T 6ow2 w2[3o2 4Kt2J2

where o = (/-/,)//< 1, <pn = arctan"'[A:/,/i//w0(3o-/i2)], and we assume 6„=0.

The GEOS-3 design tradeoff can be seen by comparing Eqs. (18-73) and (18-75). Rapid transient response is obtained by decreasing t = 2I/kD. However,

'Without loss of generality, we assume that the spacecraft is traveling north at the Equator at /=0. fThe complementary solution to the pitch equation (i.e., for zero forcing terms) may be shown to be of the form

^,(0 = exp< - «A)l/t exp ((/») + Bexp( - ¡ft)] by substitution into Eq. (18-67).

the steady-state error is reduced by increasing r and I. Consequently, for GEOS-3, satisfactory steady-state performance was achieved at the cost of poor transient performance. The parameters were 7=2157 kg-m2, 0.012 N-m-s, and thus t=42 days and the root-mean-square steady-state pitch error was approximately 0.5 deg [Lerner and Coriell 1975]

The Laplace transform of the roll-yaw equations (Eq. (18-67)) may be written in matrix form as

Jts2+^-s + hu0
0 0

Post a comment