scholarly journals Nonlinear Attitude Control Of Underactuated Spacecraft

2021 ◽  
Author(s):  
Alexander Frias
Keyword(s):  
Optimal Control ◽  
Angular Velocity ◽  
Attitude Control ◽  
Inertial Frame ◽  
Equations Of Motion ◽  
The Body ◽  
Time Varying ◽  
Ultimate Boundedness ◽  
Error Norm ◽  
Attitude Error

This dissertation investigates the nonlinear control of the attitude for an underactuated rigid-body spacecraft system in the body-orbital and inertial frames. The problem involving the stabilization of the body-orbital attitude of an underactuated output-feedback system is examined. Using sliding mode control in conjunction with finite-time nonlinear observer, a novel observer-based control law is rigorously analyzed and proven to achieve attitude convergence. Under time-varying disturbances, inertia matrix uncertainties, and high initial errors, the proposed novel law achieves attitude convergence for three-axis stability and ultimate boundedness within 5 degrees and 0.01 deg/s, for attitude error norm and angular velocity norm, respectively. Next, the attitude control problem is rigorously analyzed in the inertial frame, where the underactuated rigid-body spacecraft system equations of motion are highly nonlinear, and the linearized equations of motion are not controllable. To this end, a generalized velocity-free time-varying state feedback controller is developed to achieve globally exponential stability with respect to the homogenous norm and proven to provide ultimate boundedness of all signals with 5 degrees attitude error norm and 0.5 rad/s angular velocity error norm. Finally, the inertial frame attitude stabilization problem is treated as an optimal control problem. For this case, the Legendre pseudospectral method is used to discretized the spacecraft dynamics into Legendre-Gauss-Lobatto (LGL) node points, where the Lagrange polynomial interpolation is applied to obtain a suitable candidate optimal control sequence. Model predictive control is used to implement the optimal control in predefined control windows sequentially to achieve three-axis stability for a rest-to-rest maneuver within 0.3 orbit.

scholarly journals Nonlinear Attitude Control Of Underactuated Spacecraft

2021 ◽  
Author(s):  
Alexander Frias
Keyword(s):  
Optimal Control ◽  
Angular Velocity ◽  
Attitude Control ◽  
Inertial Frame ◽  
Equations Of Motion ◽  
The Body ◽  
Time Varying ◽  
Ultimate Boundedness ◽  
Error Norm ◽  
Attitude Error

This dissertation investigates the nonlinear control of the attitude for an underactuated rigid-body spacecraft system in the body-orbital and inertial frames. The problem involving the stabilization of the body-orbital attitude of an underactuated output-feedback system is examined. Using sliding mode control in conjunction with finite-time nonlinear observer, a novel observer-based control law is rigorously analyzed and proven to achieve attitude convergence. Under time-varying disturbances, inertia matrix uncertainties, and high initial errors, the proposed novel law achieves attitude convergence for three-axis stability and ultimate boundedness within 5 degrees and 0.01 deg/s, for attitude error norm and angular velocity norm, respectively. Next, the attitude control problem is rigorously analyzed in the inertial frame, where the underactuated rigid-body spacecraft system equations of motion are highly nonlinear, and the linearized equations of motion are not controllable. To this end, a generalized velocity-free time-varying state feedback controller is developed to achieve globally exponential stability with respect to the homogenous norm and proven to provide ultimate boundedness of all signals with 5 degrees attitude error norm and 0.5 rad/s angular velocity error norm. Finally, the inertial frame attitude stabilization problem is treated as an optimal control problem. For this case, the Legendre pseudospectral method is used to discretized the spacecraft dynamics into Legendre-Gauss-Lobatto (LGL) node points, where the Lagrange polynomial interpolation is applied to obtain a suitable candidate optimal control sequence. Model predictive control is used to implement the optimal control in predefined control windows sequentially to achieve three-axis stability for a rest-to-rest maneuver within 0.3 orbit.

