Search NASA⌕ Search

SEARCH · Search NASA

Results for “linear matrix inequality”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

A Convex Approach to Fault Tolerant Control

The design of control laws for dynamic systems with the potential for actuator failures is considered in this work. The use of Linear Matrix Inequalities allows more freedom in controller design criteria than typically available with robust control. This work proposes an extension of fault-scheduled control design techniques that can find a fixed controller with provable performance over a set of plants. Through convexity of the objective function, performance bounds on this set of plants implies performance bounds on a range of systems defined by a convex hull. This is used to incorporate performance bounds for a variety of soft and hard failures into the control design problem.

Maghami, Peiman G.↗

LPV Antiwindup Compensation for Enhanced Flight Control Performance

In this paper, we propose a saturation control scheme for linear parameter-varying (LPV) systems from an antiwindup control perspective. The proposed control approach is advantageous because it can be thought of as an augmented control algorithm from the existing control system. Moreover, the synthesis condition for an antiwindup compensator is formulated as a linear matrix inequality (LMI) optimization problem and can be solved efficiently. We have applied the LPV antiwindup controller to an F-16 longitudinal autopilot control system design to enhance aircraft safety and improve flight quality in a high angle of attack region.

Lu, Bei↗

Linear-Parameter-Varying Antiwindup Compensation for Enhanced Flight Control Performance

Actuator saturation is one of the major issues of flight control in the high angle-of-attack region. This paper presents a saturation control scheme for linear parameter varyjing (LPV) systems from an antiwindup control perspective. The proposed control approach is advantageous from the implementation standpoint because it can be thought of as an augmented control algorithm to the existing control system. Moreover, the synthesis condition for an antiwindup compensator is formulated as a linear matrix inequality (LMI) optimization problem and can be solved efficiently. We have applied te LPV antiwindup controller to an F-16 longitudinal autopilot control system design and compared it with the thrust vectoring control scheme. The nonlinear simulations show that an LPV antiwindup controller improves flight quality and offers advantages over thrust vectoring in a high angle-of-attack region.

Lu, Bei↗

Small Body GN&C Research Report: A Guidance and Control Technique for Small-Body Proximity Operations with Guaranteed Guidance Resolvability and Required Thruster Silent Time

The guidance and control (G&C) algorithms for enabling small-body proximity operations are developed by using a model predictive control approach along with a convexification of the governing dynamics, control constraints, and trajectory/state constraints. The open-loop guidance is solved ahead of time or in a resolvable, real-time manner through the use of PWG (Pseudo Way-point Generation), a technique developed in this research. The PWG scheme ensures required thruster silent times during trajectory maneuvers. The feedback control is implemented to track the PWG trajectories in a manner that guarantees the resolvability for the open-loop problem, enabling the ability to update the G&C in a model-predictive manner. The schemes incorporate gravity models and thruster ring times into discrete dynamics that are solved as a optimal control problem to minimize fuel consumption or thruster energy expenditure. The optimal control problem is cast as an LMI (Linear Matrix Inequality) and then solved through Semi-Definite Programming techniques in a computationally efficient manner that provides convergence and constraint guarantees.

guidance and control (G&C)↗

Algorithm Optimally Allocates Actuation of a Spacecraft

A report presents an algorithm that solves the following problem: Allocate the force and/or torque to be exerted by each thruster and reaction-wheel assembly on a spacecraft for best performance, defined as minimizing the error between (1) the total force and torque commanded by the spacecraft control system and (2) the total of forces and torques actually exerted by all the thrusters and reaction wheels. The algorithm incorporates the matrix vector relationship between (1) the total applied force and torque and (2) the individual actuator force and torque values. It takes account of such constraints as lower and upper limits on the force or torque that can be applied by a given actuator. The algorithm divides the aforementioned problem into two optimization problems that it solves sequentially. These problems are of a type, known in the art as semi-definite programming problems, that involve linear matrix inequalities. The algorithm incorporates, as sub-algorithms, prior algorithms that solve such optimization problems very efficiently. The algorithm affords the additional advantage that the solution requires the minimum rate of consumption of fuel for the given best performance.

Motaghedi, Shi↗

Estimating the Inertia Matrix of a Spacecraft

A paper presents a method of utilizing some flight data, aboard a spacecraft that includes reaction wheels for attitude control, to estimate the inertia matrix of the spacecraft. The required data are digitized samples of (1) the spacecraft attitude in an inertial reference frame as measured, for example, by use of a star tracker and (2) speeds of rotation of the reaction wheels, the moments of inertia of which are deemed to be known. Starting from the classical equations for conservation of angular momentum of a rigid body, the inertia-matrix-estimation problem is formulated as a constrained least-squares minimization problem with explicit bounds on the inertia matrix incorporated as linear matrix inequalities. The explicit bounds reflect physical bounds on the inertia matrix and reduce the volume of data that must be processed to obtain a solution. The resulting minimization problem is a semidefinite optimization problem that can be solved efficiently, with guaranteed convergence to the global optimum, by use of readily available algorithms. In a test case involving a model attitude platform rotating on an air bearing, it is shown that, relative to a prior method, the present method produces better estimates from few data.

