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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Component mode damping assignment techniques

A relation between the system modal damping matrix and the component modal damping matrix is derived from First Principles. An optimization problem is then formulated to select all the component modes' damping ratios that best satisfy the above derived relation. A weighting matrix is used in the cost functional to stress the relative importance of the diagonal terms in the damping matrix. Inequality constraints are also added to the optimization problem to pick only nonnegative component modes' damping factors. The optimization problem may be solved algebraically or iteratively. The proposed techniques are successfully used on a high order, finite element model of the Galileo spacecraft.

Lee, Allan Y.↗
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 NTRS1991

Review of LFTs, LMIs, and mu

The authors present a tutorial overview of linear fractional transformations (LFTs) and the role of the structured singular value, mu, and linear matrix inequalities (LMIs) in solving LFT problems. The authors first introduce the notation for LFTs and briefly discuss some of their properties. They then describe mu and its connections with LFTs. They focus on two standard notions of robust stability and performance, mu stability and performance and Q stability and performance, and their relationship is discussed. Comparisons with the L1 theory of robust performance with structured uncertainty are considered.

Doyle, John↗
NASA NTRS1993

A new approach to mixed H2/H infinity controller synthesis using gradient-based parameter optimization methods

In the past few years, the mixed H(sub 2)/H-infinity control problem has been the object of much research interest since it allows the incorporation of robust stability into the LQG framework. The general mixed H(sub 2)/H-infinity design problem has yet to be solved analytically. Numerous schemes have considered upper bounds for the H(sub 2)-performance criterion and/or imposed restrictive constraints on the class of systems under investigation. Furthermore, many modern control applications rely on dynamic models obtained from finite-element analysis and thus involve high-order plant models. Hence the capability to design low-order (fixed-order) controllers is of great importance. In this research a new design method was developed that optimizes the exact H(sub 2)-norm of a certain subsystem subject to robust stability in terms of H-infinity constraints and a minimal number of system assumptions. The derived algorithm is based on a differentiable scalar time-domain penalty function to represent the H-infinity constraints in the overall optimization. The scheme is capable of handling multiple plant conditions and hence multiple performance criteria and H-infinity constraints and incorporates additional constraints such as fixed-order and/or fixed structure controllers. The defined penalty function is applicable to any constraint that is expressible in form of a real symmetric matrix-inequity.

Ly, Uy-Loi↗
NASA NTRS1996

Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts

Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.

Gupta, Sandeep↗
NASA NTRS1994

Some Properties and Stability Results for Sector-Bounded LTI Systems

This paper presents necessary and sufficient conditions for a linear, time-invariant (LTI) system to be inside sector (n, b) in terms of linear matrix inequalities in its state-space realization matrices, which represents a generalization of similar conditions for bounded H(sub infinity)-norm systems. Further, a weaker definition of LTI systems strictly inside closed sector (a, b) is proposed, and state-space characterization of such systems is presented. Sector conditions for stability of the negative feedback interconnection of two LTI systems and for stability of LTI systems with feedback nonlinearities are investigated using the Lyapunov function approach. It is shown that the proposed weaker conditions for an LTI system to be strictly inside a sector are sufficient to establish closed-loop stability of these systems.

Gupta, Sandeep↗
NASA NTRS1996

Optimally Scaled H(sub infinity) Full Information Control Synthesis with Real Uncertainty

This paper presents an algorithm to synthesize optimal controllers for the scaled H(sub infinity). full information problem with real and complex uncertainty. The control problem is reduced to a linear matrix inequality which can be solved via a finite dimensional convex optimization. This technique is compared with the optimal scaled H(sub infinity). full information with only complex uncertainty and D - K iteration control design to synthesize controllers for a missile autopilot. Directly including real parametric uncertainty into the control design results in improved robust performance of the missile autopilot. The controller synthesized via D - K iteration achieves results similar to the optimal designs.

Balas, Gary J.↗
NASA NTRS1995

Optimal Full Information Synthesis for Flexible Structures Implemented on Cray Supercomputers

This paper considers an algorithm for synthesis of optimal controllers for full information feedback. The synthesis procedure reduces to a single linear matrix inequality which may be solved via established convex optimization algorithms. The computational cost of the optimization is investigated. It is demonstrated the problem dimension and corresponding matrices can become large for practical engineering problems. This algorithm represents a process that is impractical for standard workstations for large order systems. A flexible structure is presented as a design example. Control synthesis requires several days on a workstation but may be solved in a reasonable amount of time using a Cray supercomputer.

