567 0.3568 0.3569

Figure 7.9: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 10 996 rad s

−1

and α = 0.22 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-6 0 2 4 6 8 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-5 0 2 4 6 8 ! M (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

Figure 7.10: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 10 996 rad s

−1

(7)

t (s) 100 150 200 250 300 350 " V || (V) #10-4 2.6 2.7 2.8 2.9 3 t (s) 100 150 200 250 300 350 " V ? (V) #10-4 3 4 5 6 7 t (s) 100 150 200 250 300 350 || " V|| 2 (V 2 ) #10-7 2 3 4 5 t (s) 100 150 200 250 300 350 I || 0.3438 0.3439 0.344 0.3441

Figure 7.11: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 12 566 rad s

−1

and α = 0.22 %.

!_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 2 4 6 8 ! M (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 8

Figure 7.12: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 12 566 rad s

−1

(8)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 1.5 2 2.5 3 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2 2.5 3 3.5 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 || 0.4111 0.4111 0.4111 0.4111 0.4112

Figure 7.13: ∆V and I vs t at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

!_M (rad/s) 0 20 40 60 80 100 " V || (V) #10-5 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

Figure 7.14: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and

(9)

t (s) 4 6 8 10 12 14 " V || (V) #10-4 2 2.5 3 t (s) 4 6 8 10 12 14 " V ? (V) #10-4 2.5 3 3.5 4 4.5 t (s) 4 6 8 10 12 14 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 4 6 8 10 12 14 I || 0.398 0.3982 0.3984 0.3986

Figure 7.15: ∆V and I vs t at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

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

Figure 7.16: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and

(10)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2 2.5 3 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2 3 4 5 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 1.5 2 2.5 3 t (s) 2 4 6 8 10 12 I || 0.3835 0.3835 0.3836 0.3836

Figure 7.17: ∆V and I vs t at U = 0.1 m s

−1

, ω = 7854 rad s

−1

and α = 0.22 %.

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

Figure 7.18: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 7854 rad s

−1

and

(11)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2 2.5 3 3.5 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 3 4 5 6 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 1.5 2 2.5 3 3.5 t (s) 2 4 6 8 10 12 I || 0.37 0.3702 0.3704 0.3706 0.3708

Figure 7.19: ∆V and I vs t at U = 0.1 m s

−1

, ω = 9425 rad s

−1

and α = 0.22 %.

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

Figure 7.20: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 9425 rad s

−1

and

(12)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2.4 2.6 2.8 3 3.2 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 3 4 5 6 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 1 2 3 4 t (s) 2 4 6 8 10 12 I || 0.3565 0.3566 0.3567 0.3568

Figure 7.21: ∆V and I vs t at U = 0.1 m s

−1

, ω = 10 996 rad s

−1

and α = 0.22 %.

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

Figure 7.22: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 10 996 rad s

−1

(13)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2.4 2.6 2.8 3 3.2 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 3 4 5 6 7 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 2 3 4 5 t (s) 2 4 6 8 10 12 I || 0.3436 0.3438 0.344 0.3442

Figure 7.23: ∆V and I vs t at U = 0.1 m s

−1

, ω = 12 566 rad s

−1

and α = 0.22 %.

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

Figure 7.24: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 12 566 rad s

−1

(14)

t (s) 1.5 2 2.5 3 3.5 4 " V || (V) #10-4 -6 -4 -2 0 2 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|| 2 (V 2 ) #10-7 1 1.5 2 2.5 3 t (s) 1.5 2 2.5 3 3.5 4 I || 0.4148 0.4148 0.4149 0.4149

Figure 7.25: ∆V and I vs t at U = 1 m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

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

Figure 7.26: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 4712 rad s

−1

and

(15)

t (s) 4.5 5 5.5 6 6.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 4.5 5 5.5 6 6.5 " V ? (V) #10-4 -6 -4 -2 0 t (s) 4.5 5 5.5 6 6.5 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 3 t (s) 4.5 5 5.5 6 6.5 I || 0.4007 0.4007 0.4007 0.4007 0.4007

Figure 7.27: ∆V and I vs t at U = 1 m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

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

Figure 7.28: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 6283 rad s

−1

and

(16)

t (s) 1 1.5 2 2.5 3 3.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 1 1.5 2 2.5 3 3.5 " V ? (V) #10-4 -6 -4 -2 0 t (s) 1 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 1.5 2 2.5 3 3.5 I || 0.3863 0.3864 0.3864 0.3865 0.3865

Figure 7.29: ∆V and I vs t at U = 1 m s

−1

, ω = 7854 rad s

−1

and α = 0.22 %.

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

Figure 7.30: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 7854 rad s

−1

and

(17)

t (s) 2.5 3 3.5 4 4.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 2.5 3 3.5 4 4.5 " V ? (V) #10-4 -8 -6 -4 -2 0 t (s) 2.5 3 3.5 4 4.5 || " V|| 2 (V 2 ) #10-7 1 2 3 4 t (s) 2.5 3 3.5 4 4.5 I || 0.3722 0.3723 0.3723 0.3724 0.3724

Figure 7.31: ∆V and I vs t at U = 1 m s

−1

, ω = 9425 rad s

−1

and α = 0.22 %.

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

Figure 7.32: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 9425 rad s

−1

and

(18)

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 ? (V) #10-4 -8 -6 -4 -2 t (s) 1.5 2 2.5 3 3.5 || " V|| 2 (V 2 ) #10-7 1 2 3 4 5 t (s) 1.5 2 2.5 3 3.5 I || 0.3584 0.3585 0.3586 0.3587

Figure 7.33: ∆V and I vs t at U = 1 m s

−1

, ω = 10 996 rad s

−1

and α = 0.22 %.

