SPRING 2010 即時控制系統設計 Design of Real-Time Control Systems Lecture 23 Dynamic Analysis of Digital Control Systems Feng-Li Lian NTU-EE Feb10 – Jun10 NTUEE-RTCS23-DTAnalysis-2 Feng-Li Lian © 2010 Outline 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 NTUEE-RTCS23-DTAnalysis-3 Feng-Li Lian © 2010 Dynamic Analysis of Discrete Systems Laplace transform: z-Transform: Franklin et al. 2002 NTUEE-RTCS23-DTAnalysis-4 Feng-Li Lian © 2010 Dynamic Analysis of Discrete Systems Analysis of discrete systems by the z-transform: Franklin et al. 2002
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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
NTUEE-RTCS23-DTAnalysis-3Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems
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
NTUEE-RTCS23-DTAnalysis-6Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems
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
NTUEE-RTCS23-DTAnalysis-9Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems
Properties of the z-transform:
Astrom & Wittenmark 1997
NTUEE-RTCS23-DTAnalysis-10Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems
Properties of the z-transform:
Oppenheim et al. 1997
NTUEE-RTCS23-DTAnalysis-11Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems
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
NTUEE-RTCS23-DTAnalysis-17Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems
Relationship between s and z:
Ogata 1995
NTUEE-RTCS23-DTAnalysis-18Feng-Li Lian © 2010Dynamic Analysis of Discrete Systems
Final Value Theorem:
Franklin et al. 2002
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