Steering the Control Moment Gyroscope Clusters Onboard High-Agile Spacecraft *

Satellite Guidance and Control During Operative Optoelectronic Imagery for Disaster Management

“…Then the error quaternion is E = (e0, e) =Λ p •Λ, Euler parameters' vector is E = {e0, e}, the error's matrix is C e ≡ C(E E E) = I3 − 2[e×]Q t e with matrix Qe = I3e0 +[e×], the error's vector is δφ = {δφi} = 2e0e, and error δω={δωi} is defined as δω = ω − C e ω p . Angular mismatch vector l = −δφ l , l ∈ N0, is filtered with period Tp and then the vector values f k are applied in the developed digital control law for the GD cluster (Somov et al, 2005)…”

“…where C e k = C(E k ), G o k = Jω k + H k and for du ≡ 2/Tu, ai ≡ (duτ1i − 1)/(duτ1i + 1) elements of diagonal matrices K = diag(ki), B, C and P are computed by the relations bi ≡ (duτ2i−1)/(duτ2i +1); pi ≡ (1−bi)/(1−ai); ci ≡ pi(bi−ai) with adaptive-robust tuning the parameters τ1i, τ2i and ki. The GMC control torque vector M g k (10) is "re-calculated" into vector u g k of the GD commands using explicit function of the AM distribution between four gyrodines (Somov et al, 2005). These commands are fixed at the current step of digital control with period Tu.…”