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Mechatronic Systems, Simulation, Modeling and Control 2012 Part 7

Tham khảo tài liệu 'mechatronic systems, simulation, modeling and control 2012 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 194 Mechatronic Systems Simulation Modelling and Control Fig. 3. SRL s 2nd Generation Spacecraft Simulator Schematic The translation and attitude motion of the simulator are governed by the equations X V V m-11 Rb ụ B F ụ y yz - bT 1 where B F e R2 are the thruster inputs limited to the region n 2 with respect to each face normal and bT e R is the attitude input. 1 Rb ụ B F and bT are given by cụ - sụ sụ cụ B FT B fT B F2T -F1ca1 F2ca2 -F1sa1 F2sa2 T bT _TMed L -F1s 1 - F2s 2 where s sin c cos . The internal dynamics of the vectorable thrusters are assumed to be linear according to the following equations 1 Rb ụ 2 3 4 P1 1-1T1 2 Pl à --1T2 5 where 1 and 2 represent the moments of inertia about each thruster rotational axis respectively and T1 e R T2 e R represent the corresponding thruster rotation control input. The system s state equation given by Eq. 1 can be rewritten in control-affine system form as LaValle 2006 195 Laboratory Experimentation of Guidance and Control of Spacecraft During On-orbit Proximity Maneuvers N. x f x wigi x f x G x u x e RN 6 i 1 where Nu is the number of controls. With RNx representing a smooth Nx -dimensional manifold defined be the size of the state-vector and the control vector to be in . Defining the state vector x e R10 as xT x1 x2 . x10 X Y a1 a2 Vx Vy ax 1 2 and the control vector u e U5 as uT w1 w2 . w5 fj F2 TMED T1 T2 the system s state equation becomes x f x G x u x6 x7 x8 x9 X10 01x5 T 05x5 G1 x . 7 u where the matrix G1 x is obtained from Eq. 1 as -m 1 cx3cx4 - sx3 s x4 m 1 cx3cx5 -sx3sx5 0 0 0 -m-1 c x3s x4 s x3 c x4 m-1 c x3s x5 s x3c x5 0 0 0 G1 x -L-1s xi -J s x5L J-1 0 0 8 0 0 0 J 0 L 0 0 0 0 J-. With the system in the form of Eq. 6 given the vector fields in Eqs. 7 and 8 and given that f x the drift term and G x the control matrix of control vector fields are smooth functions it is important to note that it is not necessarily possible to obtain zero velocity due to the influence of the drift term. This fact places .