Shared Fuzzy Control of Multiple Quadrotor UAVs With Time-Dependent Delay and Bounded Control-Input Constraint

2015 ◽  
Author(s):  
Mark D. Johnson ◽  
Mohammad A. Ayoubi
Keyword(s):  
Fuzzy Control ◽  
Attitude Control ◽  
Fuzzy Controller ◽  
Equations Of Motion ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Control Input ◽  
Maximum Magnitude ◽  
Time Varying ◽  
Bounded Control

We propose a shared fuzzy controller for position and attitude control of multiple quadrotor unmanned aerial vehicles (UAVs). Using the nonlinear governing equations of motion and kinematics of a quadrotor, we develop a Takagi-Sugeno (T-S) fuzzy model for a quadrotor. Then, we consider time-varying delays due to wireless connectioninto the T-S fuzzy model. We use the sufficient stability condition based on the Lyapunov-Krasovskii stability theorem and the parallel distributed compensation (PDC) technique to determine the fuzzy control law. For practical purposes, we include actuator amplitude constraint into the design process. The problem of designing a shared fuzzy controller is cast in the form of linear matrix inequalities (LMIs). A feasible solution region is found in terms of maximum magnitude and rate of time-varying delay. In the end, the stability, performance, and robustness of the proposed shared fuzzy controller are examined via numerical simulation.

Intrinsic Time Integration Procedures for Rigid Body Dynamics

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Olivier A. Bauchau ◽  
Hao Xin ◽  
Shiyu Dong ◽  
Zhiheng Li ◽  
Shilei Han
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Equations Of Motion ◽  
Time Integration ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Rotation Tensor ◽  
Intrinsic Nature ◽  
Intrinsic Form ◽  
Angular Velocities

The treatment of rotations in rigid body and Cosserat solids dynamics is challenging. In most cases, at some point in the formulation, a parameterization of rotation is introduced and the intrinsic nature of the equations of motions is lost. Typically, this step considerably complicates the form of the equations and increases the order of the nonlinearities. Clearly, it is desirable to bypass parameterization of rotation, leaving the equations of motion in their original, intrinsic form. This has prompted the development of rotationless and intrinsic formulations. This paper focuses on the latter approach. The most famous example of intrinsic formulation is probably Euler’s second law for the motion of a rigid body rotating about an inertial point. This equation involves angular velocities solely, with algebraic nonlinearities of the second-order at most. Unfortunately, this intrinsic equation also suffers serious drawbacks: the angular velocity of the body is computed, but not its orientation, the body is “unaware” of its inertial orientation. This paper presents an alternative approach to the problem by proposing discrete statements of the rotation kinematic compatibility equation, which provide solutions for both rotation tensor and angular velocity without relying on a parameterization of rotation. The formulation is also generalized using the motion formalism, leading to very simple discretized equations of motion.

scholarly journals Applying the Large Parameter Technique for Solving a Slow Rotary Motion of a Disc about a Fixed Point

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
A. I. Ismail
Keyword(s):  
Fixed Point ◽  
Angular Velocity ◽  
Periodic Solutions ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
First Integral ◽  
The Body ◽  
Large Parameter

In this paper, the motion of a disk about a fixed point under the influence of a Newtonian force field and gravity one is considered. We modify the large parameter technique which is achieved by giving the body a sufficiently small angular velocity component r0 about the fixed z-axis of the disk. The periodic solutions of motion are obtained in the neighborhood r0 tends to 0. This case of study is excluded from the previous works because of the appearance of a singular point in the denominator of the obtained solutions. Euler-Poison equations of motion are obtained with their first integrals. These equations are reduced to a quasilinear autonomous system of two degrees of freedom and one first integral. The periodic solutions for this system are obtained under the new initial conditions. Computerizing the obtained periodic solutions through a numerical technique for validation of results is done. Two types of analytical and numerical solutions in the new domain of the angular velocity are obtained. Geometric interpretations of motion are presented to show the orientation of the body at any instant of time t.

A study of motions in a rotating liquid

1951 ◽  
Vol 206 (1084) ◽  
pp. 108-130 ◽  
Keyword(s):  
Angular Velocity ◽  
Equations Of Motion ◽  
Vertical Axis ◽  
The Body ◽  
Forced Oscillations ◽  
Infinite Cylinder ◽  
Two Dimensional ◽  
Small Motion ◽  
Axis Of Rotation ◽  
Rotating Liquid

Starting with the equations of motion for a perfect, incompressible fluid referred to a coordinate system which rotates about a vertical axis with uniform angular velocity R , the physical condition of ‘small motion’ is determined which permits the equations to be linearized. The small motions resulting from forced oscillations of a rotating liquid are investigated. It is shown that there are three types of flow depending on the relative magnitudes of the impressed frequency β and the angular velocity R of the fluid. Two of the regimes are studied in detail. A similarity law is developed which gives the solution of a class of problems of oscillations for β > 2 R in terms of the solutions to similar irrotational problems. An attempt is made to explain how slow, two-dimensional motion can be produced by introducing a boundary condition which is three-dimensional (as observed in experiments performed by G. I. Taylor), by considering problems from the moment at which the disturbance is created from rest relative to the rotating system, with the only initial assumption that the fluid is rotating uniformly like a solid body. For the particular cases studied the results are in agreement with Taylor’s experiments, in that the flow is found to become steady and two-dimensional if the disturbance which causes it approaches a steady state. If the disturbance is due to a body which moves along the axis of rotation of the fluid, the steady two-dimensional behaviour may be expected everywhere except in the neighbourhood of the surface of an infinite cylinder which encloses the body and whose generators are parallel to the axis of rotation. To resolve an apparent disagreement between certain theoretical results by Grace on the one hand, and experimental evidence by Taylor and the author’s conclusions, on the other, arguments are advanced that the various results may be in agreement, provided Grace’s are given a new interpretation.

