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Results for “Stability in control theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.

Doyle, John C.↗
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↗
NASA NTRS1987

Adaptive hybrid position/force control of robotic manipulators

The problem of position and force control for the compliant motion of the manipulators is considered. The external force and the position of the end-effector are related by a second order impedance function. The force control problem is then translated into a position control problem. For that, an adaptive controller is designed to achieve the compliant motion. The design uses the Liapunov's direct method to derive the adaptation law. The stability of the process is guaranteed from the Liapunov's stability theory. The controller does not require the knowledge of the system parameters for the implementation, and hence is easy for applications.

Pourboghrat, F.↗
NASA NTRS1993

Aerodynamic flight control to increase payload capability of future launch vehicles

In this report, we provide some examples of French, Russian, Chinese, and Japanese launch vehicles that have utilized fins in their designs. Next, the aerodynamic design of the fins is considered in Section 3. Some comments on basic static stability and control theory are followed by a brief description of an aerodynamic characteristics prediction code that was used to estimate the characteristics of a modified NLS 1.5 Stage vehicle. Alternative fin designs are proposed and some estimated aerodynamic characteristics presented and discussed. Also included in Section 3 is a discussion of possible methods of enhancement of the aerodynamic efficiency of fins, such as vortex generators and jet flaps. We consider the construction of fins for launch vehicles in Section 4 and offer an assessment of the state-of-the-art in the use of composites for aerodynamic control surfaces on high speed vehicles. We also comment on the use of smart materials for launch vehicle fins. The dynamic stability and control of a launch vehicle that utilizes both thrust vector control (engine nozzle gimballing) and movable fins is the subject addressed in Section 5. We give a short derivation of equations of motion for a launch vehicle moving in a vertical plane above a spherical earth, discuss the use of a gravity-turn nominal trajectory, and give the form of the period equations linearized about such a nominal. We then consider feedback control of vehicle attitude using both engine gimballing and fin deflection. Conclusions are stated and recommendations made in Section 6. An appendix contains aerodynamic data in tabular and graphical formats.

Cochran, John E., Jr.↗
NASA NTRS1993

Robust control design with real parameter uncertainty using absolute stability theory

The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.

How, Jonathan P.↗
DOE OSTI2021

Experimental Observation of Magnetic Island Heteroclinic Bifurcation in Tokamaks

We report empirical observations of magnetic island heteroclinic bifurcation for the first time. This behavior is observed in interacting coupled 2/1 tearing modes in the core of a DIII-D tokamak plasma. Poincaré maps constrained by measured magnetic amplitudes and phasing show bifurcation from heteroclinic to homoclinic topology in the 2/1 island as the 4/2 relative amplitude (R 4/2 ) decreases. Initially, the local electron temperature peak in the 2/1 island splits, consistent with two O points. As R 4/2 decreases a single peak forms, consistent with one O point. Lastly, these call for developing tearing stability theory and control solutions for heteroclinic islands in tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1974

Discretized partial differential equations - Examples of control systems defined on modules

The purpose of this paper is to show how the important problems of linear system theory can be solved concisely for a particular class of linear systems, namely block circulant systems, by exploiting the algebraic structure. This type of system arises in lumped approximations to linear partial differential equations. The computation of the transition matrix, the variation of constants formula, observability, controllability, pole allocation, realization theory, stability and quadratic optimal control are discussed. In principle, all questions which are solved here could also be solved by standard methods; the present paper clearly exposes the structure of the solution, and thus permits various savings in computational effort.

Brockett, R. W.↗
NASA NTRS1998

Overview of Active Flow Control at NASA Langley Research Center

The paper summarizes Active Flow Control projects currently underway at the NASA Langley Research Center. Technology development is being pursued within a multidisciplinary, cooperative approach, involving the classical disciplines of fluid mechanics, structural mechanics, material science, acoustics, and stability and control theory. Complementing the companion papers in this session, the present paper will focus on projects that have the goal of extending the state-of-the-art in the measurement, prediction, and control of unsteady, nonlinear aerodynamics. Toward this goal, innovative actuators, micro and macro sensors, and control strategies are considered for high payoff flow control applications. The target payoffs are outlined within each section below. Validation of the approaches range from bench-top experiments to wind-tunnel experiments to flight tests. Obtaining correlations for future actuator and sensor designs are implicit in the discussion. The products of the demonstration projects and design tool development from the fundamental NASA R&D level technology will then be transferred to the Applied Research components within NASA, DOD, and US Industry. Keywords: active flow control, separation control, MEMS, review

Pack, L. G.↗
NASA NTRS1975

Research study on stabilization and control. Modern sampled-data control theory. Analysis and design of the digital large space telescope system

Dynamic modeling of a low cost single axis LST system and the pointing stability of that system are investigated. The effects of nonlinear friction of the bearings of the reaction wheels, quantization, and sensor noise on the pointing error are covered. In addition, data are given on self sustained oscillations of the system induced by quantization and methods of evaluating attitude error of the digital LST.

