Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then...

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Solving Difference Equations and Inverse Z Transforms ME2025 Digital Control Jee-Hwan Ryu School of Mechanical Engineering Korea University of Technology and Education

Transcript of Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then...

Page 1: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,

Solving Difference Equations and Inverse Z Transforms

ME2025 Digital Control

Jee-Hwan Ryu

School of Mechanical Engineering

Korea University of Technology and Education

Page 2: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 3: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 4: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 5: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 6: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 7: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 8: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 9: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 10: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 11: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 12: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,

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Page 13: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 14: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,
Page 15: Solving Difference Equations and Inverse Z Transformsiris.kaist.ac.kr/download/lec_7.pdf · Then use tables to invert the z-transform, e.g. agu[n] z—a Ex. Given a difference equation,

Generalized Social Marginal Welfare Weights for Optimal Tax ......R i w iu ci dT(z i) = R i g idT(z i). ChangeintaxpaidperpersonisdT(z i)+T0(z i)dz i. Definition AreformdT(z) isbudgetneutralifandonlyif

Generalized Social Marginal Welfare Weights for Optimal Tax ......R i w iu ci dT(z i) = R i g idT(z i). ChangeintaxpaidperpersonisdT(z i)+T0(z i)dz i. Definition AreformdT(z) isbudgetneutralifandonlyif

Μετασχηματισμός Z

Μετασχηματισμός Z

Difference Sets - Mathematical and Statistical Scienceswcherowi/courses/m6406/diffsets.pdf · The (7,3,1)-difference set {0,1,3} produces the Fano plane with blocks 013, 124, 235,

Difference Sets - Mathematical and Statistical Scienceswcherowi/courses/m6406/diffsets.pdf · The (7,3,1)-difference set {0,1,3} produces the Fano plane with blocks 013, 124, 235,

[Presented at AGU-2004 AE23A-0833] R. Sonnenfeld, J ...kestrel.nmt.edu/~rsonnenf/atmospheric/Pubs/AGUPamphlet2.pdf · shaped damper 2.0, made of rip-stop nylon kept the sonde well

[Presented at AGU-2004 AE23A-0833] R. Sonnenfeld, J ...kestrel.nmt.edu/~rsonnenf/atmospheric/Pubs/AGUPamphlet2.pdf · shaped damper 2.0, made of rip-stop nylon kept the sonde well

Construction of LDPC convolutional codes via difference ...

Construction of LDPC convolutional codes via difference ...

Reinforcement Learning Lecture Temporal Difference Learning

Reinforcement Learning Lecture Temporal Difference Learning

Z V I J E Z D E (2 . dio)

Z V I J E Z D E (2 . dio)

(with and without B)€¦ · Concept in MHD turbulence z– z+ B 0 The main difference between neutral fluids and MHD is the presence of Alfvén waves Wavepackets interact nonlinearly

(with and without B)€¦ · Concept in MHD turbulence z– z+ B 0 The main difference between neutral fluids and MHD is the presence of Alfvén waves Wavepackets interact nonlinearly

Difference Bound Matrices

Difference Bound Matrices

Bs Mixing, Lifetime Difference and Rare Decays at Tevatron

Bs Mixing, Lifetime Difference and Rare Decays at Tevatron

Z Νεο ΦΥΛΛΑΔΙΟ

Z Νεο ΦΥΛΛΑΔΙΟ

Ohms Law V = IRV = IR V = voltage in volts (aka potential difference)V = voltage in volts (aka potential difference) I = Current in ampsI = Current in.

Ohms Law V = IRV = IR V = voltage in volts (aka potential difference)V = voltage in volts (aka potential difference) I = Current in ampsI = Current in.

Differential Groups and the Gamma FunctionDifferential Galois Theory of Linear Difference Equations Differential Relations Among Solutions of Linear Difference Equations Final Comments

Differential Groups and the Gamma FunctionDifferential Galois Theory of Linear Difference Equations Differential Relations Among Solutions of Linear Difference Equations Final Comments

Distribución Normal Z

Distribución Normal Z

Difference Set Transfers - Cornell Universitypi.math.cornell.edu/~djp282/documents/nums-2013.pdfDifference Sets Definition A (v;k; )-difference set is a subset D of a group G such

Difference Set Transfers - Cornell Universitypi.math.cornell.edu/~djp282/documents/nums-2013.pdfDifference Sets Definition A (v;k; )-difference set is a subset D of a group G such

Finite Difference vs. Discontinuous Galerkin: … Difference vs. Discontinuous Galerkin: ... (stuck with Matlab for DG code) ... Estimated convergence rates for 2-2 and 2-4 FD methods.

Finite Difference vs. Discontinuous Galerkin: … Difference vs. Discontinuous Galerkin: ... (stuck with Matlab for DG code) ... Estimated convergence rates for 2-2 and 2-4 FD methods.

The z Transform - UTKweb.eecs.utk.edu/~hli31/ECE316_2015_files/Chapter9.pdf · Existence of the z Transform! The z transform of x[n]=αnun−n [0], α∈ is X(z)=αnun−n [0]z−n

The z Transform - UTKweb.eecs.utk.edu/~hli31/ECE316_2015_files/Chapter9.pdf · Existence of the z Transform! The z transform of x[n]=αnun−n [0], α∈ is X(z)=αnun−n [0]z−n

5054415D003 Ixengo L - Somfy · 2015. 6. 17. · P1: Z = 78 mm P9: Z = 203 mm P2: Z = 90 mm P10: Z = 215 mm P3: Z = 102 mm P11: Z = 227 mm P4: Z = 114 mm P12: Z = 239 mm P5: Z = 155

5054415D003 Ixengo L - Somfy · 2015. 6. 17. · P1: Z = 78 mm P9: Z = 203 mm P2: Z = 90 mm P10: Z = 215 mm P3: Z = 102 mm P11: Z = 227 mm P4: Z = 114 mm P12: Z = 239 mm P5: Z = 155

Ilias Rapsodia z

Ilias Rapsodia z

Batenburg agu 2012_11_26

Batenburg agu 2012_11_26