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Systems Analysis and Control

Systems Analysis and ControlMatthew M. PeetArizona State UniversityLecture 21: Stability Margins and Closing the LoopOverviewIn this Lecture, you will learn:Closing the Loop Effect on Bode Plot Effect on StabilityStability Effects Gain Margin Phase Margin BandwidthEstimating Closed-Loop Performance using Open-Loop Data Damping Ratio Settling Time Rise TimeM. PeetLecture 21: Control Systems2 / 31 ReviewRecall: Frequency ResponseInput:u(t) =Msin( t+ )Output:Magnitude and Phase Shifty(t) =|G( )|Msin( t+ + G( ))02468101214161820 2 1 Simulation ResultsTime (sec)AmplitudeFrequency Response tosin tis given byG( )M. PeetLecture 21: Control Systems3 / 31 ReviewRecall: Bode PlotDefinition Bode Plotis a pair oflog-logand semi-logplots:1.

Bandwidth and Peak Time We can use the expression T p= ˇ! n p 1 2 to get! BW = ˇ T p p 1 2 q (1 2 2) + p 4 4 4 2 + 2 Given closed-loop and ! BW, we can nd …

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