Eigenstructure Assignment Technique Research Articles

Research on lateral-directional stability augmentation system of flying wing aircraft based on reliability model

Poor lateral-directional stability is a great risk to the design of flying wing aircraft due to the absence of vertical stabilizer. In order to improve the lateral-directional flying quality of this configuration aircraft, eigenstructure assignment technique by state feedback is adopted to design the stability augmentation system. The influence of eigenstructure on energy consumption of the control system is analyzed by citing energy consumption index in this paper. In addition, a reliability model is established to measure the reliability of the control system under uncertain factors. In order to assign eigenvalues and eigenvectors to obtain the control law of the system, a nested optimization model based on coupling degree, energy consumption and reliability is proposed. The outer optimization is used to optimize the eigenstructure, and inner optimization is used to compute the reliability of the control system in optimization process. A flying wing aircraft is used as a basis for the design of the stability augmentation system through the suggested optimization strategy. The optimization results demonstrate the validity of the method, and the lateral-directional flying quality of the aircraft has been improved greatly.

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.

Robust Power System Stabilizer Design Using Eigenstructure Assignment

This paper presents a design of a power system damping controller using partial right eigenstructure assignment. The eigenstructure assignment technique selects a set of closed-loop eigenvalues along with their right or left eigenvectors. The selection of eigenvectors offers extra flexibility which is exploited in this paper by designing a robust damping controller which provides the required damping under multiple operating conditions. A multi-input controller is used to increase the degrees of freedom available for the design. Remote measurements available from synchronised phasor measurements are also considered. The problem is formulated as a multi-objective nonlinear optimization problem and solved using the nonlinear simplex function in MATLAB. The proposed technique is used to design a robust power system stabilizer for the interconnected New England New York simplified power system model. Four contingencies are selected as additional operating conditions. The designed controller is validated using a nonlinear simulation.

Hidden Coupling Terms Inclusion in Gain-Scheduling Control Design: Extension of an Eigenstructure Assignment-Based Technique

This paper tackles the gain-scheduling control design issue when endogenous signals are selected as scheduling parameters. In this case, the gain-scheduled controller exhibits nonlinear dynamics, leading to the occurrence of hidden coupling terms in the linearized dynamics. Omitting hidden coupling terms in the synthesis process may induce performance degradation or even the destabilization of the closed-loop system. The present paper aims at extending a previous work on the design of gain-scheduled controller for hidden coupling terms inclusion via eigenstructure assignment technique. The efficiency of the proposed procedure is illustrated on a pitch-axis missile autopilot benchmark problem and is validated through nonlinear simulations.

Dominant pole and eigenstructure assignment for positive systems with state feedback

In this paper, the dominant pole assignment problem, the dominant eigenstructure assignment problem and the robust dominant pole assignment problem for linear time-invariant positive systems with state feedback are considered. The dominant pole assignment problem is formulated as a linear programming problem, and the dominant eigenstructure problem is formulated as a quasiconvex optimisation problem with linear constraints. The robust dominant pole assignment problem is formulated as a non-convex optimisation problem with non-linear constraints which is solved using particle swarm optimisation (PSO) with an efficient scheme which employs the dominant eigenstructure assignment technique to accelerate the convergence of the PSO procedure. Each of the three problems can be further constrained by requiring that the controller has a pre-specified structure, or the gain matrix have both elementwise upper and lower bounds. These constraints can be incorporated into the proposed scheme without increasing the complexity of the algorithms. Both the continuous-time case and the discrete-time case are treated in the paper.