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

Figure 7.34: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 10 996 rad s

−1

and

(19)

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 ? (V) #10-4 -8 -6 -4 -2 t (s) 1.5 2 2.5 3 3.5 || " V|| 2 (V 2 ) #10-7 2 3 4 5 t (s) 1.5 2 2.5 3 3.5 I || 0.3451 0.3452 0.3453 0.3454

Figure 7.35: ∆V and I vs t at U = 1 m s

−1

, ω = 12 566 rad s

−1

and α = 0.22 %.

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

Figure 7.36: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 12 566 rad s

−1

and

(20)

t (s) 100 150 200 250 300 350 " V || (V) #10-4 2 2.2 2.4 2.6 t (s) 100 150 200 250 300 350 " V ? (V) #10-4 2 2.5 3 3.5 t (s) 100 150 200 250 300 350 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 t (s) 100 150 200 250 300 350 I || 0.4111 0.4112 0.4113 0.4114

Figure 7.37: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-5 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

Figure 7.38: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

(21)

t (s) 100 150 200 250 300 350 " V || (V) #10-4 2.2 2.4 2.6 2.8 t (s) 100 150 200 250 300 350 " V ? (V) #10-4 2.5 3 3.5 4 4.5 t (s) 100 150 200 250 300 350 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 100 150 200 250 300 350 I || 0.3986 0.3987 0.3988 0.3989

Figure 7.39: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-5 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 4 ! 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 7.40: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

(22)

t (s) 0 20 40 60 80 100 " V || (V) #10-4 1.8 2 2.2 2.4 2.6 t (s) 0 20 40 60 80 100 " V ? (V) #10-4 2 2.5 3 3.5 t (s) 0 20 40 60 80 100 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 t (s) 0 20 40 60 80 100 I || 0.4111 0.4111 0.4112 0.4112

Figure 7.41: ∆V and I vs t at U = 10

−2

m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

Figure 7.42: FFT spectral density of ∆V vs ω

M

at U = 10

−2

m s

−1

, ω = 4712 rad s

−1

(23)

t (s) 0 20 40 60 80 100 " V || (V) #10-4 2 2.2 2.4 2.6 2.8 t (s) 0 20 40 60 80 100 " V ? (V) #10-4 2.5 3 3.5 4 4.5 t (s) 0 20 40 60 80 100 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 0 20 40 60 80 100 I || 0.3985 0.3986 0.3986 0.3987

Figure 7.43: ∆V and I vs t at U = 10

−2

m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

Figure 7.44: FFT spectral density of ∆V vs ω

M

at U = 10

−2

m s

−1

, ω = 6283 rad s

−1

(24)

t (s) 5 10 15 20 25 30 " V || (V) #10-4 2 2.2 2.4 2.6 t (s) 5 10 15 20 25 30 " V ? (V) #10-4 2 2.5 3 3.5 t (s) 5 10 15 20 25 30 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 t (s) 5 10 15 20 25 30 I || 0.4111 0.4111 0.4111 0.4111 0.4111

Figure 7.45: ∆V and I vs t at U = 3 × 10

−2

m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

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

Figure 7.46: FFT spectral density of ∆V vs ω

M

at U = 3 × 10

−2

m s

−1

, ω = 4712 rad s

−1

(25)

t (s) 5 10 15 20 25 30 " V || (V) #10-4 2 2.2 2.4 2.6 2.8 t (s) 5 10 15 20 25 30 " V ? (V) #10-4 2.5 3 3.5 4 4.5 t (s) 5 10 15 20 25 30 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 5 10 15 20 25 30 I || 0.3985 0.3986 0.3986 0.3987

Figure 7.47: ∆V and I vs t at U = 3 × 10

−2

m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

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

Figure 7.48: FFT spectral density of ∆V vs ω

M

at U = 3 × 10

−2

m s

−1

, ω = 6283 rad s

−1

(26)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 1.5 2 2.5 3 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2 2.5 3 3.5 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 || 0.4111 0.4111 0.4111 0.4111 0.4112

Figure 7.49: ∆V and I vs t at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

Figure 7.50: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and

(27)

t (s) 4 6 8 10 12 14 " V || (V) #10-4 2 2.5 3 t (s) 4 6 8 10 12 14 " V ? (V) #10-4 2.5 3 3.5 4 4.5 t (s) 4 6 8 10 12 14 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 4 6 8 10 12 14 I || 0.398 0.3982 0.3984 0.3986

Figure 7.51: ∆V and I vs t at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

Figure 7.52: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and

(28)

t (s) 2 3 4 5 6 " V || (V) #10-4 1 2 3 4 t (s) 2 3 4 5 6 " V ? (V) #10-4 2 2.5 3 3.5 4 t (s) 2 3 4 5 6 || " V|| 2 (V 2 ) #10-7 0.5 1 1.5 2 t (s) 2 3 4 5 6 I || 0.4111 0.4111 0.4112 0.4112 0.4112

Figure 7.53: ∆V and I vs t at U = 0.25 m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

!_M (rad/s) 0 50 100 150 200 250 " V || (V) #10-5 0 0.5 1 1.5 !_M (rad/s) 0 50 100 150 200 250 " V ? (V) #10-5 0 1 2 3 ! M (rad/s) 0 50 100 150 200 250 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6 8