scholarly journals Millimeter (MM) wave and microwave frequency radiation produce deeply penetrating effects: the biology and the physics

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Martin L. Pall
Keyword(s):  
Magnetic Fields ◽  
Electric Fields ◽  
Cardiac Activity ◽  
Maximum Level ◽  
Voltage Sensor ◽  
The Body ◽  
Time Varying ◽  
The Brain ◽  
Mm Waves

Abstract Millimeter wave (MM-wave) electromagnetic fields (EMFs) are predicted to not produce penetrating effects in the body. The electric but not magnetic part of MM-EMFs are almost completely absorbed within the outer 1 mm of the body. Rodents are reported to have penetrating MM-wave impacts on the brain, the myocardium, liver, kidney and bone marrow. MM-waves produce electromagnetic sensitivity-like changes in rodent, frog and skate tissues. In humans, MM-waves have penetrating effects including impacts on the brain, producing EEG changes and other neurological/neuropsychiatric changes, increases in apparent electromagnetic hypersensitivity and produce changes on ulcers and cardiac activity. This review focuses on several issues required to understand penetrating effects of MM-waves and microwaves: 1. Electronically generated EMFs are coherent, producing much higher electrical and magnetic forces then do natural incoherent EMFs. 2. The fixed relationship between electrical and magnetic fields found in EMFs in a vacuum or highly permeable medium such as air, predicted by Maxwell’s equations, breaks down in other materials. Specifically, MM-wave electrical fields are almost completely absorbed in the outer 1 mm of the body due to the high dielectric constant of biological aqueous phases. However, the magnetic fields are very highly penetrating. 3. Time-varying magnetic fields have central roles in producing highly penetrating effects. The primary mechanism of EMF action is voltage-gated calcium channel (VGCC) activation with the EMFs acting via their forces on the voltage sensor, rather than by depolarization of the plasma membrane. Two distinct mechanisms, an indirect and a direct mechanism, are consistent with and predicted by the physics, to explain penetrating MM-wave VGCC activation via the voltage sensor. Time-varying coherent magnetic fields, as predicted by the Maxwell–Faraday version of Faraday’s law of induction, can put forces on ions dissolved in aqueous phases deep within the body, regenerating coherent electric fields which activate the VGCC voltage sensor. In addition, time-varying magnetic fields can directly put forces on the 20 charges in the VGCC voltage sensor. There are three very important findings here which are rarely recognized in the EMF scientific literature: coherence of electronically generated EMFs; the key role of time-varying magnetic fields in generating highly penetrating effects; the key role of both modulating and pure EMF pulses in greatly increasing very short term high level time-variation of magnetic and electric fields. It is probable that genuine safety guidelines must keep nanosecond timescale-variation of coherent electric and magnetic fields below some maximum level in order to produce genuine safety. These findings have important implications with regard to 5G radiation.

scholarly journals Optimal control in liver kinetics

1986 ◽  
Vol 27 (3) ◽  
pp. 361-369 ◽  
Author(s):  
A. M. Fink
Keyword(s):  
Optimal Control ◽  
Minimization Problem ◽  
Enzymatic Reaction ◽  
The Body ◽  
Minimum Problem ◽  
Density Functions ◽  
Intermediate Form

AbstractWe solve a minimization problem in liver kinetics posed by Bass, et al., in this journal, (1984), pages 538–562. The problem is to choose the density functions for the location of two enzymes, in order to minimize the concentration of an intermediate form of a substance at the outlet of the liver. This form may be toxic to the rest of the body, but the second enzyme renders it harmless. It seems natural that the second enzyme should be downstream from the first. However, we can show that the minimum problem is sometimes solved by an overlap of the supports of the two density functions. Even more surprising is that, for certain forms of the kinetic functions and high levels of transformation of the first enzymatic reaction, some of the first enzyme should be located downstream from all the second enzyme. This suggests that the first reaction should be relatively slow.

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