L2-1_stability

L2-1_stability - CDS 101/110a: Lecture 2.1 Dynamic Behavior...

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1 CDS 101/110a: Lecture 2.1 Dynamic Behavior Douglas G. MacMynowski 4 October 2010 Goals: Learn to use phase portraits to visualize behavior of dynamical systems Understand different types of stability for an equilibrium point Know the difference between local/global stability and related concepts Reading: Åström and Murray, Feedback Systems, Chapter 4 [90 minutes] Advanced: S. H. Strogatz, Nonlinear Dynamics and Chaos, Chapter 6 Modeling Terminology State captures effects of the past independent physical quantities that determines future evolution (absent external excitation) Not unique (e.g. units) u(t) q Inputs describe external excitation Inputs are extrinsic to the system dynamics (externally specified) Disturbances & control inputs Dynamics describes state evolution update rule for system state function of current state and any Example: spring mass system State: position and velocity of each c k 3 m 1 m 2 q 1 2 k 2 k 1 Douglas G. MacMynowski, Caltech CDS CDS 101/110, 29 Sep 10 2 external inputs Outputs describe measured quantities Outputs are function of state and inputs not independent variables Outputs are often subset of state mass: Input: position of spring at right end of chain: u ( t ) Dynamics: basic mechanics Output: measured positions of the masses:
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2 Sense Vehicle Speed Actuate Gas Pedal Dynamic Behavior (and Stability) Goal #1: Stability Check if closed loop response is stable system input control law Compute Control “Law” Douglas G. MacMynowski, Caltech CDS CDS 101/110, 4 Oct 10 3 Goal #2: Performance
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This note was uploaded on 01/04/2012 for the course CDS 101 taught by Professor Murray,r during the Fall '08 term at Caltech.

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L2-1_stability - CDS 101/110a: Lecture 2.1 Dynamic Behavior...

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