Consider the circuit shown in Figure 3.30. The nominal transistor parameters are V T P = − 0.30 V and K p = 120 μ A/V 2 . (a) Calculate V S G , I D , and V S D . (b) Determine the variation in I D if the threshold voltage varies by ±5 percent. (Ans. (a) V S G = 1.631 V , I D = 0.2126 mA , V S D = 3.295 V ; (b) 0.2091 ≤ I D ≤ 0.2160 mA )
Consider the circuit shown in Figure 3.30. The nominal transistor parameters are V T P = − 0.30 V and K p = 120 μ A/V 2 . (a) Calculate V S G , I D , and V S D . (b) Determine the variation in I D if the threshold voltage varies by ±5 percent. (Ans. (a) V S G = 1.631 V , I D = 0.2126 mA , V S D = 3.295 V ; (b) 0.2091 ≤ I D ≤ 0.2160 mA )
Solution Summary: The author calculates the value of the current I_1, the voltage and the drain current.
Consider the circuit shown in Figure 3.30. The nominal transistor parameters are
V
T
P
=
−
0.30
V
and
K
p
=
120
μ
A/V
2
. (a) Calculate
V
S
G
,
I
D
, and
V
S
D
. (b) Determine the variation in
I
D
if the threshold voltage varies by ±5 percent. (Ans. (a)
V
S
G
=
1.631
V
,
I
D
=
0.2126
mA
,
V
S
D
=
3.295
V
; (b)
0.2091
≤
I
D
≤
0.2160
mA
)
Q4.
a) A purely derivative controller (i.e. with a zero at the origin only) is defined
by an improper transfer function. Considering its asymptotic behaviour,
explain why a purely derivative controller is difficult to implement in
practice. Relate your explanation to the potential limitations on system
performance.
b) Discuss the potential issues faced by a control system with a large cut-off
frequency. Relate your discussion to the implications on system
performance.
c)
The transfer function of a lag compensator is given by
2
KPID(S) = 2.2++0.2s
S
By using the asymptotic approximation technique:
(i) Obtain the standard form and corner frequency for each individual
component of KPID(S).
(ii) Clearly describe the asymptotic behaviour of each individual
component of KPID(S).
Module Code: EN2058
Q1. a) List the advantages and disadvantages of a closed loop system compared to
an open loop system.
b)
c)
What is the procedure for designing a control system for a bread toaster?
An RC circuit is given in Figure Q1. vi(t) and v(t) are the input and output
voltages.
(i) Derive the transfer function of the circuit.
(ii) With a unit step change vi(t) applied to the circuit, derive and sketch the
time response of the circuit.
R1 R2
v₁(t)
R3 C1
vo(t)
R₁ =R2 = 10 k
R3 = 100 kn C₁ = 100 μF
Figure Q1. RC circuit.
(iii) Assuming zero initial conditions, obtain the impulse and ramp responses
of the circuit from the step response derived in (ii). Sketching is not
needed.
Q3.
a)
The frequency response method enables the study of the steady-state
response of a system G(s). What type of inputs are used for frequency
response? If the system is linear and stable, how does the output differ
from the input? Compare the main characteristics of two types frequency
response plots.
b) Consider the control system shown in Figure Q3.
Controller
E(s)
R(s)
Desired
output
C(s)
Plant
G(s)
Y(s)
Actual
output
3(s + 3)
C(s) = k
G(s) =
= s(s - 1)(s + 10)
Figure Q3. Closed-loop system.
(i) Considering definitions in the study of bounded-input bounded-output
stability, is G(s) stable? Classify the poles and zeros of G(s).
(ii) G(s) defined in Figure Q3 is a system completely characterised by
its transfer function. Explain why this is the case.
(iii) Obtain the closed-loop transfer function P(s) = Y(s)/R(s) of the
system.
(iv) Based on your result for the previous question [Question 3b)-(iii)], use
the Routh-Hurwitz stability criterion to determine suitable values of
gain K…
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