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Systems Analysis and Control

Systems Analysis and ControlMatthew M. PeetArizona State UniversityLecture 10: Routh-Hurwitz Stability CriterionOverviewIn this Lecture, you will learn:The Routh-Hurwitz Stability Criterion: Determine whether a system is stable. An easy way to make sure feedback isn t destabilizing Construct the Routh TableM. PeetLecture 10: Control Systems2 / 28A Stability TestWe know that for a system with Transferfunction G(s) =n(s)d(s)Input-Output Stability implies that all roots ofd(s)are in the Left Half-PlaneIAll have negative real (s)Re(s)CRHPQ uestion:How do we determine if all roots ofd(s)have negative real part?Example: G(s) =s2+s+ 1s4+ 2s3+ 3s2+s+ 1M.

To improve performance, we close the loop with a gain of 1000 Controller: K^(s) = 1000 The Closed-Loop Transfer Function is 1000 s3 +10s2 +31s+1030 Question: Have we destabilized the system? M. Peet Lecture 10: Control Systems 14 / 28

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Systems Analysis and Control

control.asu.edu

The Quadratic Approximation gives the Closed-Loop Damping Ratio as M = tan 1 q 2 2 2 + p 4 4 + 1 M is from the Open-Loop Data! A Handy approximation is = M 100 Only valid out to ˘=:7. Given M, we nd closed-loop . M. Peet Lecture 21: Control Systems 17 / 31

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Partial Fractions - Lecture 7: The Partial Fraction Expansion

control.asu.edu

Partial Fractions Matthew M. Peet Illinois Institute of Technology Lecture 7: The Partial Fraction Expansion. ... Expansion using single poles Repeated Poles Complex Pairs of Poles I Inverse Laplace M. Peet Lecture 7: Control Systems 2 / 27. Recall: The Inverse Laplace Transform of a Signal To go from a frequency domain signal, u^(s), to the ...

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Spacecraft and Aircraft Dynamics

control.asu.edu

Using Calculus, this concept can be extended to rigid bodies by integration over all particles. M~ = X i M~ i = d dt H~ Definition 3. Where H~ = R (~rc ×~vc)dmis the angular momentum. Angular momentum of a rigid body can be found as H~ =Iω I where ωI =[p,q,r]T is the angular rotation vector of the body about the center of mass. • pis ...

  Dynamics, Rigid, Body, Rigid body

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