Non-iterative eigenstructure assignment technique for finite element model updating

A novel control theory-based eigenstructure assignment (ESA) technique is employed to update the finite element model (FEM) of a linear time-invariant system. The proposed method uses state feedback to produce the gain matrix which in turn updates the existing system matrices through simultaneous assignment of eigenvalue-vector pairs in the FEM generated system matrices. However, unlike general control technique no external input is used to control the system. A subspace identification algorithm is applied to develop the state space model and the eigenstructure of its state matrix is used as the target for the ESA algorithm to update the FEM. Unlike most FEM updating algorithms which use optimization techniques, this method is not iterative (and hence computationally less expensive) as the state matrix gets updated just once yielding the single best possible solution to match the desired eigenstructure. Furthermore, it naturally preserves the basic exploitable properties like symmetry, sparsity, positive definiteness of the updated matrices. The method is first validated numerically on a four-story shear frame subjected to ambient vibrations. Following this, a two-story one-bay aluminium frame is subjected to a suite of excitations in the laboratory, and the response time histories are put through canonical variate analysis algorithm to yield the real system state space model, and hence the modal parameters. Noise is taken care of by singular value decomposition of the signal and performing ensemble averaging of the state matrix in its companion form. A very close conformation of the updated model is observed when compared to the modal parameters extracted from structural response.

An iterative updating method for damped structural systems using symmetric eigenstructure assignment

An iterative method for updating finite element models with measured modal results using a symmetric eigenstructure assignment technique is developed. By the method, the updated symmetric damping and stiffness matrices can be obtained within finite iteration steps in the absence of roundoff errors by choosing a special kind of initial matrices and the measured data are embedded in the updated model. The numerical results show that the proposed method is reliable and attractive.

RECONFIGURABLE CONTROLLER DESIGN FOR ACTUATOR FAULTS IN A FOUR-TANK SYSTEM BENCHMARK

The purpose of this work is to design a state feedback controller using Parametric Eigenstructure Assignment (PAE) technique that has the capacity to be reconfigured in the case that partial actuator faults occur. The proposed controller is capable of compensating the gain losses in actuators and maintaining the control performance in faulty situations. Simulations show the performance enhancement in comparison to the non-reconfigurable controller through Integral Absolute Error (IAE) index for different fault scenarios.

Reconfigurable Controller Design For Actuator Faults In A Four-Tank System Benchmark

The purpose of this work is to design a state feedback controller using Parametric Eigenstructure Assignment (PAE) technique that has the capacity to be reconfigured in the case that partial actuator faults occur. The proposed controller is capable of compensating the gain losses in actuators and maintaining the control performance in faulty situations. Simulations show the performance enhancement in comparison to the non-reconfigurable controller through Integral Absolute Error (IAE) index for different fault scenarios.

Parametric Lyapunov Equation Approach to Stabilization of Discrete-Time Systems With Input Delay and Saturation

This paper studies the problem of stabilization of discrete-time linear systems with input delay and saturation nonlinearity. By exploring some further intricate properties of the recently developed parametric Lyapunov equation-based low-gain feedback design approach, solutions are proposed to solve the problems by both state feedback and output feedback. This new approach is not only simpler than the existing method that is based on the eigenstructure assignment technique, but also provides explicit conditions on the low-gain parameter to guarantee the stability of the closed-loop system. Moreover, it is possible by adjusting the low-gain parameter online to achieve global results when the system is subject to both input saturation and time-delay. Also, the delay in the input is allowed to be time-varying in some cases.

Systematic Approach to Synthesize a Static Synchronous Compensator Controller Using Eigenstructure Assignment

A mode-decoupling controller in which the controller gains are synthesized by means of eigenstructure assignment is proposed for a static synchronous compensator. The proposed controller, inheriting the merits of the proportional-plus-integral controller, is implemented by an output feedback approach. An equivalent transformation from the given proportional-plus-integral controllers to the state space model is performed, which allows synthesizing a set of control gains capable of maintaining the physical control loops. To determine the mode shape of the closed-loop response, the eigenstructure assignment technique is employed to attain divisible control of the active and reactive powers for the static synchronous compensator. The experimental results have confirmed the effectiveness and performance of the proposed controller.

