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Results for “feedback linearization”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Partial and robust linearization by feedback

It is argued that if the nonlinearities in a system are mild, and the controller is sufficiently stabilizing, the inaccuracies of a linear model, which is often taken to be sufficient for a controller design, can be safely neglected. For systems with severe nonlinearity a linearizing technique is described, based on the change of state coordinates and nonlinear feedback; in the total context of a stable feedback design the linearization technique is considered robust. Furthermore, attention is paid to partial linearization using the same transformations. It is found that there always exist maximally linearizing transformations which are not necessarily unique.

Krener, A. J.↗
NASA NTRS1973

Output feedback for linear multivariable systems with parameter uncertainty.

A minimax design method is applied to the problem of obtaining an acceptable output feedback matrix for linear multivariable systems with parameter uncertainty. The result is a set of nonlinear matrix equations (similar to those obtained by Levine and Athans (1970)), which must be solved for the feedback matrix. An example illustrates the technique and the fact that better results are achieved for large parameter variation than with a purely nominal design.

Basuthakur, S.↗
NASA NTRS1993

Multivariable control of the Space Shuttle Remote Manipulator System using linearization by state feedback

This thesis develops and demonstrates an approach to nonlinear control system design using linearization by state feedback. The design provides improved transient response behavior allowing faster maneuvering of payloads by the SRMS. Modeling uncertainty is accounted for by using a second feedback loop designed around the feedback linearized dynamics. A classical feedback loop is developed to provide the easy implementation required for the relatively small on board computers. Feedback linearization also allows the use of higher bandwidth model based compensation in the outer loop, since it helps maintain stability in the presence of the nonlinearities typically neglected in model based designs.

Gettman, Chang-Ching LO↗
NASA NTRS1995

Design of high performance multivariable control systems for supermaneuverable aircraft at high angle of attack

The main motivation for the work under the present grant was to use nonlinear feedback linearization methods to further enhance performance capabilities of the aircraft, and robustify its response throughout its operating envelope. The idea was to use these methods in lieu of standard Taylor series linearization, in order to obtain a well behaved linearized plant, in its entire operational regime. Thus, feedback linearization was going to constitute an 'inner loop', which would then define a 'design plant model' to be compensated for robustness and guaranteed performance in an 'outer loop' application of modern linear control methods. The motivation for this was twofold; first, earlier work had shown that by appropriately conditioning the plant through conventional, simple feedback in an 'inner loop', the resulting overall compensated plant design enjoyed considerable enhancement of performance robustness in the presence of parametric uncertainty. Second, the nonlinear techniques did not have any proven robustness properties in the presence of unstructured uncertainty; a definition of robustness (and performance) is very difficult to achieve outside the frequency domain; to date, none is available for the purposes of control system design. Thus, by proper design of the outer loop, such properties could still be 'injected' in the overall system.

Valavani, Lena↗
NASA NTRS1988

R-parametrization and its role in classification of linear multivariable feedback systems

A classification of all the compensators that stabilize a given general plant in a linear, time-invariant multi-input, multi-output feedback system is developed. This classification, along with the associated necessary and sufficient conditions for stability of the feedback system, is achieved through the introduction of a new parameterization, referred to as R-Parameterization, which is a dual of the familiar Q-Parameterization. The classification is made to the stability conditions of the compensators and the plant by themselves; and necessary and sufficient conditions are based on the stability of Q and R themselves.

Chen, Robert T. N.↗
NASA NTRS1976

Decentralization, stabilization, and estimation of large-scale linear systems

In this short paper we consider three closely related aspects of large-scale systems: decentralization, stabilization, and estimation. A method is proposed to decompose a large linear system into a number of interconnected subsystems with decentralized (scalar) inputs or outputs. The procedure is preliminary to the hierarchic stabilization and estimation of linear systems and is performed on the subsystem level. A multilevel control scheme based upon the decomposition-aggregation method is developed for stabilization of input-decentralized linear systems Local linear feedback controllers are used to stabilize each decoupled subsystem, while global linear feedback controllers are utilized to minimize the coupling effect among the subsystems. Systems stabilized by the method have a tolerance to a wide class of nonlinearities in subsystem coupling and high reliability with respect to structural perturbations. The proposed output-decentralization and stabilization schemes can be used directly to construct asymptotic state estimators for large linear systems on the subsystem level. The problem of dimensionality is resolved by constructing a number of low-order estimators, thus avoiding a design of a single estimator for the overall system.

Siljak, D. D.↗
NASA NTRS1992

Spacecraft nonlinear control

The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.

