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Time Response Analysis: Stability and Transient Behavior in Continuous and Discrete Systems

Explore stability criteria, pole locations, and system characteristics in both continuous and discrete time domains. Understand the correlations between s-plane and z-plane pole locations for system design and analysis.

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Time Response Analysis: Stability and Transient Behavior in Continuous and Discrete Systems

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  1. EEM 464 Time ResponsesandDiscreteRootLocus

  2. StabilityandTransientResponse • ContinuousSystems • Polelocations in thes-plane • A system is stablewhenallpolesarelocatedtotheleft of theimaginaryaxis

  3. DiscreteSystems • Polelocations in thez-plane • Thecharecteristics in the z-planecan be relatedtothose in thes-planebytheexpression z=esT T: Sampling time (sec/sample) s=Location in the “s-plane” z=Location in the “z-plane”

  4. TheEquationsUsed in SystemDesign ξ= Damping Ratio ωn=Natural Frequency (rad/sec) Ts=Settling Time Tr=Rise Time Mp =Maximum Overshoot

  5. Example : Considerthefollowingdiscrete transfer function MatlabCode:

  6. T=1/20

  7. Add the following commands to the above code and rerun

  8. Discrete Rooth-Locus • The characteristic equation of an unity feedback system 1+KG(z)Hzoh(z)=0 • Example:

  9. Matlab Code:

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