Automatic Control Basic Course Exercises 10

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Automatic Control Basic CourseExercises - 10

• Torbjörn Nordling
• Automatic Control School of Electrical
  Engineering
• The Royal Institute of Technology (KTH)
• www.ee.kth.se/tn/Teaching/

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Controllability Observability

• A state x is controllable if an input u,
  which brings the system from the origin to x in
  finite time exists

A state x?0 is unobservable if the output is
y0 even though the input is u0
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Task 8.10

• Controllability
• Observability
• Minimal realisation
• Range
• Nullspace

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Contr. Observ. motivation

• Discretization (ZOH
  
  )
• Linear algebra

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Controllability motivation

• Uncontrol-lable state x

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Observability motivation

Unobservable state x
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Range and nullspace

• Beta p. 110

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8.10 a) Original Block diagram
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State space descriptions
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8.10 a) Transformed Block diagram
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8.10 a) Transfer function

• Non-minimal realisation
• Minimal realisation

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Task 9.1

• State feedback
• Observer

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Block diagram
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State Feedback
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Closed loop system
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Observer
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Task 8.13

• State space description
• Linearization
• Controllability (in practice)
• det(A)?1?2?n