Answer Happy

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4. A simplified model of an axial compressor, used in jet engine control studies, is given by the following second order system 3 0 1 = Ø2 2 03 2 2 = 1 (0 + 1 – u). B2 This model captures the main surge instability between the mass flow and the pressure rise. Here, and 4 are deviations of the mass flow and the pressure rise from their set points, the control input u is the flow through the throttle, and ß is positive constant. (a) Use backstopping to obtain a control law that stabilizes the origin (0,0) = 0. (b) Use Sontag's Formula and the Control Lyapunov Function obtained in part (a) to obtain an alternative control law.