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Explanations of steps used are essential, and will be carefully accounted for in assessment. (a) Design a gain compensator, Gc(s) = K, that will produce a 20% overshoot for a step input at
Best marks are awarded to numerically correct solutions, but partial credit will be given to Vi(s).
partially complete solutions or incorrect solutions where errors have carried through the (17 marks)
calculations. State any and all assumptions that you make.
(b) Calculate the settling time for your chosen value of gain, K.
QUESTION 1 (2 marks)
A motor system is to be designed using a feedback control system. A schematic diagram of the
(c) Calculate the steady state error for your chosen value of gain, K.
motor system is shown in Figure 1. The desired speed is set using a potentiometer, which
(2 marks)
produces a voltage Vi(s). The voltage Vi(s)is compared to the speed feedback signal Vt(s) to
produce an error voltage Ve(s). You are required to design a compensator Gc(s) which uses the
(d) Find the range of K values that will maintain system stability.
error signal as input and produces a voltage Vp(s). The voltage Vp(s) controls a power amplifier
(2 marks)
with transfer function:
500 (e) Design a lead-lag compensator for Gc(s) so that the settling time is half of the value
G p ( s) =
s + 500 calculated in (b), and the error constant is increased by a factor of 10 from the value
The power amplifier drives a DC motor with the characteristics described in Table 1. The DC calculated in (c). You should assume that there is a dominant second order response. Express
motor drives the load through a gear box with a 5 : 100 ratio as shown. The load has inertia JL = your final answer as a transfer function. You do not need to consider implementation issues
1 kgm2. The speed of the load is measured using a tachometer, which converts the speed of the in your design.
load to a voltage with a constant Kv = 1 Vs/rad. The voltage from the tachometer is the speed (16 marks)
feedback signal Vt(s).
(f) Comment on the validity of your second order assumption.
(1 mark)
Input Power DC Motor
Compensator
Potentiometer
Desired
Amplifier (see Table 1) Ȧm(s)
Speed Vi(s) Ve(s) Vp(s) Ea(s)
Kpot Gc(s) Gp(s) N1=5
+
– END OF PAPER
JL = 1
Kv
Vt(s) kgm2
Tachometer ȦL(s)
N2=100


Figure 1: Schematic diagram of variable speed polishing machine


Table 1: Parameters for DC motor
Parameter Symbol Value
Armature Inertia Ja 5×10-4 kgm2
Armature Damping Da 10-2 Nms/rad
Torque Constant Kt 0.5 Nm/A
Back EMF Constant Kb 0.5 Vs/rad
Armature Resistance Ra 0.8 ȍ




Question 1 continued overleaf
Question 1 continued