Question

'Only need to answer question (f), (g)'

Answers are shown. Just need to know the steps and how you got there.

Answer:

1. You are trying to control a process temperature in a nanofabrication lab. The current open-loop response to a temperature adjustment is shown below. Use the Ziegler-Nichols tuning method to answer the questions below. 100- Temp Time (sec) 90 8 910 12 13 5 16 a) Find L and R from the plot above, show your work above and hand in this plot with your homework. b) Use these values to find the proportional gain of a proportional-only (P) controller in a closed loop. Igain and integral time of a Z-N Pl controller. find the proportional and e) Use these values to find the proportional gain integral time and differential time of a Z-N PID controller. f) Draw a block diagram of this controller, showing the gains. 1. a) Approximately 0.8 &2.08 b) 0.6 c) 0.54 2.67 d) 0.54 0.202 e) 0.72 6 04 9) 0.72 0.45 0.288

Answer 1

100 ц=0.8 Temp t 2.08 Time (sec) 90 8 9 0 2 3 14 156

From the above figures, it is observed that L = 0.8 R = X/Y = slope the the tangent line = 10/(5.6-0.8) = 2.08 approximately.

Proportional controller:

Kp = 1/(R*L) = 1(2.08*0.8) = 0.6 (Approximately).

PI controller:

Proportional gain Kp = 0.9/(R*L) = 0.9/(2.08*0.8) = 0.5409

and integral time = Ti = 3.33L = 3.33*0.8 = 2.6643

PI controller:

Proportional gain Kp = 0.9/(R*L) = 0.9/(2.08*0.8) = 0.5409

and integral gain = Kp/Ti =0.5409/2.6643 = 0.203

PID controller:

Proportional gain Kp = 1.2/(R*L) = 1.2/(2.08*0.8) = 0.7212

and integral time = Ti = 2L = 2*0.8 = 1.6

and differential time = Td = 0.5L = 0.5*0.8 = 0.4

answer to f:

0-4S Plant model 0.7 0-28S Cs Scanned with CamScanne

answer to g:

PID controller:

Proportional gain Kp = 1.2/(R*L) = 1.2/(2.08*0.8) = 0.7212

and integral gain = Kp/Ti = 0.4507

and differential gain = Kp*Td = 0.2885