State Equations for a Spacecraft With Maneuvering Flexible Appendages in Terms of Quasi-Coordinates

1989 ◽  
Vol 42 (11S) ◽  
pp. S161-S170 ◽  
Author(s):  
L. Meirovitch ◽  
M. K. Kwak
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Control Design ◽  
The State ◽  
Distributed Parameter ◽  
Main Body ◽  
State Equations ◽  
And Control ◽  
Hybrid Equations ◽  
Flexible Appendages

This paper is concerned with the derivation of the state equations of motion for a spacecraft consisting of a main rigid platform and a given number of flexible appendages changing the orientation relative to the main body. The equations are derived by means of Lagrange’s equations in terms of quasi-coordinates. Assuming that the appendages represent distributed-parameter members, the state equations of motion are hybrid. Moreover, they are nonlinear. Following spatial discretization and truncation, the hybrid equations reduce to a system of nonlinear discretized state equations, which are more practical for numerical calculations and control design. To illustrate the effect of nonlinearity on the dynamic response during reorientation, a numerical example involving spacecraft with a membrane-like antenna is presented.

scholarly journals Fast Attitude Maneuver of a Flexible Spacecraft with Passive Vibration Control Using Shunted Piezoelectric Transducers

2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Bassam A. Albassam
Keyword(s):  
Differential Equations ◽  
Electromechanical Coupling ◽  
Design Method ◽  
Equations Of Motion ◽  
Control Design ◽  
Piezoelectric Transducers ◽  
Control Input ◽  
Attitude Maneuver ◽  
Shunt Circuit ◽  
Flexible Appendages

This paper is concerned with designing a bang-bang control input to perform a quick rotational maneuver of a rigid spacecraft hub connected with flexible appendages. The control design is based on only the rigid body mode making it very simple to design and at the same time achieve the quickest maneuver possible. The induced vibrations are suppressed using piezoelectric transducers bonded to the appendages and connected to an electric circuit with the objective of converting the vibrational energy to electrical energy and then dissipating it using passive electric elements, such as a resistance and an inductor. The proposed control design method is applied to a spacecraft containing a rigid hub and flexible appendages. The attitude control torque is produced using either the reaction wheels contained inside the rigid hub or jet thrusters mounted outside it. The control design process starts with deriving the nonlinear partial differential equations of motion for the spacecraft using Hamilton’s principle which accounts for the electromechanical coupling and the presence of resistive or resistive-inductive circuits. To simplify the analysis, the nonlinear ordinary differential equations of motion are then obtained using the assumed mode method. The effectiveness of the control design method is numerically tested on a spacecraft that is required to perform a quick attitude maneuver and, simultaneously, suppress the induced vibrations. The simulations show a quick and accurate maneuver has been achieved combined with very low levels of vibrations resulting from the reduced coupling between flexible and rigid motions as well as the damping added as a result of the passive shunt circuit. Furthermore, the resistance-inductance shunt circuit is shown to be more effective in damping the vibrations than the resistance shunt circuit.

scholarly journals On modelling and control design for self-balanced two-wheel vehicle

2008 ◽  
Vol 30 (3) ◽  
Author(s):  
Nguyen Hoang Quang
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Mobile Robot ◽  
Equations Of Motion ◽  
Control Design ◽  
Modeling And Control ◽  
Linearized Equations ◽  
Stable Motion ◽  
Simulation Results ◽  
And Control

In this paper, the modeling and control design of a self-balancing mobile robot are presented. The method of sub-structures is employed to derive the differential equations of motion of the robot. Based on the linearized equations of motion, a controller is designed to maintain a stable motion of the robot. Some numerical simulation results are shown to clarify the designed controller.

Lyapunov Functions and Sliding Mode Control for Two Degrees-of-Freedom and Multidegrees-of-Freedom Fractional Oscillators

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Youan Zhang ◽  
Jian Yuan ◽  
Jingmao Liu ◽  
Bao Shi
Keyword(s):  
Differential Equations ◽  
Sliding Mode Control ◽  
Lyapunov Functions ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Control Design ◽  
State Equations ◽  
Two Degrees Of Freedom ◽  
Mode Control

This paper addresses the Lyapunov functions and sliding mode control design for two degrees-of-freedom (2DOF) and multidegrees-of-freedom (MDOF) fractional oscillators. First, differential equations of motion for 2DOF fractional oscillators are established by adopting the fractional Kelvin–Voigt constitute relation for viscoelastic materials. Second, a Lyapunov function candidate for 2DOF fractional oscillators is suggested, which includes the potential energy stored in fractional derivatives. Third, the differential equations of motion for 2DOF fractional oscillators are transformed into noncommensurate fractional state equations with six dimensions by introducing state variables with physical significance. Sliding mode control design and adaptive sliding mode control design are proposed based on the noncommensurate fractional state equations. Furthermore, the above results are generalized to MDOF fractional oscillators. Finally, numerical simulations are carried out to validate the above control designs.

Lifting the Veil

2014 ◽  
Vol 91 (4) ◽  
pp. 43-55
Author(s):  
Scott Pittman
Keyword(s):  
Los Angeles ◽  
State Government ◽  
The State ◽  
University Of California ◽  
Red Scare ◽  
National Archives ◽  
The Veil ◽  
Hiring And Firing ◽  
And Control ◽  
California Schools

The story of anti-communism in California schools is a tale well and often told. But few scholars have appreciated the important role played by private surveillance networks. This article examines how privately funded and run investigations shaped the state government’s pursuit of leftist educators. The previously-secret papers of Major General Ralph H. Van Deman, which were opened to researchers at the National Archives in Washington, D.C., only a few years ago, show that the general operated a private spy network out of San Diego and fed information to military, federal, and state government agencies. Moreover, he taught the state government’s chief anti-communist bureaucrat, Richard E. Combs, how to recruit informants and monitor and control subversives. The case of the suspicious death of one University of California, Los Angeles student – a student that the anti-communists claimed had been “scared to death” by the Reds – shows the extent of the collaboration between Combs and Van Deman. It further illustrates how they conspired to promote fear of communism, influence hiring and firing of University of California faculty, and punish those educators who did not support their project. Although it was rarely successful, Combs’ and Van Deman’s coordinated campaign reveals a story of public-private anticommunist collaboration in California that has been largely forgotten. Because Van Deman’s files are now finally open to researchers, Californians can gain a much more complete understanding of their state bureaucracy’s role in the Red Scare purges of California educators.

Analysis of the horizontal structure of a measurement and control geodetic network based on entropy

2013 ◽  
Vol 62 (1) ◽  
pp. 23-31 ◽  
Author(s):  
Maria Mrówczyńska
Keyword(s):  
Geodetic Network ◽  
The State ◽  
Observation System ◽  
Optimum Number ◽  
Optimum Structure ◽  
Horizontal Structure ◽  
The Difference ◽  
And Control ◽  
Measurement And Control ◽  
Horizontal Displacements

Abstract The paper attempts to determine an optimum structure of a directional measurement and control network intended for investigating horizontal displacements. For this purpose it uses the notion of entropy as a logarithmical measure of probability of the state of a particular observation system. An optimum number of observations results from the difference of the entropy of the vector of parameters ΔHX̂ (x)corresponding to one extra observation. An increment of entropy interpreted as an increment of the amount of information about the state of the system determines the adoption or rejection of another extra observation to be carried out.

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