Eigenstructure Assignment Control Research Articles

Experimental realization of an active non-reciprocal metamaterial using an eigen-structure assignment control strategy.

This paper presents a class of active non-reciprocal metamaterials (ANMMs) in an attempt to control the flow of acoustic waves along a one-dimensional acoustic duct. The proposed method distinguishes itself from the available approaches where the non-reciprocities are generated either actively or passively by various sources of nonlinearities, circulators and gyroscopic/gyrator components, and/or spatiotemporal modulation. The proposed method relies in its operation on a controller that is designed by simultaneous allocation of both the eigenvalues and eigenvectors. In other words, the entire eigen-structure of the closed-loop system is assigned as deemed necessary. Conventionally, the placement of the eigenvalues has been employed to enhance both the damping and response of the system. However, in this study, the focus is placed on adjusting the eigenvectors in a way that enables the spatial control and redistribution of the wave propagation along the acoustic duct in order to produce any desirable non-reciprocal behavior. During this entire process, the system continues to behave in a linear fashion. The theory governing the operation of this proposed approach is introduced, and a comprehensive experimental validation effort is presented to demonstrate the basic features, non-reciprocal behavior, and control characteristics. Generalization of the presented strategies to two-dimensional acoustic systems is a natural extension of the present work.

Active nonreciprocal metamaterial using an eigen-structure assignment control strategy.

A class of active nonreciprocal metamaterials (ANMMs) is developed to control the flow and distribution of energy along periodic dynamical systems. Such a development constitutes a radical departure from the currently available approaches where the non-reciprocities are generated either by utilizing various sources of passive nonlinearities, gyroscopic circulators, spatiotemporal modulation, or active control of nonlinear systems. The proposed ANMM cell consists of a one-dimensional acoustic duct provided with linear active control capabilities. The controller is designed by simultaneous assignment of both the eigenvalues and eigenvectors, i.e., the entire eigen-structure, of the closed-loop system. Conventionally, the placement of the eigenvalues has been considered to improve the damping and system's response. However, in this study, the emphasis is placed also on tailoring the eigenvectors in order to enable the spatial control and redistribution of the wave propagation energy flow along the acoustic duct in such a manner that it can introduce non-reciprocity as well as control its direction and reversal. During this entire process, the system remains behaving in a linear fashion. Numerical examples are presented to demonstrate the basic features and non-reciprocal behavior, as well as the energy flow characteristics.

Simple Adaptive Delta Operator Aircraft Flight Control for Accommodation of Loss of Control Effectiveness

A new proof for stability of delta operator simple adaptive control is presented in terms of a set of Linear Matrix Inequalities (LMIs). The paper shows how to design a feedforward gain to satisfy the LMIs over a polytope of loss of control effectiveness failures. The MATLAB Robust Control Toolbox is used to find the feedforward gain with the smallest norm that satisfies the LMIs. Examples are presented of the F/A-18 aircraft and the Innovative Control Effectors (ICE) tailless aircraft that show the design of a feedforward gain for a loss of control effectiveness in any one control effector. The designs use a fixed eigenstructure assignment controller for an inner loop augmented with the simple adaptive controller. Simulations of both aircraft include simultaneous loss of control effectiveness failure and lateral wind gust. Simulation results for the F/A-18 aircraft show that the adaptive controller achieves almost perfect tracking whereas the nonadaptive controller cannot achieve a coordinated turn when an aileron failure occurs. The ICE tailless aircraft uses sideslip, washed-out stability axis yaw rate, and stability axis roll rate feedback for both the inner loop eigenstructure assignment controller and the simple adaptive controller. However, the adaptive controller also uses bank angle feedback. Simulation results for the ICE tailless aircraft show that the adaptive controller achieves almost perfect tracking whereas the nonadaptive controller diverges when an all moving tip failure occurs.

Quasi-LTV Polynomial Eigenstructure Assignment Control for Formation Flying Around Sun-Earth L2 Point

AbstractA nonlinear controller based on polynomial eigenstructure assignment (PEA) is presented for the control of formation flying around Sun-Earth L2 point. The dynamics of relative motion is formulated as a nonlinear equation firstly and rewritten into QLTV model in latter application. With PEA method, the eigenstructure assignment for the controller can be completed without imposing any particular eigenvalues. Using a polynomial matrix eigenspace of the system and a coprime factorization of the desired closed-loop transfer function which can determine different control performance, the designer is only left to choose the controller structure and calculate the controller gains by several simple formulas to produce a flexible design method. To implement for nonlinear system, the PEA method used for LTI and LPV model is extended to the QLTV model to realize the independence between the closed-loop system and the operating point. To ensure the system performance, the analytic stability analysis of closed-loop system is also developed. With such PEA method, a position keeping controller for MIMO formation flying is designed with a decoupling method to complete the desired performance design. Finally, a simulation is carried out to validate the controller performance for the formation flying.

