4. Consider the discrete system in the figure, given the plan: P(s)=1/{s+1}; T=0.5, u(0)=1, u(0.5)=2, u(1)=3, y(0)=0 . Find: i) y(0.5) ; and(1) ; y(1.5) (that is y(kT) for k=1,2,3,4) as a direct solution of the difference equation of the discrete equivalent system. ii) y(k T) through the inverse Z and Z transform. Analyze the form of u(k T) to obtain the

The answer to both questions is yes. The first question asks if it is possible to find the solution ...

Resuelto 4. Consider the discrete system in the figure, given

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Pregunta: 4. Consider the discrete system in the figure, given the plan: P(s)=1/{s+1}; T=0.5, u(0)=1, u(0.5)=2, u(1)=3, y(0)=0 . Find: i) y(0.5) ; and(1) ; y(1.5) (that is y(kT) for k=1,2,3,4) as a direct solution of the difference equation of the discrete equivalent system. ii) y(k T) through the inverse Z and Z transform. Analyze the form of u(k T) to obtain the
4. Consider the discrete system in the figure, given the plan: P(s)=1/{s+1}; T=0.5, u(0)=1, u(0.5)=2, u(1)=3, y(0)=0 . Find: i) y(0.5) ; and(1) ; y(1.5) (that is y(kT) for k=1,2,3,4) as a direct solution of the difference equation of the discrete equivalent system. ii) y(k T) through the inverse Z and Z transform. Analyze the form of u(k T) to obtain the Z transform of the input
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Paso 1
The answer to both questions is yes.
Explanation:
The first question asks if it is possible to find the solution ...
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Paso 2
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Texto de la transcripción de la imagen:

4. Considere el sistema discreto de la figura, dada la planta:

P (s) = \frac{1}{s + 1}

;

T = 0.5, u (0) = 1, u (0.5) = 2, u (1) = 3, y (0) = 0 .

Encuentre : i)

y (0.5); y (1); y (1.5)

(esto es

y (k T)

para

k = 1, 2, 3, 4

) como solución de directa de la ecuación a diferencias del sistema equivalente discreto. ii) y(kT) a través de la transformada

Z

Z

inversa. Analice la forma de u(kT) para obtener la transformada

Z

de la entrada