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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Stability analysis of position and force control problems for robot arms

Stability issues involving the control of a robot arm under the influence of external forces are discussed. Several different scenarios are considered: position control with the external force as an unmodeled disturbance, compliant control for a bounded external force in some subspace, and compliant control for a force due to the interaction with an environment whose dynamical behavior can be modeled. In each of these cases, a stability analysis using the Lyapunov method is presented. An explanation of instability is put forth for the case in which the environment has flexibility and the gains are inappropriately chosen. When the environment is stiff in the force control subspace, robust stability can be achieved with the integral force feedback.

Wen, John T.↗
NASA NTRS1992

Passivity/Lyapunov based controller design for trajectory tracking of flexible joint manipulators

A passivity and Lyapunov based approach for the control design for the trajectory tracking problem of flexible joint robots is presented. The basic structure of the proposed controller is the sum of a model-based feedforward and a model-independent feedback. Feedforward selection and solution is analyzed for a general model for flexible joints, and for more specific and practical model structures. Passivity theory is used to design a motor state-based controller in order to input-output stabilize the error system formed by the feedforward. Observability conditions for asymptotic stability are stated and verified. In order to accommodate for modeling uncertainties and to allow for the implementation of a simplified feedforward compensation, the stability of the system is analyzed in presence of approximations in the feedforward by using a Lyapunov based robustness analysis. It is shown that under certain conditions, e.g., the desired trajectory is varying slowly enough, stability is maintained for various approximations of a canonical feedforward.

Sicard, Pierre↗
NASA NTRS2011

On Using Exponential Parameter Estimators with an Adaptive Controller

Typical adaptive controllers are restricted to using a specific update law to generate parameter estimates. This paper investigates the possibility of using any exponential parameter estimator with an adaptive controller such that the system tracks a desired trajectory. The goal is to provide flexibility in choosing any update law suitable for a given application. The development relies on a previously developed concept of controller/update law modularity in the adaptive control literature, and the use of a converse Lyapunov-like theorem. Stability analysis is presented to derive gain conditions under which this is possible, and inferences are made about the tracking error performance. The development is based on a class of Euler-Lagrange systems that are used to model various engineering systems including space robots and manipulators.

Patre, Parag↗
NASA NTRS1983

Stability and capture of asteroids

The problem of stability of asteroids is treated from the point of view of Hill's stability-concept and using Lyapunov's Characteristic Numbers. The quantitative measure of stability (S) introduced earlier is evaluated for over 300 asteroids and a surprisingly simple relation is established between the semi-major axes of some of the asteroids' orbits and S. A detailed analysis is presented of the Lyapunov Characteristic Numbers for two minor planets and the time-variation of these numbers is discussed. The technology of capture of asteroids is vitally dependent on their orbital stability, therefore, these two problems, i.e., capture and stability, are closely related. In fact, some predictable instabilities may be properly utilized to capture and/or change asteroidal orbits to accomplish collisions with the Earth.

Szebehely, V.↗
NASA NTRS1973

Asymptotic stability and instability of large-scale systems

The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations.

Grujic, L. T.↗
NASA NTRS1988

Decentralized adaptive control of robot manipulators with robust stabilization design

Due to geometric nonlinearities and complex dynamics, a decentralized technique for adaptive control for multilink robot arms is attractive. Lyapunov-function theory for stability analysis provides an approach to robust stabilization. Each joint of the arm is treated as a component subsystem. The adaptive controller is made locally stable with servo signals including proportional and integral gains. This results in the bound on the dynamical interactions with other subsystems. A nonlinear controller which stabilizes the system with uniform boundedness is used to improve the robustness properties of the overall system. As a result, the robot tracks the reference trajectories with convergence. This strategy makes computation simple and therefore facilitates real-time implementation.

Yuan, Bau-San↗
NASA NTRS1993

Design and implementation of fuzzy logic controllers

The main objectives of our research are to present a self-contained overview of fuzzy sets and fuzzy logic, develop a methodology for control system design using fuzzy logic controllers, and to design and implement a fuzzy logic controller for a real system. We first present the fundamental concepts of fuzzy sets and fuzzy logic. Fuzzy sets and basic fuzzy operations are defined. In addition, for control systems, it is important to understand the concepts of linguistic values, term sets, fuzzy rule base, inference methods, and defuzzification methods. Second, we introduce a four-step fuzzy logic control system design procedure. The design procedure is illustrated via four examples, showing the capabilities and robustness of fuzzy logic control systems. This is followed by a tuning procedure that we developed from our design experience. Third, we present two Lyapunov based techniques for stability analysis. Finally, we present our design and implementation of a fuzzy logic controller for a linear actuator to be used to control the direction of the Free Flight Rotorcraft Research Vehicle at LaRC.

Abihana, Osama A.↗
NASA NTRS2009

Using Covariance Analysis to Assess Pointing Performance

A Pointing Covariance Analysis Tool (PCAT) has been developed for evaluating the expected performance of the pointing control system for NASA s Space Interferometry Mission (SIM). The SIM pointing control system is very complex, consisting of multiple feedback and feedforward loops, and operating with multiple latencies and data rates. The SIM pointing problem is particularly challenging due to the effects of thermomechanical drifts in concert with the long camera exposures needed to image dim stars. Other pointing error sources include sensor noises, mechanical vibrations, and errors in the feedforward signals. PCAT models the effects of finite camera exposures and all other error sources using linear system elements. This allows the pointing analysis to be performed using linear covariance analysis. PCAT propagates the error covariance using a Lyapunov equation associated with time-varying discrete and continuous-time system matrices. Unlike Monte Carlo analysis, which could involve thousands of computational runs for a single assessment, the PCAT analysis performs the same assessment in a single run. This capability facilitates the analysis of parametric studies, design trades, and "what-if" scenarios for quickly evaluating and optimizing the control system architecture and design.

