:) Cutting forces should be kept constant during machining operations to prevent chang in spindle speeds or work position. Such changes would deteriorate the accuracy oft work's dimensions. A control system is proposed to control the cutting force. The pla is difficult to model, since the factors that affect cutting force are time varying and n easily predicted. However, assuming the simplified force control model shown Figure Q2(c). (i) Show the closed-loop transfer function for the system of the system as below K(s+3) T(s) = s* +7s³ +14s? +(8+K)s+3K ii) Determine the range K to keep the system stable using the Routh-Hurwitz criterion. R(s) 1 C(s) K(s+3) s (s + 1)(s+2)(s+4) Figure Q2 (c)

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(c) Cutting forces should be kept constant during machining operations to prevent changes
in spindle speeds or work position. Such changes would deteriorate the accuracy of the
work's dimensions. A control system is proposed to control the cutting force. The plant
is difficult to model, since the factors that affect cutting force are time varying and not
easily predicted. However, assuming the simplified force control model shown in
Figure Q2(c).
(i) Show the closed-loop transfer function for the system of the system as below
K(s+3)
T(s)=
s* +7s³ +14s? +(8+K)s+3K
Determine the range K to keep the system stable using the Routh-Hurwitz
criterion.
R(s)
1
C(s)
K(s+3)
s (s + 1)(s+2)(s+4)
Figure Q2 (c)
Transcribed Image Text:(c) Cutting forces should be kept constant during machining operations to prevent changes in spindle speeds or work position. Such changes would deteriorate the accuracy of the work's dimensions. A control system is proposed to control the cutting force. The plant is difficult to model, since the factors that affect cutting force are time varying and not easily predicted. However, assuming the simplified force control model shown in Figure Q2(c). (i) Show the closed-loop transfer function for the system of the system as below K(s+3) T(s)= s* +7s³ +14s? +(8+K)s+3K Determine the range K to keep the system stable using the Routh-Hurwitz criterion. R(s) 1 C(s) K(s+3) s (s + 1)(s+2)(s+4) Figure Q2 (c)
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