Frequency-domain instability criteria for time- varying and nonlinear systems.
Frequency domain instability criteria generated from stability criteria for time varying and nonlinear feedback problems
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A class of orthogonal nonrecursive binomial filters.
The time- and frequency-domain properties of the orthogonal binomial sequences are presented. It is shown that these sequences, or digital filters based on them, can be generated using adders and delay elements only. The frequency-domain behavior of these nonrecursive binomial filters suggests a number of applications as low-pass Gaussian filters or as inexpensive bandpass filters.
Haddad, R. A.↗
Application of optimal input synthesis to aircraft parameter identification
The Frequency Domain Input Synthesis procedure is used in identifying the stability and control derivatives of an aircraft. By using a frequency-domain approach, one can handle criteria that are not easily handled by the time-domain approaches. Numerical results are presented for optimal elevator deflections to estimate the longitudinal stability and control derivatives subject to root-mean square constraints on the input. The applicability of the steady state optimal inputs to finite duration flight testing is investigated. The steady state approximation of frequency-domain synthesis is good for data lengths greater than two time cycles for the short period mode of the aircraft longitudinal motions. Phase relationships between different frequency components become important for shorter data lengths. The frequency domain inputs are shown to be much better than the conventional doublet inputs.
Gupta, N. K.↗
Frequency domain approach for evaluation of stochastic control of elastic spacecraft
An attempt is made to develop a reduced-order filter for an elastic spacecraft. The frequency-domain approach is resorted to both for arriving at an appropriate ROF and for evaluating the resulting stochastic flight controller. The frequency-domain approach employed is contrasted to the time-domain approach previously utilized by the authors. A linearized deterministic dynamical model of a solar electric propulsion spacecraft is analyzed. Flexibility modes were incorporated profitably into the ROF model, and the stochastic controllers exhibit notching of structural resonances reminiscent of classical notch filters. Accurate estimates of modal parameters (damping, natural frequency) are deemed crucial, and use of worst-case values in the ROF design is recommended.
Larson, V.↗
Robustness of multiloop linear feedback systems
This paper presents a new approach to the frequency-domain analysis of multiloop linear feedback systems. The properties of the return difference equation are examined using the concepts of singular values, singular vectors and the spectral norm of a matrix. A number of new tools for multiloop systems are developed which are analogous to those for scalar Nyquist and Bode analysis. These provide a generalization of the scalar frequency-domain notions such as gain, bandwidth, stability margins and M-circles, and provide considerable insight into system robustness.
Doyle, J. C.↗
Time domain and frequency domain design techniques for model reference adaptive control systems
Some problems associated with the design of model-reference adaptive control systems are considered and solutions to these problems are advanced. The stability of the adapted system is a primary consideration in the development of both the time-domain and the frequency-domain design techniques. Consequentially, the use of Liapunov's direct method forms an integral part of the derivation of the design procedures. The application of sensitivity coefficients to the design of model-reference adaptive control systems is considered. An application of the design techniques is also presented.
Boland, J. S., III↗
Exponential stability of large-scale discrete systems
The concept of vector Liapunov functions is used to obtain conditions for the exponential stability of large-scale discrete systems which can be decomposed into a number of interconnected subsystems with the same stability property. Both the structurally invariant composite systems and the large-scale systems under structural perturbations are considered. Connective absolute stability of a large-scale system composed of the interconnected Lur'e-type subsystems is defined and resolved in this context, resulting in a computationally and conceptually attractive alternative to a straightforward stability analysis of the system by frequency-domain criteria.
Grujic, L. T.↗
SUSSA ACTS: A computer program for steady and unsteady, subsonic and supersonic aerodynamics for aerospace complex transportation systems
The computer program SUSSA ACTS (Steady and Unsteady, Subsonic and Supersonic Aerodynamics for Complex Transportation Systems) are presented in the final version. The numerical formulation and the description of the program and numerical results are included. In particular, generalized forces for fully unsteady (complex frequency) aerodynamics for a wing-body configuration, in both subsonic and supersonic flows, are discussed. The mathematical analysis includes completely arbitrary motion. The numerical implementation was limited to steady and oscillatory flows. A more general aerodynamic formulation in the form of a fully transient response for time-domain analysis and the aerodynamic transfer function (Laplace transform of the fully unsteady operator) for frequency-domain analysis is outlined.
Tseng, K.↗
Multirate sampled-data systems analysis via vector operators
The primary difficulties of both the time-domain switch decomposition method and the frequency-domain decomposition method are overcome by introducing certain matrix operators and performing spectral factorization of resulting matrices of polynomials in the z-transform variable. Topological operations of the switch-decomposition method are simplified. This new approach eliminates the need to solve a system of equations with rational polynomial coefficients such as arises in the frequency-decomposition method. The determination of a multirate sampled-data system's characteristic polynomial no longer requires the evaluation of a determinant of rational polynomial elements. New results on obtaining modified z-transforms from standard z-transforms at a faster rate and vice versa are presented.
