7/22/2019 Answer for Tutorial 4
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UNIVERSITI MALAYSIA PERLIS
Pusat Pengajian Kejuruteraan Bioproses
ERT 210/4 Process Dynamics and ControlTutorial 4: Transfer
Function and State-Space Models
4.2 Consider the following transfer function:
110
5
)(
)()(
+
==
ssU
sYsG
(a) What is the steady-state gain?
= 5
(b) What is the time constant?
= 10
(c) If U(s) = 2/s, what is the value of the
outputy(t) when t ?
(d) For the same U(s), what is the value ofthe output when t =
10? What is the
output when expressed as a fraction of
the new steady-state value?
(e) If U(s) = (1-e-s)/s, that is, the unit
rectangular pulse, what is the output
when t ?
(f) If )()( ttu = , that is, the unit impulse
at t= 0, what is the output when t ?
(g) If ttu 3sin2)( = , what is the value of
the output when t ?
7/22/2019 Answer for Tutorial 4
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4.8 A surge tank in Fig. E4.8 is designed with a slotted weir so
that the outflow rate, w, isproportional to the liquid level to the
1.5 power; that is,
5.1Rhw =
where R is constant. If the single stream enters the tank with
flow rate wi, find the transfer
functionH'(s)/Wi(s). Identify the gain and all time constants.
Verify units.
The cross-sectional area of the tank isA. Density is
constant.
Figure E4.8
