using automatic differentiation to create a nonlinear reduced order model aerodynamic solver a novel nonlinear reduced order modeling technique for computational aerodynamics and aeroelasticity is presented the method is based on a taylor series expansion of a frequency domain harmonic balance computational fluid dynamicsolver residual the first andsecond order gradientmatrices andtensorsof the taylorseries expansion are computed using automatic differentiation via fortran 90 95 operator overloading a ritz type expansion using proper orthogonal decomposition shapes is then used in the taylor series expansion to create the nonlinearreduced order model the nonlinear reduced order modeling technique is applied to a viscous flow about anaeroelastic nlr 7301 airfoil modelto determine limit cycle oscillations computational times are decreased from hours to seconds using the nonlinear reduced order model

design of stable parallel feedforward compensator and its application to synchronization problem this paper addresses the design problem of a stable parallel feedforward compensator v for a given siso lti plant p possibly being of non minimum phase and or having relative degree greater than one the objective of the problem is that their parallel interconnection p v becomes minimum phase having relative degree one based on the classical results of simultaneous stabilization a necessary and sufficient condition for solving the problem is presented as well as a design procedure for constructing such a compensator the proposed feedforward compensator allows the control system to have the three useful features 1 the ability that assigns the zeros of p v to a region of complex numbers having arbitrary negative real parts 2 infinite gain margin property of p v controlled by a static output feedback and 3 block diagonal structure of p v these features are extensively exploited in the synchronization problem of multi agent systems to achieve arbitrary fast convergence rate and to have the synchronized trajectory independent of the initial conditions and parameters of the involved dynamic controllers

optimal simultaneous stabilization of linear single input systems via linear state feedback control simultaneous stabilization of a collection of linear time invariant systems is considered the aim is to develop a practical method for the design of a single feedback controller such that all the systems involved are stabilized with good transient responses hurwitz s necessary and sufficient conditions are used as the required set of constraints for simultaneous stability for transient behaviour we introduce the usual quadratic objective function as performance index for each system their sum is the objective function for the collection of systems and the problem is to minimize it by choosing a feedback gain vector subject to boundedness and the hurwitz stability constraints a computational technique is proposed for solving this problem the results obtained give good transient behaviour for illustration two numerical examples are solved

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

efficient surrogate modelling of nonlinear aerodynamics in aerostructural coupling schemes this paper considers the substitution of the computational fluid dynamics solver within an aerostructural coupling scheme by an efficient reduced order surrogate model to realize high fidelity nonlinear aeroelastic analyses within a fraction of the time compared to the corresponding coupled computational fluid dynamics analysis the presented surrogate model approach is a combination of parameter reduction via proper orthogonal decomposition and system identification methods designed to cover nonlinear aerodynamic effects such as viscosity as well as transient effects the investigated test case is the thick nlr7301 airfoil that shows significant nonlinear aerodynamic behavior along with nonnegligible viscous effects the model is identified from a set of transient forced motion computational fluid dynamics analyses after identification the model is used to predict the discrete surface force distribution of the nlr7301 airfoil in static as well as transient coupled analyses it is shown that the static

simultaneous stabilization of single input single output discrete time systems the problem of finding one compensator which simultaneously stabilizes a family of single input single output siso discrete time plants is considered the family of plants is described by the transfer functions pz q q in q which are generated via a z transformation a number of assumptions describing the set of allowable plants are then given these assumptions include some regularity conditions on the plants and a minimum phase requirement the satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator c z for simultaneous stabilization an iterative computation method is provided for control design

strong stabilization over polytopes the problem considered consists of finding a stable controller assigning a closed loop characteristic polynomial over a stability domain specified as a polytopic region of the space of characteristic polynomial coefficients the controller is required to be stable with respect to the same polytopic stability region specified for the closed loop system

application of multi input volterra theory to nonlinear multi degree of freedom aerodynamic systems this paper presents a reduced order modeling approach for nonlinear multi degree of freedom aerodynamic systems using multi input volterra theory the method is applied to a two dimensional 2 degree of freedom transonic airfoil undergoing simultaneous forced pitch and heave harmonic oscillations the so called volterra cross kernels are identified and shown to successfully model the aerodynamic nonlinearities associated with the simultaneous pitch and heave motions the improvements in accuracy over previous approaches that effectively ignored the cross kernels by using superposition are demonstrated