Lind, Rick↗
NASA NTRS1999

Robust Passification via Optimal Sensor Blending and Control Allocation

Robust passification is considered for uncertain linear, time invariant, systems having redundant actuators and sensors. The approach is to obtain optimal sensor blending and control allocation matrices that maximize the region in the parameter space in which the system remains passive. The approach results in a generalized eigenvalue problem consisting of a number of linear matrix inequalities (LMIs). Reduction of the number of LMIs is investigated, and a numerical example is given for demonstrating the approach.

Joshi, S. M.↗
NASA NTRS1999

Robust Passification via Optimal Sensor Blending and Control Allocation

Robust passification is considered for uncertain linear, time invariant systems having redundant actuators and sensors. The approach is to obtain optimal sensor blending and control allocation matrices that maximize the region in the parameter space in which the system remains passive. The approach results in a generalized eigenvalue problem consisting of a number of linear matrix inequalities (LMIs). Reduction of the number of LMIs is investigated, and a numerical example is given for demonstrating the approach.

Joshi, S. M.↗
NASA NTRS1998

A Robust Control Approach for the Formation Flying of Multiple Spacecraft

We present a disturbance rejection mechanism for the formation flying of multiple spacecraft based on a robust control approach in terms of an H(sub infinity) control problem. The corresponding H(sub infinity) control problem is then solved numerically using linear matrix inequalities.

Mesbahi, M.↗
NASA NTRS2000

Synthesis Methods for Robust Passification and Control

The research effort under this cooperative agreement has been essentially the continuation of the work from previous grants. The ongoing work has primarily focused on developing passivity-based control techniques for Linear Time-Invariant (LTI) systems. During this period, there has been a significant progress made in the area of passivity-based control of LTI systems and some preliminary results have also been obtained for nonlinear systems, as well. The prior work has addressed optimal control design for inherently passive as well as non- passive linear systems. For exploiting the robustness characteristics of passivity-based controllers the passification methodology was developed for LTI systems that are not inherently passive. Various methods of passification were first proposed in and further developed. The robustness of passification was addressed for multi-input multi-output (MIMO) systems for certain classes of uncertainties using frequency-domain methods. For MIMO systems, a state-space approach using Linear Matrix Inequality (LMI)-based formulation was presented, for passification of non-passive LTI systems. An LMI-based robust passification technique was presented for systems with redundant actuators and sensors. The redundancy in actuators and sensors was used effectively for robust passification using the LMI formulation. The passification was designed to be robust to an interval-type uncertainties in system parameters. The passification techniques were used to design a robust controller for Benchmark Active Control Technology wing under parametric uncertainties. The results on passive nonlinear systems, however, are very limited to date. Our recent work in this area was presented, wherein some stability results were obtained for passive nonlinear systems that are affine in control.

Kelkar, Atul G.↗
NASA NTRS2001

Control of Flexible Systems in the Presence of Failures

Control of flexible systems under degradation or failure of sensors/actuators is considered. A Linear Matrix Inequality framework is used to synthesize H(sub infinity)-based controllers, which provide good disturbance rejection while capable of tolerating real parameter uncertainties in the system model, as well as potential degradation or failure of the control system hardware. In this approach, a one-at-a-time failure scenario is considered, wherein no more than one sensor or actuator is allowed to fail at any given time. A numerical example involving control synthesis for a two-dimensional flexible system is presented to demonstrate the feasibility of the proposed approach.

Magahami, Peiman G.↗
NASA NTRS2002

Linear Parameter Varying Control Synthesis for Actuator Failure, Based on Estimated Parameter

The design of a linear parameter varying (LPV) controller for an aircraft at actuator failure cases is presented. The controller synthesis for actuator failure cases is formulated into linear matrix inequality (LMI) optimizations based on an estimated failure parameter with pre-defined estimation error bounds. The inherent conservatism of an LPV control synthesis methodology is reduced using a scaling factor on the uncertainty block which represents estimated parameter uncertainties. The fault parameter is estimated using the two-stage Kalman filter. The simulation results of the designed LPV controller for a HiMXT (Highly Maneuverable Aircraft Technology) vehicle with the on-line estimator show that the desired performance and robustness objectives are achieved for actuator failure cases.

Shin, Jong-Yeob↗
NASA NTRS2002

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.↗
NASA NTRS2003

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↗
NASA NTRS2005

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↗
NASA NTRS2005

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)↗