Figure 7.54: FFT spectral density of ∆V vs ω

M

at U = 0.25 m s

−1

, ω = 4712 rad s

−1

(29)

t (s) 2 3 4 5 6 7 " V || (V) #10-4 1.5 2 2.5 3 3.5 t (s) 2 3 4 5 6 7 " V ? (V) #10-4 2 3 4 5 t (s) 2 3 4 5 6 7 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 2 3 4 5 6 7 I || 0.3979 0.398 0.3981 0.3982 0.3983

Figure 7.55: ∆V and I vs t at U = 0.25 m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

Figure 7.56: FFT spectral density of ∆V vs ω

M

at U = 0.25 m s

−1

, ω = 6283 rad s

−1

(30)

t (s) 1.5 2 2.5 3 3.5 4 " V || (V) #10-4 -4 -3 -2 -1 0 t (s) 1.5 2 2.5 3 3.5 4 " V ? (V) #10-4 -4 -3 -2 -1 t (s) 1.5 2 2.5 3 3.5 4 || " V|| 2 (V 2 ) #10-7 0.5 1 1.5 2 t (s) 1.5 2 2.5 3 3.5 4 I || 0.4150 0.415 0.4151

Figure 7.57: ∆V and I vs t at U = 0.5 m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

Figure 7.58: FFT spectral density of ∆V vs ω

M

at U = 0.5 m s

−1

, ω = 4712 rad s

−1

and

(31)

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 -1 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 || 0.4006 0.4006 0.4007 0.4007

Figure 7.59: ∆V and I vs t at U = 0.5 m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

!_M (rad/s) 0 100 200 300 400 500 " V || (V) #10-5 0 0.5 1 1.5 !_M (rad/s) 0 100 200 300 400 500 " V ? (V) #10-5 0 1 2 3 4 ! M (rad/s) 0 100 200 300 400 500 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -8 0 0.5 1 1.5

Figure 7.60: FFT spectral density of ∆V vs ω

M

at U = 0.5 m s

−1

, ω = 6283 rad s

−1

and

(32)

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 || 0.4148 0.4149 0.4149 0.415

Figure 7.61: ∆V and I vs t at U = 0.75 m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

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

Figure 7.62: FFT spectral density of ∆V vs ω

M

at U = 0.75 m s

−1

, ω = 4712 rad s

−1

(33)

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 || 0.4007 0.4007 0.4007 0.4007 0.4007

Figure 7.63: ∆V and I vs t at U = 0.75 m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

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

Figure 7.64: FFT spectral density of ∆V vs ω

M

at U = 0.75 m s

−1

, ω = 6283 rad s

−1

(34)

t (s) 1.5 2 2.5 3 3.5 4 " V || (V) #10-4 -6 -4 -2 0 2 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|| 2 (V 2 ) #10-7 1 1.5 2 2.5 3 t (s) 1.5 2 2.5 3 3.5 4 I || 0.4148 0.4148 0.4149 0.4149

Figure 7.65: ∆V and I vs t at U = 1 m s

−1

, ω = 4712 rad s

−1

and α = 0.22 %.

Figure 7.66: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 4712 rad s

−1

and

(35)

t (s) 4.5 5 5.5 6 6.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 4.5 5 5.5 6 6.5 " V ? (V) #10-4 -6 -4 -2 0 t (s) 4.5 5 5.5 6 6.5 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 3 t (s) 4.5 5 5.5 6 6.5 I || 0.4007 0.4007 0.4007 0.4007 0.4007

Figure 7.67: ∆V and I vs t at U = 1 m s

−1

, ω = 6283 rad s

−1

and α = 0.22 %.

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

Figure 7.68: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 6283 rad s

−1

and

(36)

(37)

Chapter 8

(38)

t (s) 0 100 200 300 400 " V || (V) #10-4 1.5 2 2.5 3 t (s) 0 100 200 300 400 " V ? (V) #10-4 2 2.5 3 3.5 4 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 1.8 t (s) 0 100 200 300 400 I || 0.4135 0.4136 0.4137 0.4138

Figure 8.1: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

!_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 ? (V) #10-5 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 -8 0 0.5 1 1.5 2

Figure 8.2: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and

(39)

t (s) 0 100 200 300 400 " V || (V) #10-4 2 2.5 3 t (s) 0 100 200 300 400 " V ? (V) #10-4 2 3 4 5 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 0 100 200 300 400 I || 0.3947 0.3947 0.3948 0.3948 0.3949

Figure 8.3: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

Figure 8.4: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and

(40)

t (s) 0 100 200 300 400 " V || (V) #10-4 2.2 2.4 2.6 2.8 3 t (s) 0 100 200 300 400 " V ? (V) #10-4 2 3 4 5 6 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 2 3 4 t (s) 0 100 200 300 400 I || 0.3848 0.3849 0.3849 0.385 0.3850

Figure 8.5: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 7854 rad s

−1

and α = 0.54 %.

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

Figure 8.6: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 7854 rad s

−1

and

(41)

t (s) 0 100 200 300 400 " V || (V) #10-4 2 2.5 3 3.5 t (s) 0 100 200 300 400 " V ? (V) #10-4 2 3 4 5 6 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 2 3 4 t (s) 0 100 200 300 400 I || 0.3669 0.367 0.3671 0.3672

Figure 8.7: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 9425 rad s

−1

and α = 0.54 %.

