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Tutorial 4 Control systems. Question 3 The control input for a continuous process is derived using a digital controller with a sample period of 0.1 s, and a control algorithm defined by the equations: u(nT)=e(nT)-e(n-1)T+0.75u(n-1)T e(nT)=r(nT)-y(nT) where r(nT) is the reference input and y(nT) is the sampled output signal. The continuous process is described by the differential equation: $\frac{dy(t)}{dt}$+4y(t)=6u(t) where u(t) is the output from a zero-order hold device. (1) Provide a block diagram of the closed-loop system labelling clearly all signals and blocks. (2) Show that the zero-order hold equivalent of the continuous process is: $G(z) = \frac{0.495}{z-0.67}$ (3) Determine the discrete transfer function of the closed-loop system. (4) Hence, find the transient response of the output, y(nT), when the input is a unit step.

          Tutorial 4 Control systems.
Question 3
The control input for a continuous process is derived using a digital controller
with a sample
period of 0.1 s, and a control algorithm defined by the equations:
u(nT)=e(nT)-e(n-1)T+0.75u(n-1)T
e(nT)=r(nT)-y(nT)
where r(nT) is the reference input and y(nT) is the sampled output signal.
The continuous process is described by the differential equation:
$\frac{dy(t)}{dt}$+4y(t)=6u(t)
where u(t) is the output from a zero-order hold device.
(1) Provide a block diagram of the closed-loop system labelling clearly all
signals and blocks.
(2) Show that the zero-order hold equivalent of the continuous process is:
$G(z) = \frac{0.495}{z-0.67}$
(3) Determine the discrete transfer function of the closed-loop system.
(4) Hence, find the transient response of the output, y(nT), when the input is
a unit step.

Tutorial 4 Control systems.
Question 3
The control input for a continuous process is derived using a digital controller
with a sample
period of 0.1 s, and a control algorithm defined by the equations:
u(nT)=e(nT)-e(n-1)T+0.75u(n-1)T
e(nT)=r(nT)-y(nT)
where r(nT) is the reference input and y(nT) is the sampled output signal.
The continuous process is described by the differential equation:
(dy(t))/(dt)+4y(t)=6u(t)
where u(t) is the output from a zero-order hold device.
(1) Provide a block diagram of the closed-loop system labelling clearly all
signals and blocks.
(2) Show that the zero-order hold equivalent of the continuous process is:
G(z) = (0.495)/(z-0.67)
(3) Determine the discrete transfer function of the closed-loop system.
(4) Hence, find the transient response of the output, y(nT), when the input is
a unit step.

Added by Amparo R.

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