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ExercisesWk78

# ExercisesWk78 - CALIFORNIA INSTITUTE OF TECHNOLOGY Control...

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CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems CDS 140b R. M. Murray Winter 2008 Problem Set, Weeks 7–8 Issued: 26 Feb 08 Due: 6 Mar 08 The Moore-Greitzer equations model rotating stall and surge in gas turbine engines describe the dynamics of a compression system, such as those in gas turbine engines. The three-state “MG3” equations have the form: dt = 1 4 B 2 l c ( φ - Φ T ( ψ )) , dt = 1 l c parenleftbigg Φ c ( φ ) - ψ + J 8 2 Ψ c ∂φ 2 parenrightbigg , dJ dt = 2 μ + m parenleftbigg Φ c ∂φ + J 8 3 Φ c ∂φ 3 parenrightbigg J, where ψ represents the pressure rise across the compressor, φ represents the mass flow through the compressor and J represents the amplitude squared of the first modal flow perturbation (cor- responding to a rotating stall disturbance). For the Caltech compressor rig, the parameters and characteristic curves are given by: B = 0 . 2 , Φ T ( ψ ) = γ radicalbig ψ, l c = 6 , Ψ c ( φ ) = 1 + 1 . 5 φ - 0 . 5 φ 3 , μ = 1 . 25 , m = 2 .
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