Modern Control Systems Dorf 11th Solutions Manual

07.11.2019

Transfer function is ω(s)/V (s) = Km RaJs2 +KbKms+KmKKt. With v(t) = t, we have V (s) = 1/s2, and Td(s) = 0. Using the final value theorem yields ess = lim s→0 sE(s) = lim s→0 1 s+ KKmRaJs+KmKb = Kb K = 0.1 K. We desire that ess = 0.1 K 1. For example, we can take K = 8.

  1. Modern Control Systems Dorf
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Modern control systems solution manual dorf pdf solutions adobe community email markrainsun at gmail dot com here are some listed pdfa briefsistemas. MODERN CONTROL SYSTEMS SOLUTION MANUAL Richard C. Dorf Robert H. Solutions Manual to Accompany Modern Control. The Design of Feedback Control Systems.492 11.

(b) The transfer function from Td(s) to ω(s) is given by ω(s) Td(s) = −10s s2 + 10s + 100. The error plot is shown in Figure AP4.4, where e(s) = −ω(s) (V (s) = 0.) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 1 2 3 4 5 6 7 8 9 10 Time (sec) e (t) FIGURE AP4.4 Error plot with a ramp disturbance input. AP4.5 (a) The transfer function from the disturbance Td(s) to the output Y (s) is Y (s) Td(s) = −s s3 + 4s2 + 4s +K. The steady-state error (when Td(s) = 1/s) is ess = lim s→0 s s s3 + 4s2 + 4s+K 1 s = 0.

Solutions Manual to Accompany Modern Control Systems, Eleventh Edition, by Richard C Dorf and Robert H. ISBN-13: 298.

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

150 CHAPTER 4 Feedback Control System Characteristics (b) The closed-loop transfer function is Y (s) R(s) = K s3 + 4s2 + 4s +K. The steady-state error (when R(s) = 1/s2) is ess = lim s→0 s(1− T (s)) 1 s2 = lim s→0 s3 + 4s2 + 4s s(s3 + 4s2 + 4s+K) = 4 K. (c) Let K = 8. Then, Y (s) Td(s) = −s s3 + 4s2 + 4s+ 8. The error plot is shown in Figure AP4.5, for r(t) = 0.0.1 -0.05 0 0.05 0.1 0.15 0 2 4 6 8 10 12 14 16 18 20 Time (sec) e (t) FIGURE AP4.5 Error plot with a step disturbance input and K=8. AP4.6 (a) The transfer function is Vo(s) V (s) = 1 +RCs 2 +RCs.

Solutions Manual to Accompany Modern Control Systems, Eleventh Edition, by Richard C Dorf and Robert H. ISBN-13: 298.

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Advanced Problems 151 (b) The system sensitivity is defined as SGC = ∂G/G ∂C/C. Therefore, the sensitivity is determined to be SGC = RCs (2 +RCs)(1 +RCs) = 1( 1 + 2RCs ) ( 1 + 1RCs ). (c) Let V (s) = 1/s.

Then Vo(s) = 1 +RCs 2 +RCs 1 s = 0.5 s + 0.5RC RCs+ 2. Taking the inverse Laplace transform yields vo(t) = 0.5(1 + e −2t/RC )u(t) where u(t) is the unit step function. A plot of vo(t) versus t/RC is shown in Figure AP4.6. 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 t / RC Vo FIGURE AP4.6 Step response. Solutions Manual to Accompany Modern Control Systems, Eleventh Edition, by Richard C Dorf and Robert H. ISBN-13: 298.

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise.

For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. 152 CHAPTER 4 Feedback Control System Characteristics AP4.7 (a) The transfer function from Td(s) to Y (s) is Y (s) Td(s) = 2s s(s+ 2) + 2K.

(b) The transfer function from N(s) to Y (s) is Y (s) N(s) = 2K s(s+ 2) + 2K. (c) Let Td(s) = A/s and N(s) = B/s.

Then, ess = −yss = lim s→0 s −2s s(s+ 2) + 2K A s + lim s→0 s −2K s(s+ 2) + 2K B s = −B. So, K has no effect on the steady-state errors.

However, choosing K = 100 will minimize the effects of the disturbance Td(s) during the transient period. AP4.8 (a) The closed-loop transfer function is T (s) = Kb s+Kb+ 1. (b) The sensitivity is determined to be STb = ∂T/T ∂b/b = s+ 1 s+Kb+ 1.

(c) The transfer function from Td(s) to Y (s) is Y (s) Td(s) = b s+Kb+ 1. So, choose K as large as possible, to make Y (s)/Td(s) as “small” as possible.

Thus, select K = 50. This also minimizes STb at low frequencies. Solutions Manual to Accompany Modern Control Systems, Eleventh Edition, by Richard C Dorf and Robert H. ISBN-13: 298.

Modern Control Systems Dorf

© 2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Design Problems 153 Design Problems The model of the traction drive, capstan roller, and linear slide was de-CDP4.1 veloped in CDP2.1: θ(s) Va(s) = Km s (Lms+Rm)(JT s+ bm) +KbKm.

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Modern Control Systems Dorf Bishop 12th Edition

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Modern Control Systems Dorf And Bishop

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