discrete time pole placement with stable controller the classical polynomial approach to pole placement involves the computation of a particular solution of a given diophantine equation the solution corresponds to a proper controller whose order is fixed by the number of nonminimum phase zeros of the plant transfer function by its order and by the desired closed loop characteristic polynomial this controller might be unstable for some desired closed loop characteristic polynomials even though the plant can be stabilized by a stable controller now unstable controllers are known to deteriorate closed loop system performances compared with stable ones hence we propose a procedure to build for a specific class of plants a stable pole placement controller when the classical pole placement controller is unstable the properties of both stable and unstable controllers are compared via simulations it appears that for the considered plants the stable controller improves at least one of the following properties compared with its unstable counterpart step response transient gain margin measurement noise rejection the results obtained with our procedure are also compared with the results obtained via middleton s approach which consists in modifying the desired closed loop poles so as to obtain a stable and minimum phase controller with the classical pole placement method finally our pole placement design with stable controller is applied to solve a particular simultaneous partial pole placement problem

a state space interpretation of simultaneous stabilization a state space interpretation of some previously known results on simultaneous stabilization is given the results reviewed were obtained using the yuola lemma

limit cycle oscillations of delta wing models in low subsonic flow a nonlinear aeroelastic analysis of a low aspect delta wing modeled as a plate of constant thickness demonstrates that limit cycle oscillations lco of the order of the plate thickness are possible the structural nonlinearity arises from double bending in both the chordwise and spanwise directions the present results using a vortex lattice aerodynamic model for a low mach number flow complement earlier studies for rectangular wing platforms that showed similar qualitative results the theoretical results for the flutter boundary beyond which lco occurs have been validated by comparison to the experimental data reported by other investigators for low aspect ratio delta wings also the limit cycle oscillations found experimentally by previous investigators but not previously quantified prior to the present work are consistent with the theoretical results reported here reduced order aerodynamic and structural models are used to substantially decrease computational cost with no loss in accuracy without the use of reduced order models calculations of the lco would be impractical a wind tunnel model is tested to provide a quantitative experimental correlation with the theoretical results for the lco response itself

nonlinear open closed loop aeroelastic analysis of airfoils via volterra series determination of the subcritical aeroelastic response to arbitrary time dependent external excitation and determination of the flutter instability of open closed loop two dimensional nonlinear airfoils constitute the main topics to address these problems volterra series and indicial aerodynamic functions are used and in the same context the pertinent aeroelastic nonlinear kernels are determined flutter instability predictions obtained within this approach compared with their counterparts generated via the frequency eigenvalue analysis and via experiments reveal excellent agreements implications of a number of important parameters characterizing the lifting surface and control law on the aeroelastic response flutter are discussed and pertinent conclusions are outlined

prediction of aeroelastic limit cycle oscillations based on harmonic forced motion oscillations aeroelastic limit cycle oscillations due to aerodynamic nonlinearities are usually investigated using coupled fluid structure interaction simulations in the time domain these simulations are compu

on the use of differentials in statistics abstract this paper explores the connections between symbolic matrix derivatives as developed in the statistical literature and the mathematical theory of differentials it is shown how many published results on symbolic matrix derivatives can be obtained by straightforward algebraic manipulations monotone operators and quadratic differential forms are used to solve certain extreme value problems in statistics in a simple and rigorous way

nonlinear inviscid aerodynamic effects on transonic divergence flutter and limit cycle oscillations by the use of a state of the art computational e uid dynamic cfd method to model nonlinear steady and unsteady transonice owsin conjunction with a linearstructural model an investigationismadeinto how nonlinear aerodynamics can effect the divergence e utter and limit cycle oscillation lco characteristics of a transonic airfoil cone guration a single degree of freedom dof model is studied for divergence and one and two dof models are studied for e utter and lco a harmonicbalancemethod in conjunction with the cfd solver is used to determine the aerodynamics for e nite amplitude unsteady excitations of a prescribed frequency a procedure for determining the lco solution is also presented for the cone guration investigated nonlinear aerodynamic effects are found to produce a favorable transonic divergence trend and unstable and stable lco solutions respectively for the one and two dof e utter models nomenclature a nondimensional location of airfoil elastic axis e b b c semichord and chord respectively cl cm coefe cients of lift and moment about elastic axis respectively e location of airfoil elastic axis measured positive aft of airfoil midchord h airfoil plunge and pitch degrees of freedom i second moment of inertia of airfoil about elastic axis