!_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 ? (V) #10-4 0 0.5 1 1.5 ! M (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 0.5 1

Figure 8.8: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 9425 rad s

−1

and

(42)

t (s) 0 100 200 300 400 " V || (V) #10-4 2.4 2.6 2.8 3 3.2 t (s) 0 100 200 300 400 " V ? (V) #10-4 2 4 6 8 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 2 3 4 5 t (s) 0 100 200 300 400 I || 0.3569 0.357 0.3571 0.3572 0.3573

Figure 8.9: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 10 996 rad s

−1

and α = 0.54 %.

!_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 ? (V) #10-4 0 0.5 1 1.5 ! M (rad/s) 0 0.2 0.4 0.6 0.8 1 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 0.5 1 1.5

Figure 8.10: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 10 996 rad s

−1

(43)

t (s) 0 100 200 300 400 " V || (V) #10-4 2.4 2.6 2.8 3 3.2 t (s) 0 100 200 300 400 " V ? (V) #10-4 2 4 6 8 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 0 100 200 300 400 I || 0.3405 0.3406 0.3407 0.3408

Figure 8.11: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 12 566 rad s

−1

and α = 0.54 %.

!_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 ? (V) #10-4 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 -7 0 0.5 1 1.5

Figure 8.12: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 12 566 rad s

−1

(44)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 1.5 2 2.5 3 3.5 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2 3 4 5 6 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 1 2 3 4 t (s) 2 4 6 8 10 12 I || 0.4134 0.4135 0.4136 0.4137 0.4138

Figure 8.13: ∆V and I vs t at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

!_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) #10-5 0 2 4 6 ! 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 8.14: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and

(45)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 1.5 2 2.5 3 3.5 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2 4 6 8 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 2 4 6 8 10 12 I || 0.3946 0.3946 0.3947 0.3947

Figure 8.15: ∆V and I vs t at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

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

Figure 8.16: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and

(46)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2 2.5 3 3.5 4 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2 4 6 8 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 2 4 6 8 10 12 I || 0.3844 0.3846 0.3848 0.385

Figure 8.17: ∆V and I vs t at U = 0.1 m s

−1

, ω = 7854 rad s

−1

and α = 0.54 %.

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

Figure 8.18: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 7854 rad s

−1

and

(47)

t (s) 0 5 10 15 " V || (V) #10-4 2 2.5 3 3.5 4 t (s) 0 5 10 15 " V ? (V) #10-4 2 4 6 8 10 t (s) 0 5 10 15 || " V|| 2 (V 2 ) #10-6 0 0.5 1 t (s) 0 5 10 15 I || 0.3669 0.367 0.3670 0.3671 0.3671

Figure 8.19: ∆V and I vs t at U = 0.1 m s

−1

, ω = 9425 rad s

−1

and α = 0.54 %.

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

Figure 8.20: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 9425 rad s

−1

and

(48)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2 2.5 3 3.5 4 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2 4 6 8 10 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-6 0 0.5 1 1.5 t (s) 2 4 6 8 10 12 I || 0.3564 0.3566 0.3568 0.357 0.3572

Figure 8.21: ∆V and I vs t at U = 0.1 m s

−1

, ω = 10 996 rad s

−1

and α = 0.54 %.

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

Figure 8.22: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 10 996 rad s

−1

(49)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 2 3 4 5 t (s) 2 4 6 8 10 12 " V ? (V) #10-3 0 0.5 1 1.5 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-6 0 0.5 1 1.5 t (s) 2 4 6 8 10 12 I || 0.3404 0.3405 0.3406 0.3407 0.3408

Figure 8.23: ∆V and I vs t at U = 0.1 m s

−1

, ω = 12 566 rad s

−1

and α = 0.54 %.

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

Figure 8.24: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 12 566 rad s

−1

(50)

t (s) 6 6.5 7 7.5 8 " V || (V) #10-4 -6 -4 -2 0 2 t (s) 6 6.5 7 7.5 8 " V ? (V) #10-4 -8 -6 -4 -2 0 t (s) 6 6.5 7 7.5 8 || " V|| 2 (V 2 ) #10-7 1 2 3 4 5 t (s) 6 6.5 7 7.5 8 I || 0.4188 0.4189 0.419 0.4191

Figure 8.25: ∆V and I vs t at U = 1 m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

!_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) #10-5 0 2 4 6 ! 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 8.26: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 4712 rad s

−1

and

(51)

t (s) 2 2.5 3 3.5 4 4.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 2 2.5 3 3.5 4 4.5 " V ? (V) #10-4 -8 -6 -4 -2 0 t (s) 2 2.5 3 3.5 4 4.5 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 2 2.5 3 3.5 4 4.5 I || 0.404 0.4041 0.4042 0.4043 0.4044

Figure 8.27: ∆V and I vs t at U = 1 m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

Figure 8.28: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 6283 rad s

−1

and

(52)

t (s) 2.5 3 3.5 4 4.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 2.5 3 3.5 4 4.5 " V ? (V) #10-3 -1 -0.5 0 t (s) 2.5 3 3.5 4 4.5 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 2.5 3 3.5 4 4.5 I || 0.3892 0.3894 0.3896 0.3898 0.39

Figure 8.29: ∆V and I vs t at U = 1 m s

−1

, ω = 7854 rad s

−1

and α = 0.54 %.