Multi-objective dynamic state and output feedback controllers for MIMO system using evolutionary algorithm and eigenstructure assignment

Most of the complex industrial plants are generally interacting multi-input multi-output (MIMO) systems. Controller design for such complex plants is a challenging task. In this paper, design of eigenstructure assignment (EA)-based multi-objective dynamic state and output feedback controllers for linear discrete MIMO system are considered. The significance of parametric eigenstructure assignment technique is that it provides more design degrees of freedom to obtain multi-objective functions. Based on parametric eigenstructure assignment, control problem is formulated to achieve conflicting multi-objective functions such as robust stability to parameter perturbation and smaller control gain to improve the transient response of the closed loop system. It is difficult to solve the conflicting objective functions using conventional optimisation techniques. In this paper, fast and elitist multi-objective evolutionary algorithm (MOEA) known as non-dominated sorting genetic algorithm-II (NSGA-II) is successfully applied for solving multi-objective problem. The robust stability and transient response are ensured by minimum condition number of eigenvector and minimum norm of controller gain. The proposed controllers use complex valued chromosomes to represent complex parametric vector. The effectiveness of the proposed controllers is validated by implementing the same in an interacting three-tank benchmark system.

Robust control for high-speed crafts using QFT and eigenstructure assignment

In this work, the problem of stabilisation of a high-speed craft with coupled dynamics is addressed. The action of the actuators to control the longitudinal dynamics (heave and pitch modes) produces a coupling in the transversal dynamics (roll mode), and vice versa. A combination of quantitative feedback theory (QFT) robust methodology and eigenstructure assignment (EA) methods is used to control the coupled system on a high-speed craft. The multi-input multi-output (MIMO) problem is firstly handled with the EA technique in order to decouple the dynamics, which results in three single-input single-output (SISO) systems to solve with QFT design. Dynamic responses of roll, pitch and heave modes of the entire fast ferry system are analysed at different sea states and angles of incidence. Time-domain simulations and frequency-domain performance analyses provide satisfactory results. It is shown that the combined EA/QFT technique is a feasible and very suitable robust method that can accomplish decoupling and damped responses and consequently a reduction in the motion sickness.

SVD based Reconfigurable Tracking Controller for Three-tank System via output/State Feedback

This paper deals with the control reconfiguration problem of partial actuator failure in a Three-Tank Multi-Input Multi-Output (MIMO) system. In order to tolerate known actuator failure, a reconfiguration in control parameter/structure is made through output/state feedback. A new Proportional-Integral (PI) Reconfigurable Controller (RC) design is proposed for servo tracking problem using Singular Value Decomposition (SVD) based Parametric Eigenstructure Assignment (PEA) technique. The main contribution of the paper is to design an optimal controller to achieve response shaping and guaranteed stability of the system. The effectiveness of the proposed controller is simulated by analyzing servo-regulatory responses of the threetank system for various fault scenarios. Finally, performance of the proposed state and output feedback controllers are compared by using various performance indices. The comparison reveals the feasibility of controller used for practical applications

Sobre projeto de observadores desacoplados de perturbação para sistemas descritores

Condições necessárias e suficientes para a existência de observadores de ordem reduzida desacoplados de perturbação para sistemas descritores lineares contínuos são apresentadas. Essas condições são baseadas na solução de uma equação de Sylvester generalizada, sob uma restrição que descreve o desacoplamento de perturbação do estado estimado e numa condição de posto que garante a existência de matrizes para a reconstrução de todas as variáveis de estado, também com desacoplamento de perturbação. Mostra-se que as condições para a existência do observador desejado estão associadas, fundamentalmente, a certas propriedades estruturais do sistema descritor. A partir destes resultados, propõe-se um algoritmo de projeto baseado em técnica de posicionamento de autoestrutura. Os resultados apresentados destinam-se, fundamentalmente, à aplicação em síntese de leis de controle do tipo realimentação de estados estimados. Um exemplo numérico ilustrativo do procedimento de projeto é apresentado.