characterizations of products of symmetric matrices abstract characterizations are obtained for matrices c of the form c a where a are n n matrices over the real field such that a is symmetric and c is nonnegative definite among others a proof of recent generalization of cochran s theorem is given

a sufficient condition for simultaneous stabilization the condition under which it is possible to find a single controller that stabilizes k single input single output linear time invariant systems p sub i s i 1 k is investigated the concept of avoidance in the complex plane is introduced and used to derive a sufficient condition for k systems to be simultaneously stabilizable a method for constructing a simultaneous stabilizing controller is also provided and is illustrated by an example

products of positive semidefinite matrices abstract we characterize the complex square matrices which are expressible as the product of finitely many positive semidefinite matrices a matrix t can be expressed as such if and only if det t 0 moreover the number of factors can always be limited to five we also determine those matrices which can be expressed as the product of two or four positive semidefinite matrices these results are analogous to the ones obtained before by c s ballantine for products of positive definite matrices

reduced order models for nonlinear unsteady aerodynamics two reduced order modeling approaches for the evaluation of nonlinear aerodynamic forces based on cfd computations are presented these reducedorder models roms provide a means for rapid calculation of frequency domain generalized aerodynamic forces which can be used in traditional flutter analysis scheme to calculate flutter characteristics about nonlinear steady flows two roms are presented one that is based on the volterra theory for nonlinear systems and a new rom that is based on step indicial responses rom kernels are identified directly from input output relations and the study focuses on issues of kernel identification and their effect on the quality of the rom first and second order roms are generated for the response of the agard 445 6 wing to forced harmon ic excitation of its elastic modes responses computed from the roms are compared to responses obtained directly from a cfd analysis in which the boundary conditions are excited harmonically results show that the quality of the volterra rom is very sensitive to the amplitudes of the impulse inputs used for identification the step response rom is shown to be more accurate than the volterra rom and less sensitive to the amplitude used for its identification

the jordan cononical form of a product of a hermitian and a positive semidefinite matrix abstract a given square complex matrix c is the product of a positive semidefinite matrix a and a hermitian matrix b if and only if c 2 is diagonalizable and has nonnegative eigenvalues this condition is equivalent to requiring that c have real eigenvalues and a jordan canonical form that is diagonal except for r copies of a 2 by 2 nilpotent jordan block we show that r is bounded from above by the rank of a the nullity of a and both the positive and negative inertia of b it follows that a product of two positive semidefinite matrices is diagonalizable and has nonnegative eigenvalues a result that leads to a characterization of the possible concanonical forms of a positive semidefinite matrix

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

transonic limit cycle oscillation analysis using aerodynamic describing functions and superposition principle limit cycle oscillation for an airfoil in transonic air flow considering aerodynamic nonlinearity is studied transonic nonlinear aerodynamic forces are calculated by solving euler equations or navier stokes equations with respect to harmonic airfoil plunging pitching motion and then the aerodynamic describing functions and the superposition principle are used to build an equivalent linearized aerodynamic model in the frequency domain hence the transonic limit cycle oscillation solutions can be obtained by the frequency domain flutter analysis method the procedures for building the aerodynamic describing function and obtaining the limit cycle oscillation solution are described in detail four examples are adopted to verify the accuracy of the present method the isogai wing model with naca 64a010 airfoil is used as the first example to verify the accuracy of the transonic linear flutter solution of the present method another naca 64a010 airfoil model with different structural parameters is then adopt

some results on simultaneous stabilization with multiple domains of stability abstract in this paper the problem of simultaneous stabilization in the case where each plant has a different domain of stability associated with it is studied specifically it is supposed that one is given plants p0 p1 pr together with domains of stability d0 dr and the objective is to find a common controller c such that the poles of the closed loop transfer matrix h pi c are all inside the corresponding domain of stability di for i 0 r this formulation of the simultaneous stabilization problem generalizes earlier problem formulations wherein it was assumed that all the domains of stability were the same and is believed to be a more realistic formulation of the problem of preserving system stability in the event of sensor or actuator failure in the paper necessary and sufficient conditions for the existence of a common controller are derived in the case where one of the domains say d0 is a subset of the rest the case of two plants p0 p1 with d0 a subset of d1 is studied in great detail and the following result is established the two plants can be simultaneously stabilized in the above generalized sense if and only if they can be simultaneously stabilized with respect to the larger of the two regions more precisely there exists a controller c such that the poles of h pi c lie inside di for i 0 1 if and only if there exists a controller such that the poles of bothh p0 c and of h p1 c lie inside the larger region d1