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NASA NTRS1971

Generalized invariance principles and the theory of stability.

Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.

Lasalle, J. P.↗

NASA NTRS1994

Three-axis stabilization of spacecraft using parameter-independent nonlinear quaternion feedback

This paper considers the problem of rigid spacecraft. A nonlinear control law which uses the feedback of the unit quaternion and the measured angular velocities is proposed and is shown to provide global asymptotic stability. The control law does not require the knowledge of the system parameters, and is therefore robust to modeling errors. The significance of the control law is that it can be used for large-angle maneuvers with guaranteed stability.

Joshi, Suresh M.↗

NASA NTRS1995

A class of stabilizing controllers for flexible multibody systems

The problem of controlling a class of nonlinear multibody flexible space systems consisting of a flexible central body to which a number of articulated appendages are attached is considered. Collocated actuators and sensors are assumed, and global asymptotic stability of such systems is established under a nonlinear dissipative control law. The stability is shown to be robust to unmodeled dynamics and parametric uncertainties. For a special case in which the attitude motion of the central body is small, the system, although still nonlinear, is shown to be stabilized by linear dissipative control laws. Two types of linear controllers are considered: static dissipative (constant gain) and dynamic dissipative. The static dissipative control law is also shown to provide robust stability in the presence of certain classes of actuator and sensor nonlinearities and actuator dynamics. The results obtained for this special case can also be readily applied for controlling single-body linear flexible space structures. For this case, a synthesis technique for the design of a suboptimal dynamic dissipative controller is also presented. The results obtained in this paper are applicable to a broad class of multibody and single-body systems such as flexible multilink manipulators, multipayload space platforms, and space antennas. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems.

Joshi, Suresh M.↗

NASA NTRS2020

Passive Roll Stabilization of the Near Earth Asteroid Scout Solar Sail Mission

The Near Earth Asteroid (NEA) Scout is a small satellite, solar sail mission set to launch on Artemis I. Analysis of the NEA Scout solar radiation pressure model determined that, for certain solar incidence angles, there exists at least one locally stable equilibrium point about the “roll” axis, or the axis normal to the solar sail plane. This analysis is extended to three other geometrically similar solar sail models, and a Lyapunov stability analysis is conducted demonstrating that the stable equilibria are locally stable for the majority of roll angles in a wide range of solar incidence angles. Under certain assumptions, it is possible that only two axis control is required for non-spinning solar sails. If the roll axis is controlled, an active rate damping controller can be designed to asymptotically stabilize the system. Simulation results are presented that follow the stability analysis, where in the homogenous case, the system enters a limit cycle and, in the actively damped case, the system asymptotically converges to the equilibrium point.

Ivan Rodrigues Bertaska↗

NASA NTRS1975

On the stabilization of bilinear systems via hyperstability

The problem of feedback stabilization for continuous and discrete bilinear systems is investigated. Attention is also given to the 'drift' term case to take into account physical systems in which preassigned values are imposed on some of the controls. A proposed set of controls for asymptotic stabilization is applicable to a fairly large class of bilinear systems. It is pointed out that the results presented can be used to design nonlinear adaptive controllers which in some cases are preferable to linear controllers.

Ionescu, T.↗

NASA NTRS1980

Damping enhancement and attitude control of large space structures

Enhancement of modal damping in large space structures (LSS) is highly desirable and sometimes essential for the stability of the primary attitude control system. This paper considers the use of a number of Annular Momentum Control Devices (AMCD's) for damping enhancement in LSS. It is proved that the closed-loop system is stable in the sense of Lyapunov. Sufficient conditions for asymptotic stability are also obtained.

Joshi, S. M.↗

NASA NTRS1996

Stability Analysis for Constrained Principal Axis Slew Maneuvers

This paper addresses the problem of reorienting a rigid spacecraft from arbitrary initial conditions to prescribed final conditions with zero angular velocity. The control law analyzed is based on quaternion feedback and leaves the user to choose two gains as functions of position, angular rate, and time. For arbitrary initial states, conditions on the controller gains are identified that guarantee global asymptotic stability. For the special case of rest-to-rest reorientations, the control law reduces to earlier results involving a principal axis rotation. The paper also addresses slew rate constraints, both, in terms of the two and infinity norms.

Seywald, Hans↗

NASA NTRS1992

Lyapunov function-based control laws for revolute robot arms - Tracking control, robustness, and adaptive control

A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to a recently proposed energy-like Liapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates (i.e., certainty equivalence adaptation).

