SPRING 2010

即時控制系統設計Design of Real-Time Control Systems

Lecture 23Dynamic Analysis of Digital Control Systems

Feng-Li LianNTU-EE

Feb10 – Jun10

NTUEE-RTCS23-DTAnalysis-2Feng-Li Lian © 2010Outline

Analysis of Discrete-Time Control Systems• By Transform methods (by transfer function)

– Poles, Zeros– Stability– Transient Response, Steady-State Response– Impulse/step response– Root locus, Bode plot

• By State-Variable methods (by state-space model)– CT -> DT– Linear, Nonlinear– Stability analysis, Sensitivity Analysis– Controllability, Observability

• The z-transform

• Relationship between s and z

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Laplace transform:

z-Transform:

Franklin et al. 2002

NTUEE-RTCS23-DTAnalysis-4Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems

Analysis of discrete systems by the z-transform:

Franklin et al. 2002

NTUEE-RTCS23-DTAnalysis-5Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems

The z-transform inversion:• Long division

Franklin et al. 2002

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The z-transform inversion:• The z-transform table

Oppenheim et al. 1997

NTUEE-RTCS23-DTAnalysis-7Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems

Franklin et al. 2002

NTUEE-RTCS23-DTAnalysis-8Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems

Franklin et al. 2002

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Properties of the z-transform:

Astrom & Wittenmark 1997

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Properties of the z-transform:

Oppenheim et al. 1997

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Relationship between s and z:

Franklin et al. 2002

NTUEE-RTCS23-DTAnalysis-12Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems

Relationship between s and z:

Franklin et al. 2002

NTUEE-RTCS23-DTAnalysis-13Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems

Relationship between s and z:

Franklin et al. 2002

NTUEE-RTCS23-DTAnalysis-14Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems

Relationship between s and z:

Franklin et al. 2002

NTUEE-RTCS23-DTAnalysis-15Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems

Relationship between s and z:

Franklin et al. 2002

NTUEE-RTCS23-DTAnalysis-16Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems

Franklin et al. 2002

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Relationship between s and z:

Ogata 1995

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Final Value Theorem:

Franklin et al. 2002