Question

sampling interval is T = 0.3 s. 1) A plant is regulated using a digital control system as shown in Figure 1 where the R(z) Y(z) E(z) K(z) U(z) G_a(z) Controller D/A converter + Plant Figure 1: Digital control system for an oscillator (a) The s-domain transfer functions of the D/A converter and the plant are respectively given by $G_{DAC}(s) = \frac{1 - e^{-sT}}{s}$ and $G(s) = \frac{1}{s^2 + P^2}$ Based on T = 0.3 s, find $G_d(z)$ the z-domain transfer function between U(z) and Y(z). P has the value determined on the cover page. [Hints: $G_d(z)$ has an equivalent s-domain transfer function of $G_{DAC}(s) \times G(s)$. You need to use the Laplace and z-transform of co- sinusoid as

          sampling interval is T = 0.3 s.
1) A plant is regulated using a digital control system as shown in Figure 1 where the
R(z)
Y(z)
E(z) K(z)
U(z)
G_a(z)
Controller
D/A converter + Plant
Figure 1: Digital control system for an oscillator
(a) The s-domain transfer functions of the D/A converter and the plant are respectively
given by
$G_{DAC}(s) = \frac{1 - e^{-sT}}{s}$ and $G(s) = \frac{1}{s^2 + P^2}$
Based on T = 0.3 s, find $G_d(z)$ the z-domain transfer function between U(z) and Y(z). P
has the value determined on the cover page. [Hints: $G_d(z)$ has an equivalent s-domain
transfer function of $G_{DAC}(s) \times G(s)$. You need to use the Laplace and z-transform of co-
sinusoid as

sampling interval is T = 0.3 s.
1) A plant is regulated using a digital control system as shown in Figure 1 where the
R(z)
Y(z)
E(z) K(z)
U(z)
Ga(z)
Controller
D/A converter + Plant
Figure 1: Digital control system for an oscillator
(a) The s-domain transfer functions of the D/A converter and the plant are respectively
given by
GDAC(s) = (1 - e^-sT)/(s) and G(s) = (1)/(s^2 + P^2)
Based on T = 0.3 s, find Gd(z) the z-domain transfer function between U(z) and Y(z). P
has the value determined on the cover page. [Hints: Gd(z) has an equivalent s-domain
transfer function of GDAC(s) × G(s). You need to use the Laplace and z-transform of co-
sinusoid as

Added by Catherine B.

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