Stability Nyquist Criterion/Estabilidad Criterio de

Pregunta: Stability Nyquist Criterion/Estabilidad Criterio de Nyquist Problema 1. Considere el modelo de la señal eléctrica que proviene de la célula ciliada del sistema auditivo de la literatura y ur sistema de control cerrado.a. Obtain and write down the Transfer function H(s)=V(s)/I(s) (Try to simplify the equation by joining parameters together and naming them,
I already have the answer to a and b, need c and d preferably.

Muestra el texto de la transcripción de la imagen
Esta pregunta aún no se resolvió!
¿No es lo que buscas?
Envía tu pregunta a un experto en la materia.
Envía a un experto
Pregunta anterior Siguiente pregunta
Texto de la transcripción de la imagen:
Stability Nyquist Criterion/Estabilidad Criterio de Nyquist Problema 1. Considere el modelo de la señal eléctrica que proviene de la célula ciliada del sistema auditivo de la literatura y ur sistema de control cerrado. a. Obtain and write down the Transfer function $H (s) = V (s) / I (s)$ (Try to simplify the equation by joining parameters together and naming them, e.g., A, B, C, ..., Z). Compare and confirm the transfer function by showing the plots of LTSpice and Simulink. Use the same time of simulation. Set $R_{1} = 2Ω, R_{2} = 100Ω, R_{3} = 50 m Ω, R_{4} = 100Ω, L_{1} = 10 mH, C =$ $200 uF$ and $I = 1 A$ . (15 puntos) b. Obtain the time dependent response of $H (s)$ in Simulink. Set $R_{1} = 2Ω, R_{2} = 100Ω, R_{3} = 50 m Ω, R_{4} = 100Ω$ , L $10 mH, C = 200 uF$ and $I = 1 A$ . Use a signal generator in Simulink and select a square waveform as an input with amplitude I and frequency of $100 rad / sec$ . Show the plot by changing the time of simulation to $0.2$ seconds. Use the next model as a guide. (10 puntos) c. Obtain and write down the state-space equation and block diagram using state-space analysis. (15 puntos) d. Obtain and write down the transfer function $V (s) /$ /I(s) of the closed-loop control system depicted above and obtain and write down the loop transfer function $H_{L} (s)$ . (5 puntos) e. Using the Nyquist criterion, obtain $H_{L}$ (jw) (10 puntos) f. Obtain $w_{Im = 0}$ of the system by forcing the imaginary part of $H_{L}$ (jw) to zero. Set $R_{1} = 0.1Ω, R_{2} = 1Ω, R_{3} = 1Ω, R_{4} =$ $100Ω, L_{1} = 2 H, C = 1 F$ , and gain of 1 . (10 puntos) g. Using $W_{Im = 0}$ , evaluate $H_{I .} (W_{Im = 0})$ and write down the solution in the form of $R + jX$ . Use gain $k$ of 1 . Is the system stable? Explain your answer by comparing the point of stability and your results. (15 puntos) h. Verify the stability of the system by plotting $H_{L}$ (jw) for angular frequencies from 0 to $1000 rad / sec$ , and gains $k$ [1 10 1001000 ]. Set $R_{1} = 0.1Ω, R_{2} = 1Ω, R_{3} = 1Ω, R_{4} = 100Ω, L_{1} = 2 H, C = 1 F$ . Show the plot of imaginary vs. real. For presenting your results, set the $y$ limit to $([- 0.50.5])$ and the $x$ limit to ([-1.1 1 $])$ . (10 puntos) i. Mention the applications of this model of the auditory system in the biomedical area. Mention the applications of the Nyquist criterion when applying it in physiological models in the biomedical area. (10 puntos)

Texto de la transcripción de la imagen:

Stability Nyquist Criterion/Estabilidad Criterio de Nyquist Problema 1. Considere el modelo de la señal eléctrica que proviene de la célula ciliada del sistema auditivo de la literatura y ur sistema de control cerrado. a. Obtain and write down the Transfer function

H (s) = V (s) / I (s)

(Try to simplify the equation by joining parameters together and naming them, e.g., A, B, C, ..., Z). Compare and confirm the transfer function by showing the plots of LTSpice and Simulink. Use the same time of simulation. Set

R_{1} = 2Ω, R_{2} = 100Ω, R_{3} = 50 m Ω, R_{4} = 100Ω, L_{1} = 10 mH, C =

200 uF

and

I = 1 A

. (15 puntos) b. Obtain the time dependent response of

H (s)

in Simulink. Set

R_{1} = 2Ω, R_{2} = 100Ω, R_{3} = 50 m Ω, R_{4} = 100Ω

, L

10 mH, C = 200 uF

and

I = 1 A

. Use a signal generator in Simulink and select a square waveform as an input with amplitude I and frequency of

100 rad / sec

. Show the plot by changing the time of simulation to

0.2

seconds. Use the next model as a guide. (10 puntos) c. Obtain and write down the state-space equation and block diagram using state-space analysis. (15 puntos) d. Obtain and write down the transfer function

V (s) /

/I(s) of the closed-loop control system depicted above and obtain and write down the loop transfer function

H_{L} (s)

. (5 puntos) e. Using the Nyquist criterion, obtain

H_{L}

(jw) (10 puntos) f. Obtain

w_{Im = 0}

of the system by forcing the imaginary part of

H_{L}

(jw) to zero. Set

R_{1} = 0.1Ω, R_{2} = 1Ω, R_{3} = 1Ω, R_{4} =

100Ω, L_{1} = 2 H, C = 1 F

, and gain of 1 . (10 puntos) g. Using

W_{Im = 0}

, evaluate

H_{I .} (W_{Im = 0})

and write down the solution in the form of

R + jX

. Use gain

k

of 1 . Is the system stable? Explain your answer by comparing the point of stability and your results. (15 puntos) h. Verify the stability of the system by plotting

H_{L}

(jw) for angular frequencies from 0 to

1000 rad / sec

, and gains

k

[1 10 1001000 ]. Set

R_{1} = 0.1Ω, R_{2} = 1Ω, R_{3} = 1Ω, R_{4} = 100Ω, L_{1} = 2 H, C = 1 F

. Show the plot of imaginary vs. real. For presenting your results, set the

y

limit to

([- 0.50.5])

and the

x

limit to ([-1.1 1

])

. (10 puntos) i. Mention the applications of this model of the auditory system in the biomedical area. Mention the applications of the Nyquist criterion when applying it in physiological models in the biomedical area. (10 puntos)

Estudia mejor, ¡ahora en español!