Wen, John T.↗

NASA NTRS1988

A new class of energy based control laws for revolute robot arms - Tracking control, robustness enhancement and adaptive control

A class of joint-level control laws for all-revolute robot arms is introduced. The analysis is similar to the recently proposed energy Liapunov function approach except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. By using energy Liapunov functions with the modified potential energy, a much simpler analysis can be used to show closed-loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness-enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted, and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the nonadaptive control laws by their estimates.

Wen, John T.↗

NASA NTRS1997

Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers

An investigation is conducted on several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes use explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order variant of the schemes proposed by Rusanov and by Kutier, Lomax, and Warming (RKLW), and third- and fourth-order Runge-Kutta schemes. In each scheme, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(sub t) + aU(sub x) = alpha U(sub xx). Accuracy is also verified on the nonlinear problem, U(sub t) + F(sub x) = 0. Numerical treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for several sixth- and eighth-order central-difference schemes. Damping of high wave-number data is accomplished with explicit filters of arbitrary order. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients exist.

Kennedy, Christopher A.↗

NASA NTRS1977

An implementable digital adaptive flight controller designed using stabilized single-stage algorithms

An explicit adaptive controller, which makes direct use of on-line parameter identification, has been developed and applied to both the linearized and nonlinear equations of motion for the F-8 aircraft. This controller is composed of an on-line weighted least squares parameter identifier, a Kalman state filter, and a real model following control law designed using single-stage performance indices. The corresponding control gains are readily adjustable in accordance with parameter changes to ensure asymptotic stability if the conditions of perfect model following are satisfied, and stability in the sense of boundedness otherwise. Simulation experiments with realistic measurement noise indicate that the controller was effective in compensating for parameter variations and capable of rapid recovery from a set of erroneous initial parameter estimates which defined a set of destabilizing gains.

Alag, G.↗

NASA NTRS1979

Stability bounds for the control of large space structures

Balas (1977) has discussed the stability problem of reduced-order regulators and estimators in terms of control and observation 'spillover'. The term 'control spillover' was used to define that part of the feedback control which excites the uncontrolled (or residual) modes, and 'observation spillover' was used to define that part of the measurement which is contaminated by residual modes. In this paper, two sufficient conditions are derived via Lyapunov methods for asymptotic stability of large space structures using a class of reduced-order controllers. These conditions give allowable bounds on the spectral norms of control and observation spillover terms. The sufficient condition given by a specified inequality equation appears to be less conservative, and should be useful as a design tool for the control of large space structures.

Joshi, S. M.↗

NASA NTRS2014

Stability Assessment and Tuning of an Adaptively Augmented Classical Controller for Launch Vehicle Flight Control

Recently, a robust and practical adaptive control scheme for launch vehicles [ [1] has been introduced. It augments a classical controller with a real-time loop-gain adaptation, and it is therefore called Adaptive Augmentation Control (AAC). The loop-gain will be increased from the nominal design when the tracking error between the (filtered) output and the (filtered) command trajectory is large; whereas it will be decreased when excitation of flex or sloshing modes are detected. There is a need to determine the range and rate of the loop-gain adaptation in order to retain (exponential) stability, which is critical in vehicle operation, and to develop some theoretically based heuristic tuning methods for the adaptive law gain parameters. The classical launch vehicle flight controller design technics are based on gain-scheduling, whereby the launch vehicle dynamics model is linearized at selected operating points along the nominal tracking command trajectory, and Linear Time-Invariant (LTI) controller design techniques are employed to ensure asymptotic stability of the tracking error dynamics, typically by meeting some prescribed Gain Margin (GM) and Phase Margin (PM) specifications. The controller gains at the design points are then scheduled, tuned and sometimes interpolated to achieve good performance and stability robustness under external disturbances (e.g. winds) and structural perturbations (e.g. vehicle modeling errors). While the GM does give a bound for loop-gain variation without losing stability, it is for constant dispersions of the loop-gain because the GM is based on frequency-domain analysis, which is applicable only for LTI systems. The real-time adaptive loop-gain variation of the AAC effectively renders the closed-loop system a time-varying system, for which it is well-known that the LTI system stability criterion is neither necessary nor sufficient when applying to a Linear Time-Varying (LTV) system in a frozen-time fashion. Therefore, a generalized stability metric for time-varying loop=gain perturbations is needed for the AAC.

VanZwieten, Tannen↗

NASA NTRS1993

Attitude stabilization of a rigid spacecraft using two momentum wheel actuators

It is well known that three momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished using smooth feedback. If failure of one of the momentum wheel actuators occurs, it is demonstrated that two momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished. Although the complete spacecraft equations are not controllable, the spacecraft equations are small time locally controllable in a reduced nonlinear sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to any equilibrium attitude using a time-variant continuous feedback control law, but discontinuous feedback control strategies are constructed which stabilize any equilibrium attitude of the spacecraft in finite time. Consequently, reorientation of the spacecraft can be accomplished using discontinuous feedback control.

