By Benjamin C. Kuo, Farid Golnaraghi

ISBN-10: 0471134767

ISBN-13: 9780471134763

Real-world applications--Integrates real-world research and layout purposes in the course of the textual content. Examples contain: the sun-seeker procedure, the liquid-level regulate, dc-motor keep an eye on, and space-vehicle payload keep watch over. * Examples and problems--Includes an abundance of illustrative examples and difficulties. * Marginal notes through the textual content spotlight small print.

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Additional info for Automatic Control Systems, 8th ed. (Solutions Manual)

Example text

479 e  (c) Characteristic equation: (d) ∆( s ) = s 2 + 80 . 65 s + 322 From the state equations we see that whenever there is to increase the effective value of Ra by (1 + K ) Rs . =0 . 58 Ra there is ( 1 + K ) Rs . Thus, the purpose of R is s This improves the time constant of the system. 18 θr. The equations are in the form of CCF with v as the input. 1434 e  −1 (b) (c) Characteristic equati on: 2 . 782 Eigenvalues: (d) ∆ ( s ) = s + 90 . 91 s + 818 Same remark as in part (d) of Problem 5-14.

B) S = [B AB ] = 0 d   1 − a  AB 1 −1 1  A B  = 1 −1 1    1 −1 1  The system is controllable for d ≠ 0. 5-35 (a) S = B 2 S is singular. The system is uncontrollable.

5-21(a)]: 0 1 0  A1 =  0 0 1     −3 −2 −1  State equations [Fig. 5 s −1 −1 −3 + 20 . 5 s X ( s) X (s) −2 − 20 . 5  (b) G (s) Y ( s) = Y (s) U ( s) = 10 s −3 = 10 s −3 + 20 1 + 4. 5 s A and B are in CCF X (s) −2 X (s) X (s) X ( s) = −4. 5  1 0 0  0  B=  0  1    0 (c) G (s) Y (s) = Y (s) U ( s) = 5s −2 State equations: = 5( s s(s X (s) + 1) + 2 )( s + 10 ) + 5s −3 X (s) = 5s −2 1 + 12 s + 5s −1 X (s) A and B are in CCF −3 + 20 s X (s) −2 X (s) = U ( s ) − 12 x& ( t ) = Ax ( t ) + B u ( t ) 54 s −1 X (s) − 20 s −2 X ( s) 0  0 1  A= 0 0 1    0 −20 −12  0  B = 0    1  A and B are in CCF (d) G ( s) = Y ( s) = Y (s ) U (s ) s −4 = ( 1 ) s ( s + 5) s + 2s + 2 X ( s) 2 X (s) = = U ( s) − 7s s −4 X (s ) −1 −2 1 + 7 s + 12 s + 10 s −1 −2 X ( s ) − 12 s X (s) −3 − 10 X (s ) s −3 State diagram: x& ( t ) = Ax ( t ) + B u ( t ) State equations: 0 0  0 1 0 0 1 0   A=  0 0 0 1  0 −10 −12 −7    0  0  B=   0  1    A and B are in CCF 5-24 (a) G (s) = Y (s) U ( s) = 10 s 3 + 8 .