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Instructor's Solutions Manual for Modern Control Systems, by Richard C. Dorf, Robert H. Bishop

By Richard C. Dorf, Robert H. Bishop

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Upper Saddle River, NJ. All rights reserved. This publication 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. , Upper Saddle River, NJ 07458. 19 (a) Noninverting op-amp circuit. (b) Voltage follower circuit. Z1 = ∞ (open circuit) and Z2 = 0. Therefore, the transfer function is Vo (s) Z1 = = 1.

B) Taking the Laplace transform yields (M1 s2 + b1 s + K1 )X1 (s) − K1 X2 (s) = b1 sX3 (s) −K1 X1 (s) + (M2 s2 + b2 s + K1 + K2 )X2 (s) = (b2 s + K2 )X3 (s) . (c) Let G1 (s) = K2 + b2 s G2 (s) = 1/p(s) G3 (s) = 1/q(s) G4 (s) = sb1 , where p(s) = s2 M2 + sf2 + K1 + K2 and q(s) = s2 M1 + sf1 + K1 . , Upper Saddle River, NJ. All rights reserved. This publication 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.

25 Exercises where A is very large. We have the relationship R1 vo . 6 vin . AR1 R1 +R2 . Then the expression for R1 + R2 vin . R1 Given y = f (x) = ex and the operating point xo = 1, we have the linear approximation y = f (x) = f (xo ) + ∂f ∂x x=xo (x − xo ) + · · · where df dx f (xo ) = e, = e, x=xo =1 and x − xo = x − 1. Therefore, we obtain the linear approximation y = ex. 7. 7 Block diagram model. , Upper Saddle River, NJ. All rights reserved. This publication 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.

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