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Mechatronic Systems, Simulation, Modeling and Control Part 8

Tham khảo tài liệu 'mechatronic systems, simulation, modeling and control part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 200 Mechatronic Systems Simulation Modelling and Control so that dim L a Nx 6 . In order to verify that this is the minimum number of actuators required to ensure STLC the Lie algebra is reinvestigated for each possible combination of controls. The resulting analysis as summarized in Table 2 demonstrates that the system is STLC from the systems equilibrium point at x0 0 given either two rotating thrusters in complementary semi-circle planes or fixed thrusters on opposing faces providing a normal force vector to the face in opposing directions and a momentum exchange device about the center of mass. For instance in considering the case of control inputs BFy BTz TMED Eq. 9 becomes x Í x g 1 X u g2 X U2 T -1. .-1. -1 IT .- 19 x4 x5 x6 0 0 0 10 0 0 m sx3 m cx3 JZL U1 10 0 0 0 0 Jz 1 u2 where u u1 u2 BFy BTZ e U2. The equilibrium point p such that f p 0 is p x1 x2 x3 0 0 0 T . The L a is formed by considering the associated distribution A x and successive Lie brackets as f f g 1 f f g 1 g 1 f g 1 g 2 f g 1 f f f g 1 g1 g 1 g2 f g 1 g2 g 1 g 1 g2 g 2 g 1 g 2 f f g 1 g2 g2 f g2 f f g2 g1 f g2 g2 f g2 f f f g2 f g 1 f g 1 The sequence can first be reduced by considering any bad brackets in which the drift vector appears an odd number of times and the control vector fields each appear an even number of times to include zero. In this manner the Lie brackets g1 f g 1 and g 2 f g 2 can be disregarded. By evaluating each remaining Lie bracket at the equilibrium point p the linearly independent vector fields can be found as g 1 0 0 0 -m 1sx3 m 1cx3 - Jz1l g 2 0 0 0 0 0 Jz-1 T f g 1 Vg 1 f - Vf g 1 m-1sx3 -m-1cx3 - J-1L 0 0 0 T f g2 Vg2 f - Vf g2 0 0 -Jz-1 0 0 0 T 20 f 1 V f Vff- f 0.0.0. m 1J 1cx . m 1J 1sx.01 g 1 g2 v g2 g 1 vg 1 g2 m Jz cx3 m Jz sx3 f f 11 v f f Vf f 1 2Lm-1 J-1cx .2Lm-1 J-1sx .0.0.0.01 g 1 g 1 V g 1 g 1 V g 1 g 1 2Lm Jz cx3 2Lm Jz sx3 0 0 0 0 201 Laboratory Experimentation of Guidance and Control of Spacecraft During On-orbit Proximity Maneuvers Therefore the