A note on systems with ordinary and impulsive controls

We investigate an everywhere defined notion of solution for control systems whose dynamics depend nonlinearly on the control $u$ and state $x,$ and are affine in the time derivative $\dot u.$ For this reason, the input $u,$ which is allowed to be Lebesgue integrable, is called impulsive, while a second, bounded measurable control $v$ is denominated ordinary. The proposed notion of solution is derived from a topological (non-metric) characterization of a former concept of solution which was given in the case when the drift is $v$-independent. Existence, uniqueness and representation of the solution are studied, and a close analysis of effects of (possibly infinitely many) discontinuities on a null set is performed as well.Comment: Article published in IMA J. Math. Control Infor

Discrete Model Reference Adaptive Control for Gimbal Servosystem of Control Moment Gyro with Harmonic Drive

The double-gimbal control moment gyro (DGCMG) demands that the gimbal servosystem should have fast response and small overshoot. But due to the low and nonlinear torsional stiffness of harmonic drive, the gimbal servo-system has poor dynamic performance with large overshoot and low bandwidth. In order to improve the dynamic performance of gimbal servo-system, a model reference adaptive control (MRAC) law is introduced in this paper. The model of DGCMG gimbal servo-system with harmonic drive is established, and the adaptive control law based on POPOV super stable theory is designed. The MATLAB simulation results are provided to verify the effectiveness of the proposed control algorithm. The experimental results indicate that the MRAC could increase the bandwidth of gimbal servo-system to 3 Hz and improve the dynamic performance with small overshoot

Characterization and Modeling of a Control Moment Gyroscope

The Air Force Research Laboratory (AFRL) is developing a spacecraft simulator that uses Control Moment Gyroscopes (CMGs). Prior to the research herein, the Air Force Institute of Technology (AFIT) designed and built six laboratory-rated CMGs for use on the AFRL spacecraft simulator. The main contributions of this research are in the testing and modeling of a single CMG. Designing, building, and operating spacecraft simulators is time consuming and expensive, but less so than tests with on-orbit spacecraft. Reductions in cost and schedule can be realized by investing in modeling the spacecraft simulator and payload before testing. A model of the spacecraft simulator was created in previous research efforts, but was an ideal model; it did not include dynamics based on real CMGs. The objective of this research is to characterize and model a single CMG to determine the effects the real CMG\u27s performance will have on the performance of the AFRL spacecraft simulator. The gimbal motor utilizes a planetary gearbox, which has gear lash of 5 deg . Gear lash makes the existence of gravitational disturbance torques noticeable in the gimbal angular position measurements. An analytical model of the CMG gimbal was created in MATLAB. The model predicts the nonlinear dynamic behavior of the real CMG. A model of the spacecraft simulator was run through a sequence of pointing commands to generate gimbal angle commands which were then used to command the CMG to evaluate the system\u27s performance under realistic conditions. Gear slack has a cumulative time delay effect on vehicle slew responses of approximately one second over five maneuvers. The results of the tests performed in this thesis can be used to predict performance of CMG and spacecraft simulator behavior

Controllability of spacecraft attitude using control moment gyroscopes

This paper describes an application of nonlinear controllability theory to the problem of spacecraft attitude control using control moment gyroscopes (CMGs). Nonlinear controllability theory is used to show that a spacecraft carrying one or more CMGs is controllable on every angular momentum level set in spite of the presence of singular CMG configurations, that is, given any two states having the same angular momentum, any one of them can be reached from the other using suitably chosen motions of the CMG gimbals. This result is used to obtain sufficient conditions on the momentum volume of the CMG array that guarantee the existence of gimbal motions which steer the spacecraft to a desired spin state or rest attitude.© IEE

Controllability of spacecraft attitude using Control Moment Gyroscopes

This technical note describes an application of nonlinear controllability theory to the problem of spacecraft attitude control using control moment gyroscopes (CMGs). Nonlinear controllability theory is used to show that a spacecraft carrying one or more CMGs Is controllable on every angular momentum level set In spite of the presence of singular CMG configurations, that Is, given any two states having the same angular momentum, any one of them can be reached from the other using suitably chosen motions of the CMG gimbals. This result is used to obtain sufficient conditions on the momentum volume of the CMG array that guarantee the existence of gimbal motions which steer the spacecraft to a desired spin state or rest attitude

Controllability of spacecraft attitude using control moment gyroscopes

This paper describes an application of nonlinear controllability theory to the problem of spacecraft attitude control using control moment gyroscopes (CMGs). Nonlinear controllability theory is used to show that a spacecraft carrying one or more CMGs is controllable on every angular momentum level set in spite of the presence of singular CMG configurations, that is, given any two states having the same angular momentum, any one of them can be reached from the other using suitably chosen motions of the CMG gimbals. This result is used to obtain sufficient conditions on the momentum volume of the CMG array that guarantee the existence of gimbal motions which steer the spacecraft to a desired spin state or rest attitude.© IEE

Design and analysis of zero cogging torque brusless DC motor for spaceeraft applications

Abstract Control moment gyroscopes (CMG) are used in modern satellite applications for attitude control of satellites References [1] S. P. Bhat and P. Tiwari, "Controllability of spacecraft attitude using control moment gyroscopes," IEEE Transactions on Automatic Control, vol. 54,NO. 3, pp. 585-590, March 2009. [2] R. P. Praven, "Design and analysis of zero cogging torque brusless DC motor for spaceeraft applications," Proc. International Conference ECTI-CON, pp. 254-258, May 2010