Question

A1 A water heating system is represented by the block diagram shown in figure A1. The valve mixes hot and cold water to obtain the desired water temperature using an integral controller of gain K. The water temperature is controlled by sensing the output temperature 0o and comparing with the desired temperature 0d. Write down an expression, in Bode form, for the open-loop frequency response function in terms of K and frequency o. Hence draw the open-loop Bode plot for the system using straight line asymptote approximations for a gain K-0.5. (a) Determine the value of K for a phase margin of 420 140 %! (b)Draw the corresponding Nichols plot for the system in part (a) for K 0.5. Determine the value of K for a peak closed-loop gain of +3dB. What is the corresponding peak resonant frequency? [30 %] (c) To ensure adequate mixing of the water the temperature sensor is placed some distance downstream from the mixer valve. (i) edraw the system block diagram to include the time delay thus introduced and (ii) Calculate the time delay between the valve and the sensor that will just cause briefly comment on the effect of the system instability for the gain in part (a) corresponding to a phase margin of 42 [30 %] 4 θο Controller Mixer Valve Figure A1

Answer 1

Pd es s(s+2) 火- ー20 IV

uuA 220 10 ん(40小a) | b. b*I 2 10 Bede Plot

sCs2) 2 ん w t 22 4

46 4-0