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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. Magnitude Plot:20 log10|G( )| 2. Phase Plot: G( ) Bite-Size Chucks: G( )= i Gi( )M.

Review Recall:Frequency Response Input: u(t) = Msin(!t+ ˚) Output: Magnitude and Phase Shift y(t) = jG({!)jMsin(!t+ ˚+ \G({!)) 0 2 4 6 8 10 12 14 16 18 20-2-1.5-1-0.5 0 0.5 1 1.5 2 2.5 Linear Simulation Results Time (sec) Amplitude Frequency Response to sin!tis given by G({!) M. Peet Lecture 21: Control Systems 3 / 31

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