Robust Eigenstructure Assignment Research Articles

Mode decoupling robust eigenstructure assignment applied to the lateral-directional dynamics of the F-16 aircraft

In this paper, a robust controller is designed which is based on the eigenstructure assignment technique. With this technique, the physical modes of the system are decoupled by the appropriate shaping of the eigenvectors. While keeping the desired eigenvector structure as much as possible, Nelder–Mead optimization algorithm is implemented for the search of the optimal robust solution. Different optimization cost functions are investigated in terms of eigenvalue sensitivity and stability robustness. Design solutions are compared with each other and with a fundamental solution in terms of robustness measures. Furthermore, a small amount of flexibility is included in the selection of the eigenvalue locations and the improvement in the robustness is evaluated by singular value analysis. The effectiveness of the control system is demonstrated with nonlinear simulations on the F-16 aircraft mathematical model.

Neurodynamics-Based Robust Pole Assignment for High-Order Descriptor Systems.

In this paper, a neurodynamic optimization approach is proposed for synthesizing high-order descriptor linear systems with state feedback control via robust pole assignment. With a new robustness measure serving as the objective function, the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem. A neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high-order singular systems with guaranteed optimality and exact pole assignment. Two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach.

Robust Eigenstructure Assignment in Geometric Control Theory

In this paper we employ the Rosenbrock system matrix pencil for the computation of output-nulling subspaces of linear time-invariant systems which appear in the solution of a large number of control and estimation problems. We also consider the problem of finding friends of these output-nulling subspaces, i.e., the feedback matrices that render such subspaces invariant with respect to the closed-loop map and output-nulling with respect to the output map, and which at the same time deliver a robust closed-loop eigenstructure. We show that the methods presented in this paper offer considerably more robust eigenstructure assignment than the other commonly used methods and algorithms.

ROBUST EIGENSTRUCTURE ASSIGNMENT: NEW APPROACH

This paper considers the problem of robust eigenstructure assignment, which involves finding a feedback gain matrix that makes the closed-loop system insensitive to perturbations or parameter variations. The main contribution of the paper is to derive a new robustness measure using the matrix perturbation theory. The new measure is used to formulate a new method for robust control of the system via state or output feedback. The freedom provided by eigenvalue assignment of multivariable systems is applied to optimize the new index using genetic algorithms. The new results expressed in this paper confirm the previously derived results on robust eigenstructure assignment. In the case of state feedback design, the new robustness index verifies a previously proposed robustness measure. A numerical example is presented to illustrate the effectiveness of the proposed method.

ENTIRELY LEFT EIGENSTRUCTURE-ASSIGNMENT FOR FAULT DIAGNOSIS OBSERVERS

In this paper a unified geometrically-embedded methodology of synthesis of static decoupled residual generators is presented that leads to a sub-optimal solution to a robust eigenstructure assignment problem based on a predetermined set of eigenvalues. Robustness of this design means that its eigenvector matrix is sufficiently well conditioned. An original idea of a convenient parameterization of corresponding attainable eigensubspaces is developed and new conditions for disturbance decoupling are derived solely in terms of the left eigenvectors of a system observation state-transition matrix. The resolved completely-static disturbance-decoupling design problem can be treated as an effective preliminary-design stage of an integral synthesis of residual generators. A numerical example illustrates the effectiveness of the presented method.

Observer-Based Model Reference Sliding-Mode Control of Active Suspension Systems

In this paper a model reference variable structure controller (VSC) for an active suspension system is designed. A half vehicle model is used in which, the vertical and pitch motions of the mass supported by the suspension and the vertical motion of the suspension masses are considered. Sliding mode controller is applied for the purpose of disturbance attenuation. Unit vector approach, which is a sliding mode control structure for multivariable systems, is used and a robust adaptive nonlinear controller is designed. A reduced-order observer is designed to use only output information. Robust eigenstructure assignment method is implemented in the line of sliding surface design. Simulation results verify the effectiveness of the proposed nonlinear controller scheme in comparison with the passive suspension system and also H∞ technique. The output of the closed-loop system can also smoothly track a set point in a manner that the vertical position of vehicle may be regulated toward the desired point.

Robust eigenstructure assignment with minimum subspace separation

AbstractA computation method for delivering a state feedback controller that assigns closed‐loop eigenstructure with a minimum subspace separation and is robust towards unstructured perturbations is presented. The subspace separation is measured via the difference between two subspace projections, while the eigenstructure robustness is achieved by maximizing an upper bound on the allowable perturbation size such that the closed‐loop system remains stable. By exploiting the Sylvester equation parametrization, the constraint of pole assignment can be satisfied intrinsically and the robust eigenstructure assignment design essentially becomes an unconstrained optimization task. Analytical gradient formulas of the objective functions to be handled are developed. The design approach is demonstrated through numerical examples. Copyright © 2004 John Wiley & Sons, Ltd.