!_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 0.5 1 ! 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 8.30: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 7854 rad s

−1

and

(53)

t (s) 5.5 6 6.5 7 7.5 8 " V || (V) #10-4 -6 -4 -2 0 t (s) 5.5 6 6.5 7 7.5 8 " V ? (V) #10-3 -1 -0.5 0 t (s) 5.5 6 6.5 7 7.5 8 || " V|| 2 (V 2 ) #10-6 0 0.5 1 t (s) 5.5 6 6.5 7 7.5 8 I || 0.3748 0.375 0.3752 0.3754 0.3756

Figure 8.31: ∆V and I vs t at U = 1 m s

−1

, ω = 9425 rad s

−1

and α = 0.54 %.

Figure 8.32: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 9425 rad s

−1

and

(54)

t (s) 2 2.5 3 3.5 4 " V || (V) #10-4 -6 -4 -2 0 t (s) 2 2.5 3 3.5 4 " V ? (V) #10-3 -1 -0.5 0 t (s) 2 2.5 3 3.5 4 || " V|| 2 (V 2 ) #10-6 0 0.5 1 1.5 t (s) 2 2.5 3 3.5 4 I || 0.3606 0.3608 0.361 0.3612 0.3614

Figure 8.33: ∆V and I vs t at U = 1 m s

−1

, ω = 10 996 rad s

−1

and α = 0.54 %.

!_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 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 8.34: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 10 996 rad s

−1

and

(55)

t (s) 2 2.5 3 3.5 4 4.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 2 2.5 3 3.5 4 4.5 " V ? (V) #10-3 -1.5 -1 -0.5 0 t (s) 2 2.5 3 3.5 4 4.5 || " V|| 2 (V 2 ) #10-6 0 0.5 1 1.5 t (s) 2 2.5 3 3.5 4 4.5 I || 0.3468 0.347 0.3472 0.3474 0.3476

Figure 8.35: ∆V and I vs t at U = 1 m s

−1

, ω = 12 566 rad s

−1

and α = 0.54 %.

Figure 8.36: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 12 566 rad s

−1

and

(56)

t (s) 0 100 200 300 400 " V || (V) #10-4 1.5 2 2.5 3 t (s) 0 100 200 300 400 " V ? (V) #10-4 2 2.5 3 3.5 4 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 1.2 1.4 1.6 1.8 t (s) 0 100 200 300 400 I || 0.4135 0.4136 0.4137 0.4138

Figure 8.37: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

!_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 ? (V) #10-5 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 -8 0 0.5 1 1.5 2

Figure 8.38: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

(57)

t (s) 0 100 200 300 400 " V || (V) #10-4 2 2.5 3 t (s) 0 100 200 300 400 " V ? (V) #10-4 2 3 4 5 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 t (s) 0 100 200 300 400 I || 0.3947 0.3947 0.3948 0.3948 0.3949

Figure 8.39: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

Figure 8.40: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

(58)

t (s) 0 20 40 60 80 100 " V || (V) #10-4 1.5 2 2.5 3 t (s) 0 20 40 60 80 100 " V ? (V) #10-4 2 3 4 5 6 t (s) 0 20 40 60 80 100 || " V|| 2 (V 2 ) #10-7 1 2 3 4 t (s) 0 20 40 60 80 100 I || 0.4136 0.4136 0.4137 0.4137 0.4137

Figure 8.41: ∆V and I vs t at U = 10

−2

m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

Figure 8.42: FFT spectral density of ∆V vs ω

M

at U = 10

−2

m s

−1

, ω = 4712 rad s

−1

(59)

t (s) 0 20 40 60 80 100 " V || (V) #10-4 2 2.5 3 3.5 t (s) 0 20 40 60 80 100 " V ? (V) #10-4 2 4 6 8 t (s) 0 20 40 60 80 100 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 0 20 40 60 80 100 I || 0.3947 0.3947 0.3948 0.3948 0.3949

Figure 8.43: ∆V and I vs t at U = 10

−2

m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

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

Figure 8.44: FFT spectral density of ∆V vs ω

M

at U = 10

−2

m s

−1

, ω = 6283 rad s

−1

(60)

t (s) 0 10 20 30 40 " V || (V) #10-4 1.5 2 2.5 3 t (s) 0 10 20 30 40 " V ? (V) #10-4 2 3 4 5 6 t (s) 0 10 20 30 40 || " V|| 2 (V 2 ) #10-7 1 2 3 4 t (s) 0 10 20 30 40 I || 0.4135 0.4136 0.4136 0.4137 0.4137

Figure 8.45: ∆V and I vs t at U = 3 × 10

−2

m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

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

Figure 8.46: FFT spectral density of ∆V vs ω

M

at U = 3 × 10

−2

m s

−1

, ω = 4712 rad s

−1

(61)

t (s) 0 10 20 30 40 " V || (V) #10-4 2 2.5 3 3.5 t (s) 0 10 20 30 40 " V ? (V) #10-4 2 4 6 8 t (s) 0 10 20 30 40 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 0 10 20 30 40 I || 0.3946 0.3947 0.3947 0.3948

Figure 8.47: ∆V and I vs t at U = 3 × 10

−2

m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

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

Figure 8.48: FFT spectral density of ∆V vs ω

M

at U = 3 × 10

−2

m s

−1

, ω = 6283 rad s

−1

(62)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 1.5 2 2.5 3 3.5 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2 3 4 5 6 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 1 2 3 4 t (s) 2 4 6 8 10 12 I || 0.4134 0.4135 0.4136 0.4137 0.4138

Figure 8.49: ∆V and I vs t at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