Acikmese, Behcet↗

LMI-Based Fuzzy Optimal Variance Control of Airfoil Model Subject to Input Constraints

This paper presents a study of fuzzy optimal variance control problem for dynamical systems subject to actuator amplitude and rate constraints. Using Takagi-Sugeno fuzzy modeling and dynamic Parallel Distributed Compensation technique, the stability and the constraints can be cast as a multi-objective optimization problem in the form of Linear Matrix Inequalities. By utilizing the formulations and solutions for the input and output variance constraint problems, we develop a fuzzy full-state feedback controller. The stability and performance of the proposed controller is demonstrated through its application to the airfoil flutter suppression.

optimal variance control↗

LMI-Based Multiobjective Optimization and Control of Flexible Aircraft Using VCCTEF

This paper considers the control of coupled aeroelastic aircraft model with Variable Camber Continuous Trailing Edge Flap (VCCTEF) system. The relative motion between two adjacent flaps is constrained and this actuation constraint problem is converted into an output covariance constraint problem, and therefore can be formulated using linear matrix inequalities (LMIs). A set of LMI conditions is derived for the design of an observer-based dynamic output feedback controller for VCCTEF configured aeroelastic aircraft model. The proposed controller is then applied to the NASA Generic Transport Model (GTM) for simulation, and the results demonstrate the efficacy of the proposed approach.

LMI control↗

Modeling and Control of Robot-Structure Coupling During In-Space Structure Assembly

This paper considers the problem of robot-structure coupling dynamics during in-space robotic assembly of large flexible structures. A two-legged walking robot is used as a construction agent, whose primary goal is to stably walking on the flexible structure while carrying a substructure component to a designated location. The reaction forces inserted by the structure to the walking robot are treated as bounded disturbance inputs, and a trajectory tracking robotic controller is proposed that combines the standard full state feedback motion controller and an adaptive controller to account for the disturbance inputs. In this study, a reduced-order Euler-Bernoulli beam structure model is adapted, and a finite number of co-located sensors and actuators are distributed along the span of the beam structure. The robot-structure coupling forces are treated as a bounded external forcing function to the structure, and hence an output covariance constraint problem can be formulated, in terms of linear matrix inequality, for optimal structure control by utilizing the direct output feedback controllers. The numerical simulations show the effectiveness of the proposed robot-structure modeling and control methodology.

Swei, Sean↗

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASA’s Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach.

Weinstein, Rose↗

Robust Controller Synthesis for Vision-based Spacecraft Guidance and Control

This work develops a method for Robust Controller for Vision-based Spacecraft (RCVS) guidance and control, integral to the robust autonomy framework for multi-spacecraft for- mation control and reconfiguration applications. The method is built around the use of a photo-realistic simulator, where a camera is deployed on a tracking spacecraft (ego) in order to observe an uncontrolled spacecraft (target) in a Low Earth Orbit (LEO). In this direction, the proposed approach performs the relative state (attitude and position) estimation of the target spacecraft using Convolutional Neural Network (CNN). The state estimation error is then modeled and the corresponding error-bounds are obtained around a nominal trajectory of the ego and target spacecraft. Next, this work proposes a linear matrix inequalities (LMIs) based approach to controller synthesis, guaranteed to be robust against both model uncertainties and measurement errors, resulting from vision-based estimation. This controller is comprised of two distinct components, one synthesized based on the nominal trajectory, while the “robust” component corrects for deviations from the nominal trajectory. Finally, a tracking scenario that directly utilize the image data for spacecraft guidance and control, is presented to showcase the performance of the proposed robust autonomy framework.

Rahmani, Amir↗

LPV Modeling and Control for Active Flutter Suppression of a Smart Airfoil

In this paper, a novel technique of linear parameter varying (LPV) modeling and control of a smart airfoil for active flutter suppression is proposed, where the smart airfoil has a groove along its chord and contains a moving mass that is used to control the airfoil pitching and plunging motions. The new LPV modeling technique is proposed that uses mass position as a scheduling parameter to describe the physical constraint of the moving mass, in addition the hard constraint at the boundaries is realized by proper selection of the parameter varying function. Therefore, the position of the moving mass and the free stream airspeed are considered the scheduling parameters in the study. A state-feedback based LPV gain-scheduling controller with guaranteed H infinity performance is presented by utilizing the dynamics of the moving mass as scheduling parameter at a given airspeed. The numerical simulations demonstrate the effectiveness of the proposed LPV control architecture by significantly improving the performance while reducing the control effort.

Smart Airfoil↗

A generalized Lyapunov theory for robust root clustering of linear state space models with real parameter uncertainty

The problem of analyzing and designing controllers for linear systems subject to real parameter uncertainty is considered. An elegant, unified theory for robust eigenvalue placement is presented for a class of D-regions defined by algebraic inequalities by extending the nominal matrix root clustering theory of Gutman and Jury (1981) to linear uncertain time systems. The author presents explicit conditions for matrix root clustering for different D-regions and establishes the relationship between the eigenvalue migration range and the parameter range. The bounds are all obtained by one-shot computation in the matrix domain and do not need any frequency sweeping or parameter gridding. The method uses the generalized Lyapunov theory for getting the bounds.

Yedavalli, R. K.↗