Sheen, Jyh-Jong↗
NASA NTRS1987

An analytical and experimental investigation of output feedback vs. linear quadratic regulator

This paper presents analytical and experimental comparison of three control laws for a laboratory structure designed to simulate large space structures. The first control law is the standard time invariant linear quadratic regulator with state estimation, which requires model reduction for practical implementation. This model reduction is associated with the so-called spillover instability. Two new simple direct output feedback control laws guaranteeing stability are proposed. One minimizes the maximum control force, and the other minimizes the same quadratic performance index as the linear quadratic regulator. The three control laws are found to give comparable performance for the modes retained in the reduced model. However, the standard linear quadratic regulator with state estimation provides almost no margin of stability for the unmodeled modes, while the simpler direct feedback laws provide significant stability margins to all modes. The analytical results were verified experimentally using a digital implementation of the control laws. Good agreement between the analytical predictions and experimental measurements was observed.

Martinovic, Zoran N.↗
NASA NTRS1987

Robust nonlinear attitude control of flexible spacecraft

This paper presents an approach to large-angle rotational maneuvers of a spacecraft-beam-tip body configuration based on nonlinear invertibility and linear feedback stabilization. A control law u sub d is derived for the decoupled control of attitude angles, lateral elastic deflections, slopes due to bending and angular deflection due to torsion at the tip of the beam using torquers and force actuators. For the stabilization of the elastic modes, a linear feedback control law u sub s is obtained based on a linearized model augmented with a servocompensator. Simulation results are presented to show that large slewing and elastic mode stabilization can be accomplished.

Singh, Sahjendra N.↗
NASA NTRS1986

Nonlinear attitude control of elastic spacecraft-antenna system

An approach to large angle rotational maneuvers of a spacecraft-beam-tip body (an antenna or a reflector) configuration based on nonlinear invertibility and linear feedback stabilization is presented. A control law u sub d is derived to obtain independent decoupled control of attitude angles, lateral elastic deflections, slopes due to bending and angular deflection due to torsion at the tip of the beam using torquers and force actuators. For the stabilization of the elastic oscillations, a linear feedback control law, u sub s, is obtained based on a linearized model about the terminal state augmented with a servo-compensator. Simulation results obtained for single axis control, for simplicity, show that large slewing and elastic mode stabilization can be accomplished in spite of uncertainty in the system using the total control u = u sub d + u sub s.

Singh, S. N.↗
NASA NTRS1991

A geometric approach to regulator and tracker design for an aerospace plane

The paper presents a nonlinear design approach drawing from singular perturbations, feedback linearization, and variable structure control, that leads to regulators with automatic gain scheduling which exhibit similar dynamic behavior over the entire flight envelope of the aerospace plane. Additionally, design approach provides for a systematic way to counter disturbance effects as well as modeling uncertainties. The unifying feature of the three nonlinear feedback control methodologies is that they all have a geometric interpretation. First, the translational dynamics are decomposed into reduced-order slow and fast dynamics by way of a formal singular perturbation analysis. After feedback linearization the fast dynamics are robustly stabilized via a variable structure control approach. The slow dynamics are stabilized using conventional proportional-integral compensation based on the nominal slow dynamics. A number of sample command and disturbance responses at opposite ends of the flight envelope are presented for a nonlinear aerospace plane model.

Van Buren, Mark A.↗
NASA NTRS1987

Effects of joint rate and displacement constraints on stability regions

A block diagram showing plant dynamics in normal mode coordinates, a linear feedback controller with command limits, and actuator dynamics with rate and displacement limits is given. The objective is to examine the effects of joint rate and displacement saturation limits on the stability regions. An unstable short period dynamic model is transformed into normal mode coordinates and is augmented with actuator dynamics. A linear feedback controller is used to provide closed-loop stability. The stability with constrained actuator rate limits under varying bandwidth, displacement and command limits is examined.

Shrivastava, P. C.↗
NASA NTRS1994

Robust stability of second-order systems

Nonlinear control using feedback linearization or inverse dynamics for robotic manipulators yields good results in the absence of modeling uncertainty. However, modeling uncertainties due to unknown joint friction coefficients and payload variations can give rise to undesirable characteristics when these control systems are implemented. It is shown how passivity concepts can be used to supplement the feedback linearization control design technique, in order to make it robust with respect to the uncertain effects mentioned above. Results are obtained for space manipulators with freely floating base; however, they are applicable to fixed base manipulators as well. The controller guarantees asymptotic tracking of the joint variables. Closed-loop simulation results are illustrated for planar space manipulators for cases where uncertainty exists in friction modeling and payload inertial parameters.

Chuang, C.-H.↗
NASA NTRS2022

Adaptive Force Control for Small Celestial Body Sampling

An adaptive force control algorithm for small celestial body sampling for a variety of surface properties is developed. The control algorithm consists of an adaptive controller combined with feedback linearization. When a spacecraft makes contact with the surface, it must maintain a desired contact force in order to capture a sample. The properties of the surface are unknown or uncertain before contact with the surface is made. The adaptive controller performs system identification online to create an input-output model of the feedback linearized system. From the input-output model a block observable canonical form is realized and the control input is determined by model predictive control (MPC) to maintain a desired contact force in spite of the unknown surface properties. The approach is applied to a variety of surface properties with linear and nonlinear contact models.

Quadrelli, Marco M↗