Figure 8.50: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and

(63)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 1.5 2 2.5 3 3.5 t (s) 2 4 6 8 10 12 " V ? (V) #10-4 2 4 6 8 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 2 4 6 8 10 12 I || 0.3946 0.3946 0.3947 0.3947

Figure 8.51: ∆V and I vs t at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

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

Figure 8.52: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and

(64)

t (s) 2 3 4 5 6 7 " V || (V) #10-4 1 2 3 4 t (s) 2 3 4 5 6 7 " V ? (V) #10-4 0 2 4 6 8 t (s) 2 3 4 5 6 7 || " V|| 2 (V 2 ) #10-7 0 1 2 3 4 t (s) 2 3 4 5 6 7 I || 0.4132 0.4134 0.4136 0.4138

Figure 8.53: ∆V and I vs t at U = 0.25 m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

Figure 8.54: FFT spectral density of ∆V vs ω

M

at U = 0.25 m s

−1

, ω = 4712 rad s

−1

(65)

t (s) 2 3 4 5 6 7 " V || (V) #10-4 1 2 3 4 t (s) 2 3 4 5 6 7 " V ? (V) #10-4 0 2 4 6 8 t (s) 2 3 4 5 6 7 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 2 3 4 5 6 7 I || 0.3944 0.3945 0.3946 0.3947 0.3948

Figure 8.55: ∆V and I vs t at U = 0.25 m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

Figure 8.56: FFT spectral density of ∆V vs ω

M

at U = 0.25 m s

−1

, ω = 6283 rad s

−1

(66)

t (s) 1 2 3 4 5 " V || (V) #10-4 -6 -4 -2 0 t (s) 1 2 3 4 5 " V ? (V) #10-4 -8 -6 -4 -2 0 t (s) 1 2 3 4 5 || " V|| 2 (V 2 ) #10-7 0 1 2 3 4 t (s) 1 2 3 4 5 I || 0.4189 0.4189 0.419 0.4190 0.4191

Figure 8.57: ∆V and I vs t at U = 0.5 m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

!_M (rad/s) 0 100 200 300 400 500 " V || (V) #10-5 0 1 2 3 !_M (rad/s) 0 100 200 300 400 500 " V ? (V) #10-5 0 2 4 6 ! M (rad/s) 0 100 200 300 400 500 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -9 0 2 4 6

Figure 8.58: FFT spectral density of ∆V vs ω

M

at U = 0.5 m s

−1

, ω = 4712 rad s

−1

and

(67)

t (s) 1 2 3 4 5 " V || (V) #10-4 -5 -4 -3 -2 -1 t (s) 1 2 3 4 5 " V ? (V) #10-4 -8 -6 -4 -2 0 t (s) 1 2 3 4 5 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 1 2 3 4 5 I || 0.4042 0.4043 0.4044 0.4045

Figure 8.59: ∆V and I vs t at U = 0.5 m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

!_M (rad/s) 0 100 200 300 400 500 " V || (V) #10-5 0 1 2 3 !_M (rad/s) 0 100 200 300 400 500 " V ? (V) #10-5 0 2 4 6 8 ! M (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

Figure 8.60: FFT spectral density of ∆V vs ω

M

at U = 0.5 m s

−1

, ω = 6283 rad s

−1

and

(68)

t (s) 2 2.5 3 3.5 4 4.5 " V || (V) #10-4 -6 -4 -2 0 t (s) 2 2.5 3 3.5 4 4.5 " V ? (V) #10-4 -8 -6 -4 -2 0 t (s) 2 2.5 3 3.5 4 4.5 || " V|| 2 (V 2 ) #10-7 0 2 4 6 t (s) 2 2.5 3 3.5 4 4.5 I || 0.4188 0.4189 0.419 0.4191

Figure 8.61: ∆V and I vs t at U = 0.75 m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

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

Figure 8.62: FFT spectral density of ∆V vs ω

M

at U = 0.75 m s

−1

, ω = 4712 rad s

−1

(69)

Figure 8.63: ∆V and I vs t at U = 0.75 m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

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

Figure 8.64: FFT spectral density of ∆V vs ω

M

at U = 0.75 m s

−1

, ω = 6283 rad s

−1

(70)

t (s) 6 6.5 7 7.5 8 " V || (V) #10-4 -6 -4 -2 0 2 t (s) 6 6.5 7 7.5 8 " V ? (V) #10-4 -8 -6 -4 -2 0 t (s) 6 6.5 7 7.5 8 || " V|| 2 (V 2 ) #10-7 1 2 3 4 5 t (s) 6 6.5 7 7.5 8 I || 0.4188 0.4189 0.419 0.4191

Figure 8.65: ∆V and I vs t at U = 1 m s

−1

, ω = 4712 rad s

−1

and α = 0.54 %.

Figure 8.66: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 4712 rad s

−1

and

(71)

Figure 8.67: ∆V and I vs t at U = 1 m s

−1

, ω = 6283 rad s

−1

and α = 0.54 %.

Figure 8.68: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 6283 rad s

−1

and

(72)

(73)

Chapter 9

(74)

t (s) 0 100 200 300 400 " V || (V) #10-4 1.5 2 2.5 3 t (s) 0 100 200 300 400 " V ? (V) #10-4 1 2 3 4 5 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 1.5 2 t (s) 0 100 200 300 400 I || 0.4102 0.4104 0.4106 0.4108

Figure 9.1: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and α = 1.62 %.

