Pendekatan kalkulus variasional pada sistem kontrol daya dorong roket

Oleh :
Niken Madu Meta - M0103043 - Fak. MIPA

ABSTRAK Variational calculus is one of the calculus’ branch that can be used to de- termine a extrema value of a functional at a domain and or a contraint given. The function resulted in a extrema value is called extremal. Control system is a problem found in variasional calculus which can be optimized by choosing the control vector so that the performance index becomes minimized or maximized. The aims of the research are to solve the control systems of a rocket thrust in three cases, namely without air friction, with air friction, and for extremal that satisfy 0 ≤ u ≤ β(< 2g). The method used in this research is literature study. Based on discussions, the control systems of rocket thrust in the above three cases by order are (1) u0(t) = 3(h+gT2 2 )(T−t) T3 , (2) u0(t) = (h+g[T−1+e−T ])(1−e−(T−t)) T−3 2+2e−T−e−2T 2 , (3) u0(t) =      β , t < τ β(T−t) √T2−2h , t ≥ τ , with switch time τ = T − √T2 − 2h. Key words: variational calculus, optimal control system, rocket.