closed-loop_stability

# closed-loop_stability - Closed-Loop Stability 1. 2. 3. 4....

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Closed-Loop Stability 1. Motivating example 2. General stability criterion 3. Routh stability criterion 4. Direct substitution method 5. Summary 6. Simulink example

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Motivating Example Transfer functions Step response 1 1 1 2 1 1 5 1 + = + = + = = = s G s G s G G K G m v d p c c s K s s s s K Y G G G G G G G K Y c c sp m p v c p v c m 1 1 8 17 10 ) 1 ( 1 2 3 + + + + + = + =
Linear Stability Linear system stability » A linear system is stable if the output response is bounded for all bounded inputs. Otherwise the system is unstable. Open-loop stability » System that have poles with positive real part are unstable. » Integrating systems are unstable. The closed-loop stability problem » Determine the range of controller parameter values for which the closed- loop system.

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Closed-loop transfer function for setpoint changes Step response for distinct poles Characteristic equation ) ( ) ( 1 1 s D s N G G G G K G G G G G G G K Y Y c c OL p v c m m p v c p v c m sp = + = + = 0 ) ( 1 ) ( = + = s G s D OL c t p n t p t p n sp m p v c p v c m n e A e A e A A t y p s p s p s s s
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closed-loop_stability - Closed-Loop Stability 1. 2. 3. 4....

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