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

Figure 9.2: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and

(75)

t (s) 0 100 200 300 400 " V || (V) #10-4 1.5 2 2.5 3 3.5 t (s) 0 100 200 300 400 " V ? (V) #10-4 0 2 4 6 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 3 t (s) 0 100 200 300 400 I || 0.3928 0.3928 0.3929 0.3929 0.393

Figure 9.3: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and α = 1.62 %.

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

Figure 9.4: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and

(76)

t (s) 0 100 200 300 400 " V || (V) #10-4 1 2 3 4 t (s) 0 100 200 300 400 " V ? (V) #10-4 0 2 4 6 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 2 3 4 t (s) 0 100 200 300 400 I || 0.3816 0.3818 0.382 0.3822

Figure 9.5: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 7854 rad s

−1

and α = 1.62 %.

!_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V || (V) #10-5 0 2 4 6 8 !_M (rad/s) 0 0.2 0.4 0.6 0.8 1 " V ? (V) #10-4 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 -7 0 0.5 1

Figure 9.6: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 7854 rad s

−1

and

(77)

t (s) 0 100 200 300 400 " V || (V) #10-4 1 2 3 4 t (s) 0 100 200 300 400 " V ? (V) #10-4 0 2 4 6 8 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 2 3 4 5 t (s) 0 100 200 300 400 I || 0.3674 0.3676 0.3678 0.368 0.3682

Figure 9.7: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 9425 rad s

−1

and α = 1.62 %.

!_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 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 -7 0 0.5 1 1.5

Figure 9.8: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 9425 rad s

−1

and

(78)

t (s) 0 100 200 300 400 " V || (V) #10-4 1 2 3 4 t (s) 0 100 200 300 400 " V ? (V) #10-4 0 2 4 6 8 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 0 100 200 300 400 I || 0.3539 0.354 0.3541 0.3542 0.3543

Figure 9.9: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 10 996 rad s

−1

and α = 1.62 %.

!_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 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 -7 0 0.5 1 1.5 2

Figure 9.10: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 10 996 rad s

−1

(79)

t (s) 0 100 200 300 400 " V || (V) #10-4 1 2 3 4 t (s) 0 100 200 300 400 " V ? (V) #10-3 0 0.5 1 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 0 2 4 6 8 t (s) 0 100 200 300 400 I || 0.3404 0.3406 0.3408 0.341

Figure 9.11: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 12 566 rad s

−1

and α = 1.62 %.

!_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 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 -7 0 1 2 3

Figure 9.12: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 12 566 rad s

−1

(80)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 1 2 3 4 t (s) 2 4 6 8 10 12 " V ? (V) #10-3 0 0.5 1 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-6 0 0.5 1 1.5 t (s) 2 4 6 8 10 12 I || 0.4101 0.4102 0.4103 0.4104 0.4105

Figure 9.13: ∆V and I vs t at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and α = 1.62 %.

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

Figure 9.14: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 4712 rad s

−1

and

(81)

t (s) 5 10 15 " V || (V) #10-4 1 2 3 4 5 t (s) 5 10 15 " V ? (V) #10-3 0 0.5 1 1.5 t (s) 5 10 15 || " V|| 2 (V 2 ) #10-6 0 0.5 1 1.5 t (s) 5 10 15 I || 0.398 0.3981 0.3982 0.3983

Figure 9.15: ∆V and I vs t at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and α = 1.62 %.

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

Figure 9.16: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 6283 rad s

−1

and

(82)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 1 2 3 4 5 t (s) 2 4 6 8 10 12 " V ? (V) #10-3 0 0.5 1 1.5 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-6 0 1 2 3 t (s) 2 4 6 8 10 12 I || 0.3816 0.3818 0.382 0.3822 0.3824

Figure 9.17: ∆V and I vs t at U = 0.1 m s

−1

, ω = 7854 rad s

−1

and α = 1.62 %.

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

Figure 9.18: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 7854 rad s

−1

and

(83)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 0 2 4 6 t (s) 2 4 6 8 10 12 " V ? (V) #10-3 0 0.5 1 1.5 2 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-6 0 1 2 3 t (s) 2 4 6 8 10 12 I || 0.3675 0.368 0.3685

Figure 9.19: ∆V and I vs t at U = 0.1 m s

−1

, ω = 9425 rad s

−1

and α = 1.62 %.

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

Figure 9.20: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 9425 rad s

−1

and

(84)

t (s) 2 4 6 8 10 12 " V || (V) #10-4 0 2 4 6 t (s) 2 4 6 8 10 12 " V ? (V) #10-3 0 0.5 1 1.5 2 t (s) 2 4 6 8 10 12 || " V|| 2 (V 2 ) #10-6 0 1 2 3 4 t (s) 2 4 6 8 10 12 I || 0.3535 0.354 0.3545 0.355

Figure 9.21: ∆V and I vs t at U = 0.1 m s

−1

, ω = 10 996 rad s

−1

and α = 1.62 %.

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

Figure 9.22: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 10 996 rad s

−1

(85)

t (s) 5 10 15 " V || (V) #10-4 0 2 4 6 8 t (s) 5 10 15 " V ? (V) #10-3 0 0.5 1 1.5 2 t (s) 5 10 15 || " V|| 2 (V 2 ) #10-6 0 1 2 3 4 t (s) 5 10 15 I || 0.34 0.3405 0.341 0.3415

Figure 9.23: ∆V and I vs t at U = 0.1 m s

−1

, ω = 12 566 rad s

−1

and α = 1.62 %.