Integrated Structural/Control Design for Robust Vibration Control of Flexible Structures

This paper presents methods of integrated structural/control design for active vibration control of flexible structures. Two different approaches are introduced from the viewpoint of closed-loop system robustness. One is based on a frequency-shaped design of the feedback force by using the dynamics of the component structure. The method is applied to the design of a flexible tendon control system. The other is a robust eigenstructure assignment approach, which minimizes the condition number to suppress the deviation of the closed-loop eigenvalues caused by system uncertainties. This paper introduces a new index of condition number for improving the solvability and computational effort in the optimization. The method is applied to the structural/control design of a truss structure.

Mixed time- and frequency-domain robust eigenstructure assignment

This paper considers robust eigenstructure assignment for multivariable systems. The time-domain performance specifications provided by eigenstructure assignment and robust performance specifications in the frequency domain considered by H infinity control are combined to realize joint optimal robust control design. A parametric expression for state-feedback eigenstructure assignment is introduced on the basis of a set of free parameters. The mixed performance index used as the cost function consists of two parts: robustness in the frequency domain; and system eigenstructure constraints in the time domain. The analytical gradient calculation of the cost function with respect to the free parameters is derived for optimal robust eigenstructure assignment using gradientbased optimization. The mixed time- and frequency-domain robust eigenstructure assignment is demonstrated in the design of a mode-decoupled roll-yaw autopilot.

Optimisation approach to robust eigenstructure assignment

A systematic optimisation approach to robust eigenstructure assignment for control systems with output feedback is presented. The proposed scheme assigns the maximum allowable number of closed-loop eigenvalues to desired locations, and determines the corresponding closed-loop eigenvectors as close to desired ones as possible. Additionally, the stability of the remaining closed-loop eigenvalues is guaranteed by the satisfaction of an appropriate Lyapunov equation. The overall design is robust with respect to time-varying parameter perturbations. The approach is applied to a literature example, where it is shown to capture the shape of the desired transient response.

Robust controller design for a skid to turn missile

The design and analysis of Robust Autopilot for skid-to-turn missile is presented. Two of the popular Robust Controller design approaches, The Loop Shaping Design Procedure (LSDP) and The Robust Eigenstructure Assignment are considered. The missile model considered in the present work is having lightly damped modes and non-minimum phase zeros, with stringent performance requirements. Numerical results are presented to evaluate the Robustness of stability and performance of the controller. Merits and demerits of the above said methodologies are brought out clearly as applied to this specific plant.

Modal coupling in linear control systems using robust eigenstructure assignment

Eigenvalue assignment methods are used widely in the design of control and state-estimation systems. The corresponding eigenvectors can be selected to ensure robustness. For specific applications, eigenstructure assignment can also be applied to achieve more general performance criteria. In this paper a new output feedback design approach using robust eigenstructure assignment to achieve prescribed mode input and output coupling is described. A minimisation technique is developed to improve both the mode coupling and the robustness of the system, whilst allowing the precision of the eigenvalue placement to be relaxed. An application to the design of an automatic flight control system is demonstrated.

Robust eigenstructure assignment combining time- and frequency-domain performance specifications

This paper is concerned with robust eigenstructure assignment for multivariable systems. It combines time-domain performance specifications provided by eigenstructure assignment and robust performance specifications in the frequency domain considered by H∞ control to realize joint optimal robust control design. A unified parametric solution for state-feedback eigenstructure assignment is derived for both the case where the sets of closed- and open-loop eigenvalues do not intersect and the case where these sets do intersect. This is based on a set of free parameters. All complex operations are converted into the real field so that the algorithm which is developed for the controller design can be easily implemented on computers. It uses a robustness index defined in the frequency domain as the cost function to be optimized. The analytical gradient calculation of the cost function with respect to the free parameters is given. Using gradient-based optimization, the robustness index is minimized by making full use of the freedom provided by eigenstructure assignment. © 1998 John Wiley & Sons, Ltd.

Robust Controller Design of Multi variable Systems via Eigenstructure Assignment

Abstract This paper is concerned with robust eigenstructure assignment for multivariable systems. It combines time-domain performance specifications provided by eigenstructure assignment and robust performance specifications in the frequency domain considered by H ∞ control to realize joint optimal robust control design. A unified parametric solution for state-feedback eigenstructure assignment derived for the cases where the sets of closed- and open-loop eigenvalues intersect or do not. This based on a set of free parameters. It uses a robustness index defined in the frequency domain as the cost function to be optimized. The analytical gradient calculation of the cost function with respect to the free parameters is given. Using gradient-based optimization, the robustness index is minimized by making full use of the freedom provided by eigenstructure assignment.

