7 The input u(t) output y(t) relationship of an open loop plant is given by the differential equation d'y(t) dy(t) dt² dt + + y(t) = u(t) a) Determine the transfer function G(s) of the open loop plant, stating any assumptions made. ii) b) i) Find the characteristic equation of the open loop plant. Determine the poles of the open loop plant.

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7
The input u(t) output y(t) relationship of an open loop plant is given by the
differential equation
d'y(t) dy(t)
+
dt² dt +y(t) = u(t)
a) Determine the transfer function G(s) of the open loop plant, stating any
assumptions made.
b) i) Find the characteristic equation of the open loop plant.
ii) Determine the poles of the open loop plant.
1
c)
35
A controller with the transfer function C(s) = 1 + is added to the feedback
path and a closed loop system is formed. Determine the transfer function of
the closed loop system.
Transcribed Image Text:7 The input u(t) output y(t) relationship of an open loop plant is given by the differential equation d'y(t) dy(t) + dt² dt +y(t) = u(t) a) Determine the transfer function G(s) of the open loop plant, stating any assumptions made. b) i) Find the characteristic equation of the open loop plant. ii) Determine the poles of the open loop plant. 1 c) 35 A controller with the transfer function C(s) = 1 + is added to the feedback path and a closed loop system is formed. Determine the transfer function of the closed loop system.
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