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problem10

# problem10 - EE221A Linear System Theory Problem Set 10...

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EE221A Linear System Theory Problem Set 10 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2010 Issued 12/2; Due 12/9 Problem 1: Controllability and Observability. An approximate linear model of the longitudinal dynamics of a certain aircraft, for a particular set of flight conditions, has the linearized state and control vectors: x = v α θ q u = bracketleftbigg δ μ bracketrightbigg (1) where v represents the change in forward velocity, α the change in angle of attack, θ the change in pitch angle, and q the change in pitch rate. The two inputs are δ , the deflection of the elevators, and μ , the throttle position. The state space equation for this model is ˙ x = Ax + Bu where A = - 0 . 045 0 . 036 - 32 - 2 - 0 . 4 - 3 - 0 . 3 250 0 0 0 1 0 . 002 - 0 . 04 0 . 001 - 3 . 2 B = 0 0 . 1 - 30 0 0 0 - 10 0 (2) (a) Suppose a malfunction prevents manipulation of the input δ . Is it possible to completely control the aircraft using only μ ? Only δ ?

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problem10 - EE221A Linear System Theory Problem Set 10...

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