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Explore phase-variable, controllable, observable, and diagonal & Jordan canonical forms in modern control systems. Learn how to model differential and dynamical equations using transfer functions in control system design. This lecture includes examples and remarks on these canonical forms and Jordan blocks.
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Lecture 4 Modeling (iii) –canonical forms 4.1 Phase-variable canonical form 4.2 Controllable canonical form 4.3 Observable canonical form 4.4 Diagonal & Jordan canonical form
Differential equation Dynamical equation or Transfer function Modern Control Systems
Phase-variable canonical form Modern Control Systems
… ∫ ∫ ∫ ∫ ＋ ＋ Modern Control Systems
Example 1 Modern Control Systems
controllable canonical form Modern Control Systems
… … ∫ ∫ ∫ ∫ ＋ ＋ ＋ Modern Control Systems
… ∫ ∫ ∫ ∫ + ＋ ＋ Modern Control Systems
Example 2 Answer 2 Modern Control Systems
observable canonical form Modern Control Systems
… ∫ ∫ ∫ … + + + + … Modern Control Systems
Example 3 Remark Modern Control Systems
Diagonal & Jordan canonical form Modern Control Systems
+ + + + Modern Control Systems
Jordan block Modern Control Systems
Example 4 Modern Control Systems
