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.TH fusee 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
fusee - a set of Scilab macro for a landing rocket problem
.SH FUSEE
.nf
[xdot]=fusee(t,x)
.fi
Dynamical motion equation for the rocket
.SH FINIT
.nf
finit()
.fi
Initialises the following parameters for rocket landing.
.TP
k
: The acceleration of the rocket engines
.TP
gamma
: The moon gravity acceleration.
.TP
umax
: the gaz ejection flow out.
.TP
mcap
: the mass of the space capsule.
.TP
cpen
: penalisation in the cost function of the final state.
.LP
.SH FUSEEGRAD
.nf
[ukp1]=fuseegrad(niter,ukp1,pasg)
.fi
.TP
niter
: number of gradient iteration steps.
.TP
ukp1
: initial control value ( vector of sie 135 )
.TP
pasg
: the gradient step value.
.SH DESCRIPTION
Iterate a gradient method and returns the computed control.
.SH FUSEEP
.nf
[pdot]=fuseep(t,p)
.fi
.SH DESCRIPTION
adjoint equation for the landing rocket problem.
.SH POUSSE
.nf
[ut]=pousse(t)
.fi
return the value of a piece wise constant control
build on the discrete control \fVuk\fR
.SH UBANG
.nf
[uk]=ubang(tf,tcom)
.fi
returns a bang-bang control, 0 form time 0 to tcom
and 1 form tcom to tf.
.SH FCOUT
.nf
[c,xk,pk,ukp1]=fcout(tf,uk,pasg)
.fi
.SH DESCRITION
optimise the following cost function by gradient iterations.
.nf
c = -m(tf) + C*( h(tf)**2 + v(tf)**2)
.fi
.SH SFUSEE
.nf
[]=sfusee(tau,h0,v0,m0,Tf)
.fi
.SH DESCRIPTION
computes the rocket trajectory when a bang-bang control is used
\fVtau\fR is the commutation time.
.TP
h0
: The initial position (high)
.TP
v0
: The initial speed ( negative if the rocket is landing )
.TP
m0
: The total initial mass ( capsule and fuel).
.TP
Tf
: Time horizon.
.LP
.SH EQUAD
.SH DESCRIPTION
.nf
[xk,pk]=equad(tf,uk)
.fi
Computes the state and adjoint state of the rocket system for a given
control \fVur\fR.
.SH TRAJ
.nf
[xt]=traj(t)
.fi
returns a piece wise value of the mass evolution.
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