Boykin, W. H.↗
Some properties of extremal solutions of zero-sum differential games
Necessary conditions for infinite-time linear-quadratic two-player differential games with perfect state information are examined in the light of Willems' work on the algebraic Riccati equation. Necessary conditions for the nonzero-sum game do not always reduce precisely to those of the zero-sum game, when the weighting parameters of the cost index are taken as those of a zero-sum game. Formulation of zero-sum game problems in extended L2-spaces reveals the existence of nonstabilizing but infimal controls, and explicit frequency-domain conditions for existence of solutions and stabilizing solutions are established through the algebraic Riccati equation (ARE).
Johnson, T. L.↗
Methods for Combining Payload Parameter Variations with Input Environment
Methods are presented for calculating design limit loads compatible with probabilistic structural design criteria. The approach is based on the concept that the desired limit load, defined as the largest load occuring in a mission, is a random variable having a specific probability distribution which may be determined from extreme-value theory. The design limit load, defined as a particular value of this random limit load, is the value conventionally used in structural design. Methods are presented for determining the limit load probability distributions from both time-domain and frequency-domain dynamic load simulations. Numerical demonstrations of the methods are also presented.
Merchant, D. H.↗
Methods for combining payload parameter variations with input environment
Methods are presented for calculating design limit loads compatible with probabilistic structural design criteria. The approach is based on the concept that the desired limit load, defined as the largest load occurring in a mission, is a random variable having a specific probability distribution which may be determined from extreme-value theory. The design limit load, defined as a particular of this random limit load, is the value conventionally used in structural design. Methods are presented for determining the limit load probability distributions from both time-domain and frequency-domain dynamic load simulations. Numerical demonstrations of the method are also presented.
Merchant, D. H.↗
On least-squares design of recursive digital filters
Time-domain methods for the design of recursive digital filters using a squared error criterion are compared with a frequency-domain technique. Levy's method, which has been used to estimate transfer functions of continuous-time systems is modified to obtain design equations for digital filters. A special case of Levy's method is shown to be essentially equivalent to the time-domain methods.
Shenoi, K.↗
Measurement techniques for the characterization in the frequency domain of regulated energy-storage DC-to-DC converters
Procedures are presented for obtaining valid frequency-domain transfer functions of regulated reactor energy-storage dc-to-dc converters. These procedures are for measuring loop gain, closed loop gain, output impedance, and audio susceptibility. The applications of these measurements are discussed.
Bahler, D. D.↗
Dynamic response and stability analysis of flexible, multibody systems
A general version of Lagrange's equations, including auxiliary nonholonomic, rheonomic conditions of constraint, is used in the dynamic simulation and stability analysis of interconnected flexible bodies. Modeling of the nonlinear flexible/rigid dynamic coupling effects, the interaction forces/torques, and the elastic deformation effects is discussed. A digital computer program is developed to obtain time-domain solution for the nonlinear response of systems represented as a collection of individual bodies, numerical linearization of system-governing equations, time-domain solution for the perturbation response about a nominal state, and a frequency-domain stability analysis corresponding to the linearization. The digital simulation code is employed to study the dynamic behavior of a typical satellite and a spacecraft with deployable experiment booms.
Bodley, C. S.↗
Frequency domain compensation of a DYNGEN turbofan engine model
Following Rosenbrock's ideas regarding the advantages of dominance in linear multivariable control systems, a new graphical technique is used for the design of compensators that achieve dominance. The technique is illustrated with an application to the problem of designing compensators for a linear turbofan-engine model. The resulting design is put into perspective by examining it in the light of two other multivariable frequency-domain methods. One, MacFarlane's method of characteristic loci, is used to realize a final design for stability and low interaction. The other is a direct technique based upon the algebraic expansion of the determinant of the return difference in terms of it's elements. Results from simulations carried out on the NASA DYNGEN software are included.
Schafer, R. M.↗
Time-domain Green's Function Method for three-dimensional nonlinear subsonic flows
The Green's Function Method for linearized 3D unsteady potential flow (embedded in the computer code SOUSSA P) is extended to include the time-domain analysis as well as the nonlinear term retained in the transonic small disturbance equation. The differential-delay equations in time, as obtained by applying the Green's Function Method (in a generalized sense) and the finite-element technique to the transonic equation, are solved directly in the time domain. Comparisons are made with both linearized frequency-domain calculations and existing nonlinear results.
Tseng, K.↗
Instrumental variables algorithm for modal parameter identification in flutter testing
The paper is concerned with the task of estimating modal parameters from system response measurement in aircraft flutter testing. A frequency-domain derivation of an instrumental-variables algorithm is presented for a linear time-invariant dynamic system of order n. Basically, this algorithm fits a set of poles and zeros to the measured transfer function. An illustrative example is provided regarding the application of the algorithm to aeroelasticity testing. It is shown that the algorithm can be implemented for on-line data reduction with a microcomputer-based analysis system. By using instrumental variables the sensitivity of the modal parameter estimates to noise in the system-response measurements is reduced greatly. The algorithm is expected to be a powerful and valuable tool for on-line estimation of modal parameters in flutter testing and should be useful in control system and structural dynamics tests.
Johnson, W.↗