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

Figure 9.24: FFT spectral density of ∆V vs ω

M

at U = 0.1 m s

−1

, ω = 12 566 rad s

−1

(86)

t (s) 1.5 2 2.5 3 3.5 4 " V || (V) #10-4 -6 -4 -2 0 2 t (s) 1.5 2 2.5 3 3.5 4 " V ? (V) #10-3 -1.5 -1 -0.5 0 t (s) 1.5 2 2.5 3 3.5 4 || " V|| 2 (V 2 ) #10-6 0 0.5 1 1.5 t (s) 1.5 2 2.5 3 3.5 4 I || 0.419 0.4192 0.4194 0.4196

Figure 9.25: ∆V and I vs t at U = 1 m s

−1

, ω = 4712 rad s

−1

and α = 1.62 %.

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

Figure 9.26: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 4712 rad s

−1

and

(87)

t (s) 1 2 3 4 5 " V || (V) #10-4 -6 -4 -2 0 2 t (s) 1 2 3 4 5 " V ? (V) #10-3 -1.5 -1 -0.5 0 t (s) 1 2 3 4 5 || " V|| 2 (V 2 ) #10-6 0 0.5 1 1.5 2 t (s) 1 2 3 4 5 I || 0.3974 0.3976 0.3978 0.398 0.3982

Figure 9.27: ∆V and I vs t at U = 1 m s

−1

, ω = 6283 rad s

−1

and α = 1.62 %.

!_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 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 0.5 1 1.5 2

Figure 9.28: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 6283 rad s

−1

and

(88)

t (s) 2 2.5 3 3.5 4 " V || (V) #10-4 -6 -4 -2 0 t (s) 2 2.5 3 3.5 4 " V ? (V) #10-3 -1.5 -1 -0.5 0 t (s) 2 2.5 3 3.5 4 || " V|| 2 (V 2 ) #10-6 0 1 2 3 t (s) 2 2.5 3 3.5 4 I || 0.3894 0.3896 0.3898 0.39 0.3902

Figure 9.29: ∆V and I vs t at U = 1 m s

−1

, ω = 7854 rad s

−1

and α = 1.62 %.

!_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 0.5 1 1.5 2 ! 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 9.30: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 7854 rad s

−1

and

(89)

t (s) 2 3 4 5 6 " V || (V) #10-4 -6 -4 -2 0 t (s) 2 3 4 5 6 " V ? (V) #10-3 -2 -1.5 -1 -0.5 0 t (s) 2 3 4 5 6 || " V|| 2 (V 2 ) #10-6 0 1 2 3 t (s) 2 3 4 5 6 I || 0.369 0.3695 0.37 0.3705

Figure 9.31: ∆V and I vs t at U = 1 m s

−1

, ω = 9425 rad s

−1

and α = 1.62 %.

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

Figure 9.32: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 9425 rad s

−1

and

(90)

t (s) 1.5 2 2.5 3 3.5 " V || (V) #10-4 -8 -6 -4 -2 0 t (s) 1.5 2 2.5 3 3.5 " V ? (V) #10-3 -2 -1.5 -1 -0.5 0 t (s) 1.5 2 2.5 3 3.5 || " V|| 2 (V 2 ) #10-6 0 1 2 3 4 t (s) 1.5 2 2.5 3 3.5 I || 0.3605 0.361 0.3615 0.362

Figure 9.33: ∆V and I vs t at U = 1 m s

−1

, ω = 10 996 rad s

−1

and α = 1.62 %.

!_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 ! M (rad/s) 0 200 400 600 800 1000 || " V|| 2 -h || " V|| 2 i (V 2 ) #10 -7 0 0.5 1

Figure 9.34: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 10 996 rad s

−1

and

(91)

t (s) 1.5 2 2.5 3 3.5 " V || (V) #10-4 -8 -6 -4 -2 0 t (s) 1.5 2 2.5 3 3.5 " V ? (V) #10-3 -2 -1.5 -1 -0.5 0 t (s) 1.5 2 2.5 3 3.5 || " V|| 2 (V 2 ) #10-6 0 1 2 3 4 t (s) 1.5 2 2.5 3 3.5 I || 0.3465 0.347 0.3475 0.348

Figure 9.35: ∆V and I vs t at U = 1 m s

−1

, ω = 12 566 rad s

−1

and α = 1.62 %.

!_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 ! 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 9.36: FFT spectral density of ∆V vs ω

M

at U = 1 m s

−1

, ω = 12 566 rad s

−1

and

(92)

t (s) 0 100 200 300 400 " V || (V) #10-4 1.5 2 2.5 3 t (s) 0 100 200 300 400 " V ? (V) #10-4 1 2 3 4 5 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 1.5 2 t (s) 0 100 200 300 400 I || 0.4102 0.4104 0.4106 0.4108

Figure 9.37: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

and α = 1.62 %.

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

Figure 9.38: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 4712 rad s

−1

(93)

t (s) 0 100 200 300 400 " V || (V) #10-4 1.5 2 2.5 3 3.5 t (s) 0 100 200 300 400 " V ? (V) #10-4 0 2 4 6 t (s) 0 100 200 300 400 || " V|| 2 (V 2 ) #10-7 1 1.5 2 2.5 3 t (s) 0 100 200 300 400 I || 0.3928 0.3928 0.3929 0.3929 0.393

Figure 9.39: ∆V and I vs t at U = 10

−3

m s

−1

, ω = 6283 rad s

−1

and α = 1.62 %.

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

Figure 9.40: FFT spectral density of ∆V vs ω

M

at U = 10

−3

m s

−1

, ω = 6283 rad s

−1