Kuo, B. C.↗
NASA NTRS1987

Stability theory applications to laminar-flow control

In order to design Laminar Flow Control (LFC) configurations, reliable methods are needed for boundary-layer transition predictions. Among the available methods, there are correlations based upon R sub e, shape factors, Goertler number and crossflow Reynolds number. The most advanced transition prediction method is based upon linear stability theory in the form of the e sup N method which has proven to be successful in predicting transition in two- and three-dimensional boundary layers. When transition occurs in a low disturbance environment, the e sup N method provides a viable design tool for transition prediction and LFC in both 2-D and 3-D subsonic/supersonic flows. This is true for transition dominated by either TS, crossflow, or Goertler instability. If Goertler/TS or crossflow/TS interaction is present, the e sup N will fail to predict transition. However, there is no evidence of such interaction at low amplitudes of Goertler and crossflow vortices.

Malik, Mujeeb R.↗
NASA NTRS1921

Statical longitudinal stability of airplanes

This report, which is a continuation of the "Preliminary report on free flight testing" (report no. NACA-TR-70), presents a detailed theoretical analysis of statical stability with free and locked controls and also the results of many free flight test on several types of airplanes. In developing the theory of stability with locked controls an expression for pitching moment is derived in simple terms by considering the total moment as the sum of the moments due to wings and tail surface. This expression, when differentiated with respect to angle of incidence, enables an analysis to be made of the factors contributing to the pitching moment. The effects of slipstream and down wash are also considered and it is concluded that the C. G. Location has but slight effect or stability, and that stability is much improved by increasing the efficiency of the tail surfaces, which may be done by using an "inverted" tail plane. The results of free flight tests with locked controls are discussed at length and it is shown that the agreement between the experimental results and theory is very satisfactory. The theory of stability with free controls is not amendable to the simple mathematical treatment used in the case of locked controls, but a clear statement of the conditions enables several conclusions to be drawn, one of which is that the fixed tail surfaces should be much larger than the movable surfaces.

Warner, Edward P↗
NASA NTRS1974

Research study on stabilization and control modern sampled-data control theory

The methods of continuous and discrete describing function analysis were applied to predicting the existence of self-sustained oscillations in the single-axis model of the large space telescope system with nonlinear control moment gyroscope friction characteristics. It is shown that the stability equations may be solved by a numerical-iterative technique using the describing function analysis, instead of the usual graphical methods. The numerical method is found to be effective in leading to a convergent solution rapidly, with an appropriate guess of the initial condition.

Kuo, B. C.↗
NASA NTRS1975

Research study on stabilization and control: Modern sampled-data control theory. Design of the large space telescope system

Conditions of self-sustained oscillations in a two-axis model of the nonlinear LST system are studied. The describing function of the CMG frictional nonlinearity of the LST system is used for the analysis, as well as continuous-data and discrete-data models of the simplified LST control system. A numerical-iterative method is described for the analysis of the two-axis system. Approximation methods and the direct plotting of the stability equation are implemented in the study. It is shown that although the dynamics of the two axes are identical, the amplitudes of self-sustained oscillations in the two axes may in principle be different. Analysis shows that the LST systems are of equal amplitudes but with 180-degree phase shift.

Kuo, B. C.↗
NASA NTRS1974

Research study on stabilization and control: Modern sampled-data control theory. Continuous and discrete describing function analysis of the LST system

The dynamics of the Large Space Telescope (LST) control system were studied in order to arrive at a simplified model for computer simulation without loss of accuracy. The frictional nonlinearity of the Control Moment Gyroscope (CMG) Control Loop was analyzed in a model to obtain data for the following: (1) a continuous describing function for the gimbal friction nonlinearity; (2) a describing function of the CMG nonlinearity using an analytical torque equation; and (3) the discrete describing function and function plots for CMG functional linearity. Preliminary computer simulations are shown for the simplified LST system, first without, and then with analytical torque expressions. Transfer functions of the sampled-data LST system are also described. A final computer simulation is presented which uses elements of the simplified sampled-data LST system with analytical CMG frictional torque expressions.

Kuo, B. C.↗