Robust eigenstructure assignment using the genetic algorithm and constrained state feedback

This paper describes a robust eigenstructure assignment methodology for a constrained state feedback problem. The method, which is based upon the linear quadratic regulator and involves the minimization, via the genetic algorithm, of a multiobjective cost function, is applied to L1011 Tristar aircraft lateral dynamics. The design example generates a fixed-gain state feedback solution which shows independent phase margins of 51· in each channel, while exhibiting an eigenstructure close to that desired, lying well within specified handling quality requirements. If two states are made unavailable for feedback, the robustness properties are seriously eroded. When a dynamic feedback compensator is then used, there is a substantial recovery of the robustness. It is concluded that the genetic algorithm approach described here is easy to use and generates good multivariable stability margins.

Parallel implementation of a genetic algorithm

This paper considers the parallel implementation of a genetic algorithm using a network of transputers. The context of the work is the design of a flight control system using a novel approach to Robust Eigenstructure Assignment. The robustness properties of the Linear Quadratic Regulator are exploited and Eigenstructure Assignment is performed to achieve desired aircraft handling qualities by projecting the desired eigenstructure into an output feedback constrained LQR subspace using a cost function minimisation approach. Both the motivation for parallelisation and the actual transputer implementations are considered. Indications of scalability and complexity are discussed in the light of specific implementation issues.

The state estimation of flow demands in gas networks from sparse pressure telemetry

This paper presents novel observer-based techniques for the estimation of flow demands in gas networks, from sparse pressure telemetry. A completely observable model is explored, constructed by incorporating difference equations that assume the flow demands are steady. Since the flow demands usually vary slowly with time, this is a reasonable approximation. Two techniques for constructing robust observers are employed: robust eigenstructure assignment and singular value assignment. These techniques help to reduce the effects of the system approximation. Modelling error may be further reduced by making use of known profiles for the flow demands. The theory is extended to deal successfully with the problem of measurement bias. The pressure measurements available are subject to constant biases which degrade the flow demand estimates, and such biases need to be estimated. This is achieved by constructing a further model variation that incorporates the biases into an augmented state vector, but now includes information about the flow demand profiles in a new form.

Robust eigenstructure assignment for the extended medium range air-to-air missile

A new sufficient condition for the robust stability of a linear time invariant system subject to linear time varying structured state space uncertainty is presented. This sufficient condition is a sum of terms each of which involves the ith right eigenvector, the ith left eigenvector, and the real part of the ith eigenvalue. This new robustness result is less conservative than an earlier result which involves the modal matrix and the real part of the eigenvalue which is closest to the imaginary axis in the complex plane. A robust design is computed for the Extended Medium Range Air-to-Air Missile and the new design is compared with an earlier orthogonal projection eigenstructure assignment design. The new design method uses the MATLAB TM Optimization Toolbox to minimize the integral of the deviations of the integrated roll rate (which is approximately the bank angle) from zero. The integral is approximated by a sum of discrete samples of the integrated roll rate while normalizing the integration width to unity. Constraints are placed on the real part of the Dutch roll and roll mode eigenvalues, the damping ratios of the Dutch roll and roll mode, the aileron and rudder deflection rates, and the sufficient condition for robust stability. The new design satisfies the robustness condition while also yielding an improved transient response.

Control design for robust eigenstructure assignment in linear uncertain systems

A generalized eigenstructure assignment procedure for designing a controller that has the best eigenstructure achievable while simultaneously maintaining stability robustness to time-varying parametric variations is presented. The approach taken is the constrained minimization of the difference between the actual and desired eigenstructure. The minimization is made subject to the constraints of the eigenstructure equation and the closed-loop Lyapunov equation. The capability of the formulation is illustrated in the design of a mode-decoupling roll-yaw autopilot for a generic, non-axisymmetrical airframe. >

Robust eigenstructure assignment with structured state-space uncertainty and unmodelled dynamics

New time domain stability robustness results have been obtained for a non-strictly proper linear time-invariant plant which is subject to simultaneous time-varying structured state-space uncertainly and norm bounded unmodelled dynamics. Sufficient conditions for robust stability are obtained both for a constant gain output feedback controller and an output feedback dynamic compensator. The robustness conditions are explicitly in terms of the closed-loop eigenvalues and eigenvectors so that these new results are especially well suited for a robust eigenstructure assignment design method. An example is presented of a robust eigenstructure assignment autopilot using dynamic compensation for the yaw/roll dynamics of a bank-to-turn missile.