Simple adaptive control for aircraft control surface failures

This work extends the so-called simple adaptive control approach to direct model reference adaptive control of multi-input multi-output systems to include loss of control effectiveness failures. It is proven that all signals are bounded for loss of control effectiveness failures during a bounded input disturbance. A state space approach is introduced for computing the feedforward compensator that is required by the stability result. The adaptive algorithm is applied to a three input model of the linearized lateral dynamics of the F/A-18 aircraft. Simulation results are obtained with single, double, and triple control effectiveness failures of 88% during the occurrence of a lateral gust. These results show that the adaptive controller exhibits improved model following as compared with a fixed gain eigenstructure assignment controller.

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.

확률적 불확실성을 갖는 선형 연속 시간 시스템의 고유구조 지정제어

확률적 불확실성을 갖는 선형 연속 시간 시스템의 고유구조 지정제어

Eigenstructure versus optimal control for decoupling

Abstract A study about how to design a control law that not only keeps following a reference attitude but also maintains attitude decoupling due to the vehicle manoeuvres has been performed. A control law was designed for a satellite launcher vehicle using eigenstructure assignment and optimal control method in order that the vehicle tracks a reference attitude and also to decouple the yaw response from roll and pitch manoeuvres and to decouple the pitch response from roll and yaw manoeuvres. It has been noticed that in order to achieve this objective it is necessary to use a linear coupled model to design the control law instead of the usual linear uncoupled model used to design the tracking control law. The design was based on a complete linear coupled model obtained from the complete vehicle non-linear model by linearisation at each trajectory point. A comparison of the system stability working with both control laws has also been performed. After all, the design was assessed with the vehicle time varying non-linear model showing a good performance and robustness. The used design method is explained and a case study for the Brazilian satellite launcher VLS is reported. By the end of the work some suggestions about how to implement this control law have also been studied.

A design example with eigenstructure assignment control whose loop transfer function is fully realized

We present a common 4th-order, 2-input and 2-output nonminimum-phase plant system, and the systematic design of a corresponding feedback control which can assign arbitrarily given poles and the corresponding eigenvectors. The loop transfer function of this control is fully realized. This highly desirable result is not achievable by other design methods. The controller order of our design is different from the order of existing state observers and static output feedback controllers.

Simultaneous Structural/Control Optimum Design of Composite Plate with Piezoelectric Actuators

An integrated structural/control design for the vibration suppression of a composite plate with segmented piezoelectric (PZT)actuators isexamined. Theelectricpowerused bythePZT materialsbecomesa very important factorforrealapplication to thecontrol of e exiblestructures.Themethod to predictpowerrequired forthecontrol ispresented, andthepowerisused asa partoftheobjectivefunctions. Thestructuralweight, thestateerrorenergy, control energy, stability robustness, and the electric power required for vibration control are considered as the objectivefunction.ThelocationsofthePZTactuatorsareconsideredascontroldesignvariables.Theplyorientation and thickness coefe cients of the laminated composite plate are considered as structural design variables. The improved compromise multiobjective optimization by using a reduction factor of performance indices is applied to solve this optimization problem. The sequential linear programming method with move limits is used. The sensitivity analysis, which is required in the optimization process, is performed for the eigenstructure assignment control scheme and the performance indices with respect to the design parameters. The optimized results showed a signie cant amount of reduction in the structural weight as well as the control performance indices. The required electric power is also decreased.

Improved Eigenstructure Assignment Controller Design Using a Substructure-Based Coordinate System

A new control coordinate system based on the Craig–Bampton substructure representation is examined for reduced-order-model-based controller design. Eigenstructure assignment controller design using the proposed modeling approach is shown to exhibit improved accuracy over conventional normal mode modeling in both closed-loop eigenvalue and eigenvector attainment. The improvement is due to the coordinate system’s ability to accurately predict actuator boundary conditions and, thus, actuator command forces, when extensive model reduction has been employed. Two multi-input/multi-outputdesign examples are used to illustrate the practicality of the method and the resulting improved closed-loop behavior.

Robust eigenstructure assignment with structured state space uncertainty

Recent sufficient conditions for robust stability and robust performance of linear time-invariant systems subject to structured state-space uncertainty are utilized to obtain a robust eigenstructure assignment design method. This new approach optimizes either the sufficient condition for stability or performance robustness while constraining the dominant eigenvalues to lie within chosen regions in the complex plane. This constrained optimization problem is solved by using the sequential unconstrained minimization technique with a quadratic extended interior penalty function. The use of constraints on certain eigenvector entries and the effect of these constraints on robustness and nominal performance are considered. Conservatism of the robustness conditions is reduced by simultaneously introducing a similarity transformation, a positive real diagonal weighting, and a unitary weighting into the design procedure. An example that illustrates the design of a robust eigenstructure assignment controller for a pitch pointing/vertical translation maneuver of the AFTIF-16 aircraft is presented.