Tham khảo tài liệu 'model predictive control part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Predictive Control of Tethered Satellite Systems 233 T 1 m1 m2 mt .2 29 which accounts for the fact that the tether is modeled as stationary inside the deployer and is accelerated to the deployment velocity after exiting the deployer. This introduces a thrust-like term into the equations of motion which affects the value of the tether tension. The system gravitational potential energy is assuming a second order gravity-gradient expansion V m mm 2 1 3cos2 e cos2 f R 2R3 The Lagrangian may be formed as L 2m R2 R2i2 1 m l2 f2 i 6 cos2 f 1 m m2 mt mm mm 12 2 0 I 1 3cos e cos 2 m R 2 R3 v 30 31 Under the assumption of a Keplerian reference nondimensional equations of motion can be written as orbit for the center of mass the e 2 q 1 esini m1 m2 m A f tan f---- _2_ k Qq mm A 3 . sin e cos e 2 k m A2L2ri2 cos2 f 32 m-1 m2 m A L . 2 3 id Qf --- 2 2 f - e 1 cos2 e I sin f cosf ---- r k m Á2lịi2 2esini 2m1 m m A 2 A A . .VẦ k m1 m2 mt A 1 3cos2 e cos2 f 1 k m-ịi2Lr m2 mt m 2 e sin i f f - 2----- -----T k mm A 33 m2 mt è 0 T A f72 e 1 2 cos2 f 34 . mt where A l Lr is the nondimensional tether length Lr is a reference tether length T is the tether tension and d di . The generalized forces Qe and Qf are due to distributed forces along the tether which are typically assumed to be negligible. 3. Sensor models The full dynamic state of the tether is not directly measurable. Furthermore the presence of measurement noise means that some kind of filtering is usually necessary before directly using measurements from the sensors in the feedback controller. The following measurements are assumed to be available 1 Tension force at the deployer 2 Deployment rate 3 GPS position of the subsatellite. Models of each of these are developed in the subsections below. 234 Model Predictive Control Tension Model The tension force measured at the deployer differs from the force predicted by the control model due to the presence of tether oscillations and sensor noise. The magnitude and .
