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aileron aircraft algorithm altitude automatic landing system BODE PLOT closed-loop system command design model command model command vector commanded path commanded trajectory complementary filter constant command control commands control law design control structure control system desired glideslope desired trajectory digital automatic landing dynamic compensation eigenvalues eigenvector equations feedback control design feedback control law feedback vector feedforward and feedback feedforward control gains feedforward control law FIGURE flare forcing vector full state feedback given by Eq glideslope capture I I I incremental implementation initial Langley Research Center linear longitudinal longitudinal/vertical loop Lyapunov equations NASA necessary conditions NONLINEAR SIMULATION noted obtained open-loop plant optimal control perfect tracking plant design model plant model selected stochastic feedforward stochastic optimization stochastic output feedback touchdown transition matrix variables velocity vertical position white noise zero