Skid-to-turn missile autopilot design using scheduled eigenstructure assignment technique

This paper presents an application of adaptive control techniques to the design of skid-to-turn missile autopilot. The involved simplified adaptive controller is developed by combining gain scheduling approach with the eigenstructure assignment control design. A linear interpolation method is proposed to generate linear parameter-varying controller from a finite set of linear time-invariant controllers. Results of simulations are reported to demonstrate the performance, stability, and robustness of the considered autopilot.

New Model Correcting Method for Quadratic Eigenvalue Problems Using a Symmetric Eigenstructure Assignment

Finite element model correction of quadratic eigenvalue problems (QEPs) using a symmetric eigenstructure assignment technique was proposed by Zimmerman and Widengren and incorporates the measured model data into the finite element model to produce an adjusted finite element model on the damping and stiffness matrices that matches the experimental model data and minimizes the distance between the analytical and corrected models. Slightly different from the cost function proposed by Zimmerman and Widengren, based on the penalty function given by Friswell et al. , a cost function is considered that which measures the distance between the analytical and corrected models in a least-squares sense. An efficient algorithm is developed to solve the corresponding optimization problem. The resulting matrices obtained by the new method are necessary and sufficient to the optimization problem. Furthermore, the computational cost of the proposed algorithm requires only O(nm 2 ) floating-point operations, where n is the size of coefficient matrices of the QEP and m is the number of the measured modes

Fault Diagnosis and Reconfigurable Control of a Pressurizer in a Nuclear Power Plant

In this paper, an integrated approach to the design of fault diagnosis and reconfigurable fault-tolerant control system against actuator and sensor faults in a nuclear power plant pressurizer is proposed. The scheme uses a reconfigurable proportional-integral (PI) control structure and a setpoint adjustment technique to achieve required performance at both the dynamic and steady-state conditions. A singular value decomposition (SVD) based eigenstructure assignment (EA) technique is used to achieve on-line automatic redesign of the controller. Fault diagnosis and controller reconfiguration mechanisms are carried out using statistical hypothesis tests based on the information from a two stage adaptive Kalman filter. The proposed approach has been evaluated under different type of Unanticipated actuator faults: e.g. abrupt and incipient faults; total and partial faults; single, multiple and consecutive faults under both set-point regulation and set-point tracking. Through set-point tracking, specified performance degradation in the presence of actuator fault. can be eexplicitly considered. Detection and isolation of sensor faults are achieved by voting among outputs from several hardware redundant sensors. The effectiveness of the approach is demonstrated via simulation using a pressurizer model.

Eigenstructure assignment design for proportional-integral observers: the discrete-time case

A complete parametric design approach for proportional-integral observers of multivariable discrete-time linear systems is proposed based on an eigenstructure assignment technique. Complete parameterizations for all the observer gains as well as the eigenvector matrix of the observer system matrix are established in terms of three sets of design parameters that satisfy three basic and simple constraints. The proposed approach provides all the degrees of freedom and has great potential in applications. An illustrative example shows the effect of the proposed approach.

GRACEFUL PERFORMANCE DEGRADATION IN ACTIVE FAULT-TOLERANT CONTROL SYSTEMS

In this paper, a new design approach is proposed for active Fault-Tolerant Control Systems (FTCS), which allows one to explicitly incorporate possible graceful performance degradation into the design process. The method is based on explicit model-following and reference input adjustment techniques. The performance degradation is represented through a reference model. Only actuator faults are considered herein. When a fault is detected by the Fault Detection and Diagnosis (FDD) algorithm, the reconfigurable controller will be designed automatically so that the dynamics of the closed-loop system match that of the reference model. The system command input is also adjusted on-line to prevent the actuators from saturating during the initial period of controller reconfiguration. An eigenstructure assignment technique has been used for designing feedback part of the reconfigurable controller. The proposed method has been evaluated using lateral dynamics of an F-8 aircraft subject to actuator failures and constraints on the actuator dynamic ranges. Satisfactory results have been obtained.