Bayard, David↗
NASA NTRS1998

Sufficient Conditions for the Stability of a Lur'e System With Two Nonzero Inputs Based on Lyapunovs Direct Method

The Lur'e problem is a famous problem in nonlinear control theory. The analysis of this system is usually restricted to Lur'e systems in which the external input is zero. One form of this problem involves the stability analysis of the Lur'e system with two nonzero inputs. The stability analysis of this type of system is traditionally performed based on L stability theory. The objective of this paper is to present sufficient conditions for the stability of this system based on Lyapunov's direct method. This is a conceptually simpler approach to the existing analysis based on L stability theory and it provides some additional information about the stability of the system.

Adetona, Olawale↗
NASA NTRS2019

Nonlinear Analysis of a Two-Parachute System Undergoing Pendulum Motion

Motion resembling that of a pendulum undergoing large-amplitude limit cycle oscillation was observed during a series of flight tests of an unoccupied Orion Capsule Parachute Assembly System (CPAS) comprised of two parachutes and a capsule payload. Large excursions away from vertical by the capsule could cause it to strike the ground or ocean at a large angle with respect to vertical, or at a large horizontal speed. These conditions are undesirable because they would endanger the occupants of the capsule in an actual mission. A simplified planar dynamics model in conjunction with a nonlinear normal force coefficient vs. angle of attack model serves as the basis of an analytical investigation of the fundamental dynamics of this pendulum motion. Output error methodology from system identification theory was used to identify the parameters of the nonlinear aerodynamics model. The identified model yielded excellent comparison with portions of flight test data where the pendulum motion occurred. Due to the inherent nonlinear nature of the pendulum motion limit cycle, traditional nonlinear analysis techniques were applied to gain further insight into the system. Lyapunov’s direct method provided mathematical proof in the absolute stability of the pendulum mode. Describing Function method was used to predict the amplitude and frequency of the limit cycle oscillation. Finally, phase plane analysis allowed easy visualization on the size and shape of the limit cycle with respect to variations in key aerodynamic parameters.

Pei, Jing↗
NASA NTRS1991

Lyapunov exponent of magnetospheric activity from AL time series

A correlation dimension analysis of the AE index indicates that the magnetosphere behaves as a low-dimensional chaotic system with a dimension close to 4. Similar techniques are used to determine if the system's behavior is due to an intrinsic sensitivity to initial conditions and thus is truly chaotic. The quantity used to measure the sensitivity to initial conditions is the Liapunov exponent. Its calculation for AL shows that it is nonzero (0.11 + or - 0.05/min). This gives the exponential rate at which initially similar configurations of the magnetosphere evolve into completely different states. Also, predictions of deterministic nonlinear models are expected to deviate from the observed behavior at the same rate.

Vassiliadis, D.↗
NASA NTRS1987

Mean-square error bounds for reduced-error linear state estimators

The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Lyapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.

Baram, Y.↗
NASA NTRS1990

A first-order Lyapunov robustness method for linear systems with uncertain parameters

A method for stability-robustness analysis based on a quadratic Liapunov function that varies linearly with uncertainty parameters is derived. Linear time-invariant systems with structured uncertainties are discussed. The Liapunov function is optimized numerically to maximize the robustness region in parameter space. Numerical results are given for four examples in which the first-order method is compared to previous Liapunov methods. While the zero-order method is slightly better than the first-order method for one example, the first-order method is clearly superior in the other three (more realistic) examples. The first-order method is especially superior for the active control of flexible structures, where robustness with respect to (1) unmodeled coupling between modeled modes and (2) unmodeled modes is important. For such applications, the first-order method is much better at detecting the increased robustness associated with increased separation between frequencies.

Leal, M. A.↗
NASA NTRS2010

A Spectral Lyapunov Function for Exponentially Stable LTV Systems

This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.

Zhu, J. Jim↗
NASA NTRS2010

Predictor-Based Model Reference Adaptive Control

This paper is devoted to the design and analysis of a predictor-based model reference adaptive control. Stable adaptive laws are derived using Lyapunov framework. The proposed architecture is compared with the now classical model reference adaptive control. A simulation example is presented in which numerical evidence indicates that the proposed controller yields improved transient characteristics.

Lavretsky, Eugene↗
NASA NTRS2011

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Nguyen, Nhan T.↗
NASA NTRS2017

Fuzzy Logic Controller Stability Analysis Using a Satisfiability Modulo Theories Approach

While many widely accepted methods and techniques exist for validation and verification of traditional controllers, at this time no solutions have been accepted for Fuzzy Logic Controllers (FLCs). Due to the highly nonlinear nature of such systems, and the fact that developing a valid FLC does not require a mathematical model of the system, it is quite difficult to use conventional techniques to prove controller stability. Since safety-critical systems must be tested and verified to work as expected for all possible circumstances, the fact that FLC controllers cannot be tested to achieve such requirements poses limitations on the applications for such technology. Therefore, alternative methods for verification and validation of FLCs needs to be explored. In this study, a novel approach using formal verification methods to ensure the stability of a FLC is proposed. Main research challenges include specification of requirements for a complex system, conversion of a traditional FLC to a piecewise polynomial representation, and using a formal verification tool in a nonlinear solution space. Using the proposed architecture, the Fuzzy Logic Controller was found to always generate negative feedback, but inconclusive for Lyapunov stability.

Fuzzy Logic Controller↗