Problem 4 5 points for circling just the correct answer. 3 points if 2 are circl

Question

Problem 4 5 points for circling just the correct answer. 3 points if 2 are circled and one is correct) A PI current control is developed for a de machine based on pole zero cancelation. The following parameters are known: ki 32 kpwm 25 (integral gain) k 0.16 (proportional gain) (converter constant) R.-0.4 S2 (armature resistance) a) The closed loop transfer function is given as 25.32 32-0.16 11) 25.32 illi) iii) iv) 20.16 25.32 0.15 25.32 S + s+s+32.0.16 0.4 0.4 b) What is the system bandwidth? ii) 25:32.0.16 0.4 32-0.16 25.32 0.4 iv) 0.16-0.4 0.4 c) What is the electrical time constant of the machine? 0.16 32-25 25 1+0.16.32-25 0.16.32-25 1+0.16.32 0.16 32 iv)

Explanation / Answer

Given data :

KI=25

Kp=0.16

k(pwm)=25

Ra=0.4 ohm

a)

It is understood from the given condition as we know that

For PI Controller

e(s)=Kp+Ki/s

Hence , we get iv) ans

As , (Ki*Kp)/(s2+Kp/Ra+Ki*KP)

b)

Bandwidth =1/(Time differece)

Td=Kp*R/(Ki*K(pwn))

Td=0.16*0.4/(32*25)

Hence , Bandwidth = (32*25)/(0.16*0.4)

c)

Itt is clear that

Tc=Kp/(Ki*K(pwn))

Hence , =0.16/(32*25)

It is simple as we know

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