Krishnan, Hariharan↗

NASA NTRS1991

Model reference adaptive control of robots

This project presents the results of controlling two types of robots using new Command Generator Tracker (CGT) based Direct Model Reference Adaptive Control (MRAC) algorithms. Two mathematical models were used to represent a single-link, flexible joint arm and a Unimation PUMA 560 arm; and these were then controlled in simulation using different MRAC algorithms. Special attention was given to the performance of the algorithms in the presence of sudden changes in the robot load. Previously used CGT based MRAC algorithms had several problems. The original algorithm that was developed guaranteed asymptotic stability only for almost strictly positive real (ASPR) plants. This condition is very restrictive, since most systems do not satisfy this assumption. Further developments to the algorithm led to an expansion of the number of plants that could be controlled, however, a steady state error was introduced in the response. These problems led to the introduction of some modifications to the algorithms so that they would be able to control a wider class of plants and at the same time would asymptotically track the reference model. This project presents the development of two algorithms that achieve the desired results and simulates the control of the two robots mentioned before. The results of the simulations are satisfactory and show that the problems stated above have been corrected in the new algorithms. In addition, the responses obtained show that the adaptively controlled processes are resistant to sudden changes in the load.

Steinvorth, Rodrigo↗

NASA NTRS2014

Spacecraft Stabilization and Control for Capture of Non-Cooperative Space Objects

This paper addresses stabilization and control issues in autonomous capture and manipulation of non-cooperative space objects such as asteroids, space debris, and orbital spacecraft in need of servicing. Such objects are characterized by unknown mass-inertia properties, unknown rotational motion, and irregular shapes, which makes it a challenging control problem. The problem is further compounded by the presence of inherent nonlinearities, signi cant elastic modes with low damping, and parameter uncertainties in the spacecraft. Robust dissipativity-based control laws are presented and are shown to provide global asymptotic stability in spite of model uncertainties and nonlinearities. It is shown that robust stabilization can be accomplished via model-independent dissipativity-based controllers using thrusters alone, while stabilization with attitude and position control can be accomplished using thrusters and torque actuators.

Joshi, Suresh↗

NASA NTRS1985

Dynamic modeling and adaptive control for space stations

Of all large space structural systems, space stations present a unique challenge and requirement to advanced control technology. Their operations require control system stability over an extremely broad range of parameter changes and high level of disturbances. During shuttle docking the system mass may suddenly increase by more than 100% and during station assembly the mass may vary even more drastically. These coupled with the inherent dynamic model uncertainties associated with large space structural systems require highly sophisticated control systems that can grow as the stations evolve and cope with the uncertainties and time-varying elements to maintain the stability and pointing of the space stations. The aspects of space station operational properties are first examined, including configurations, dynamic models, shuttle docking contact dynamics, solar panel interaction, and load reduction to yield a set of system models and conditions. A model reference adaptive control algorithm along with the inner-loop plant augmentation design for controlling the space stations under severe operational conditions of shuttle docking, excessive model parameter errors, and model truncation are then investigated. The instability problem caused by the zero-frequency rigid body modes and a proposed solution using plant augmentation are addressed. Two sets of sufficient conditions which guarantee the globablly asymptotic stability for the space station systems are obtained.

Ih, C. H. C.↗

NASA NTRS1989

On the stability of robotic systems with random communication rates

Control problems of sampled data systems which are subject to random sample rate variations and delays are studied. Due to the rapid growth of the use of computers more and more systems are controlled digitally. Complex systems such as space telerobotic systems require the integration of a number of subsystems at different hierarchical levels. While many subsystems may run on a single processor, some subsystems require their own processor or processors. The subsystems are integrated into functioning systems through communications. Communications between processes sharing a single processor are also subject to random delays due to memory management and interrupt latency. Communications between processors involve random delays due to network access and to data collisions. Furthermore, all control processes involve delays due to casual factors in measuring devices and to signal processing. Traditionally, sampling rates are chosen to meet the worst case communication delay. Such a strategy is wasteful as the processors are then idle a great proportion of the time; sample rates are not as high as possible resulting in poor performance or in the over specification of control processors; there is the possibility of missing data no matter how low the sample rate is picked. Asymptotical stability with probability one for randomly sampled multi-dimensional linear systems is studied. A sufficient condition for the stability is obtained. This condition is so simple that it can be applied to practical systems. A design procedure is also shown.

Kobayashi, H.↗