Automatic Control in Aerospace 1994 (Aerospace Control '94). by D. Schaechter, K.R. Lorell

By D. Schaechter, K.R. Lorell

A massive, profitable region for keep an eye on structures improvement is that of cutting-edge aeronautical and area comparable applied sciences. top researchers and practitioners inside of this box were given the chance to replace rules and speak about effects on the IFAC symposia on automated keep watch over in aerospace. the major examine papers awarded on the most up-to-date within the sequence were prepare during this book to supply an in depth review of current and destiny advancements of those regulate method applied sciences

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Extra info for Automatic Control in Aerospace 1994 (Aerospace Control '94). A Postprint Volume from the IFAC Symposium, Palo Alto, California, USA, 12–16 September 1994

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R4 ri (11) 3. O P E N - L O O P T R A J E C T O R Y T h e open-loop trajectory is computed first. 1 Spiral For motion only in the ecliptic plane, Eqn. 2 can be denoted in state space form where = [χ, y, ix, v]T, (13) u i a. (14) Segment T h e spiral segment is computed by increasing the spacecraft energy relative to E a r t h as fast as possible to reach near-escape conditions. 2 Transition Control (15) The cost function is the transfer time: / at. (16) Jto All the initial and the terminal states are prescribed so the necessary conditions of optimality are as follows: X = f(x,u,t), (17) λ = -H„ (18) j (19) χ ( ί β) x(tj) = a H(tj) — Xo /> X arg m a x Η, a (21) = 0, (22) arg m a x E, α (25) Segment Since the shooting method has a smaller number of unknowns than the gradient method, it was used first in the trial and error stage.

Whenever φ G (-π/2, π / 2 ) , Sc converges exponentially to the optimum value δ* with time constant 2/KA2 rcos(cp). Important properties can be derived from the above analysis— ( P I ) In the average 6 C tends exponentially to its optimal value δ* for wide ranges of φ, Κ, and Γ . /(δ) δ(0 = 7(δ*) + ΐ Γ ( δ - δ * ) = Sc(t) (3) + Asin ( ω 0 0 (4) bc = - K 7 ( 6 ( f ) M s i n ( c » y - < P ) ; δ,(0) (P2) Biases on the measurements do not affect this result because, from Eqs. ( 6 ) to ( 8 ) , their averaged effect on Eq.

6, pp. 5 1 8 - 5 2 5 . Zhukov, A. N. and V. N. Lebedev ( 1 9 6 4 ) . Variational Problem of Transfer Between Heliocentric Circular Orbits by Means of a Solar Sail. Translated from Kosmicheskie Issledovaniya, Vol. 2, No. 1, J a n - F e b , pp. 4 5 - 5 0 . Breakwell, J . V. and Η. E . Rauch ( 1 9 6 6 ) . Optim u m Guidance for a Low T h r u s t Interplanetary Vehicle. AIAA Journal, April, pp. 6 9 3 704. Bryson, A. E . J r . and Y . C. Ho ( 1 9 7 5 ) . Applied Optimal Control, Hemisphere, Washington.

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