Download Digital Control Systems by Prof. Dr.-Ing. Rolf Isermann (auth.) PDF

By Prof. Dr.-Ing. Rolf Isermann (auth.)

ISBN-10: 3662023199

ISBN-13: 9783662023198

ISBN-10: 3662023210

ISBN-13: 9783662023211

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6-2) and Eq. 6-11) From Eq. 6-12) is also valid. Here xn(k+1) comes from Eq. 6-5), so finally we have (bn-boan)x 1 (k)+(bn_ 1 -b 0 an_ 1 lx 2 (k)+ ... +(b 1 -b 0 a 1 )xn(k)+b 0 u(k). 6-13) In vector notation, the extended output equation becomes y(k) = ((bn-boan) ... 6 State Variable Representation y(k) = ~T~(k) + du(k). e. for a non-jumping system, Eq. 6-15) y(k) Fig. 1 shows a block diagram in "regulator form" of the state representation for a difference equation directly taken from Eq. Eq. 6-5) and Eq.

1-9), then becomes -kT 0 s . 2-5) since x*(s+ivw 0 ) = x*(s) This can easily be shown by substituting s by s+ivw 0 in Eq. 2-4). 2-7) which means that x*(s) is repeated for all vw 0 . e. one strip in the s-plane, it is known completely. lementary strips for higher frequencies. 2 Sampling Theorem If the continuous signal x(t) is sampled with a small sample time T0 =Lt, the Laplace-trans form of the continuous signal, Eq. 1 a) Magnitude of the Fourier-transform of a continuous signal b) Magnitude of the Fourier-transform of a sampled signal c) Magnitude of the frequency response of an ideal bandpass filter 3.

6-5), so finally we have (bn-boan)x 1 (k)+(bn_ 1 -b 0 an_ 1 lx 2 (k)+ ... +(b 1 -b 0 a 1 )xn(k)+b 0 u(k). 6-13) In vector notation, the extended output equation becomes y(k) = ((bn-boan) ... 6 State Variable Representation y(k) = ~T~(k) + du(k). e. for a non-jumping system, Eq. 6-15) y(k) Fig. 1 shows a block diagram in "regulator form" of the state representation for a difference equation directly taken from Eq. Eq. 6-5) and Eq. 6-12). f. Fig. 2). 2 Block diagram of a first order vector difference equation 42 3.

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Digital Control Systems by Prof. Dr.-Ing. Rolf Isermann (auth.)


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