Sol_HW6

# Sol_HW6 - 4.4 The DC-motor speed control in Fig 4.38 is...

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1 4.4 The DC-motor speed control in Fig. 4.38 is described by the differential equation 60 600 1500 , a y yv w + =− ± where y is the motor speed, v a is the armature voltage, and w is the load torque. Assume the armature voltage is computed using the PI control law ( ) 0 , t apI vk e k e d t =+ where ery . (a) Compute the transfer function from W to Y as a function of k p and k I . (b) Compute values for k p and k I so that the characteristic equation of the closed-loop system will have roots at 60 ± 60j. Figure 4.38: Unity feedback system with preÞlter for Problem 4.4 2 1,2 Solution: ( ) Transfer function: Set ( ) 0, then ( ) ( ) 600 ( ) 1500 ( ) ( ) ( 60) ( ) 1500 ( ) 60(1 10 ) 600 ( ) For roots at 60 60, I p pI aR s E s Y s k kY sW s s Ys s s Ws s k s k bs j == ⎛⎞ −+ ⎜⎟ ⎝⎠ = + = ++ + ± 12 60(1 10 ) 120 0.1, 12 7200 600 p I ss k kk k += − + = ⇒= = 4.26 Consider the system shown in Fig. 4.49 with PI control. ( ) Determine the transfer function from to . ( ) Determine the transfer function from to . ( ) Use Routh's crite Y bW Y c ria to find the range of ( , ) for which the system is stable. (d*) Pick and so that the closed-loop system is stable. What is the steady state error when ( ) 1( ) and

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## This note was uploaded on 02/19/2009 for the course MAE 171A taught by Professor Idan during the Spring '09 term at UCLA.

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Sol_HW6 - 4.4 The DC-motor speed control in Fig 4.38 is...

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