An electrically heated stirred tank is described by the following first-order differential equations:
1)dT/dt=w/m(Ti-T)+ he Ae/mC(Te-T)
2)dTe/dt=Q/me Ce - he Ae/me Ce(Te-T)
At t =0,Qsuddenly changed from 5000kca l/m in to 5400kca l/m in, and T is 100°C. m m
(a) Convert the equations to deviation variable form, T,Te,Q
b) ) Using the deviation variables (T,Te,Q) determine the transfer function between temperature T and heat input Q, that is determine
T (s)/Q (s)
(c) Write the transfer function Q (s) for a step function of 400°C.
d) Using your result in parts (b) and (c)
determine T (s).
(e) Express equations (1) and (2) in a state - space model and solve for the poles, i. e.
Use these conditions:
m/W = 10min.
he Ae me Ce= 1.0min
me Ce/wC=1.0min.
1/wC= 0.05°Cmi n/k cal