Abstract: This paper presents a line interfaced inverter that employs a dc-dc converter to actively shape its ac current waveform. The duty cycle applied to this converter to control the current is determined in a closed loop fashion. The incremental dynamic response of the power circuit is found to be highly dependent on the ac voltage and current waveforms and therefore varies on a 60 Hz basis. With fixed feedback gains this variance would give closed loop poles that moved during the cycle. To avoid the problems that a time-varying system response would cause, a novel control scheme is proposed. This scheme uses periodically varying feedback gains to counteract the power circuit's time dependent response in a way that gives closed loop poles that do not move. Results of a Parity Simulation are included to verify the validity of this approach.

Abstract: In this paper the non-minimal real state-space realization for n-dimensional transfer functions with polylinear numerators and denominators is stated and proved. It is also shown that the every existing realization of an n-dimensional transfer function can be achieved from the companion matrix of some (n + 1)-variable polynomial linear with respect to one of its variables.

Abstract: A numerically stable algorithm for the evaluation of the transfer function matrix corresponding to a state space description is proposed. The algorithm performs orthogonal similarity transformations on the system matrices. Eigenvalue computations are used for pole and zero determinations.

Abstract: The problem of factorizing the transfer function of single-input single-output 2-D systems to a product of two 1-D transfer functions using state feedback is considered. It is shown that if the numerator of the open-loop transfer function can, by itself, be written as a product of two 1-D polynomials, then the closed-loop transfer function can, under certain conditions, be factorized as a product of two 1-D transfer functions. In cases where the numerator is not by itself factorizable, then the present results restrict themselves to factoring the denominator of the closed-loop system to a product of two 1-D polynomials.

Abstract: A simple numerical method for computing the time domain response of linear time invariant systems described by their transfer functions is presented. The method does not require computation of transfer function poles or residues; it is not influenced by the multiplicity of poles or zeroes, nor does it require computation of the matrix exponential. Rather, it is based on a numerical method for inverting Laplace transforms. It is equivalent to very high order, absolutely stable numerical integration. Stiff systems present no problems.

Abstract: The poles of the particle-hole Green's function are classified with respect to their pole strengths as main and secondary poles. A sum rule is established which connects these main and secondary poles. Numerical results are given for the example of the water molecule in the INDO approximation.

Abstract: A confocal feedback system (CFS) has been modified in three ways to include space variance, time sampling, and a second feedback loop. The space-variant system performs analog solution of partial differential equations (PDE’s) with variable coefficients. The time-sampling system solves PDE’s in three dimensions. The CFS with a second feedback loop has a more flexible feedback transfer function and can solve an extended range of PDE’s. Finally, a combination of time sampling and a second feedback loop can solve four-dimensional problems. Experimental results verifying the abilities of each of these new confocal feedback systems have been obtained.

Abstract: Gradient matrices are formulated for open-loop and closed-loop linear dynamic multivariable systems. The incremental motions of the poles, the zeros, and the coefficients of the numerator and denominator transfer function polynomials are determined as a function of the variation in the elements of the open-loop system matrices.

Abstract: Some properties of the set of poles of a transfer-function matrix which are not poles of the corresponding characteristic gain function are examined. In particular, its relationship with the set of modes which are fixed with reference to a. completely decentralized regulator structure is noted.

Abstract: : The standard results of linearized optimal control theory are explored and examined to see how they can be applied to flight control systems A feedback control system operating on the elevators of an aircraft-like gliding projectile is investigated The projectile is required to closely follow a predetermined maximum range trajectory in the face of initial disturbances Equations of motion are set up and linearized Approximate solutions for the maximum range trajectory are given and approximate analytical expressions for the eigenvalues of the plant matrix and derived After assigning weighting values to the state and control variables in the integral quadratic performance index, solutions to the Riccati matrix equation are computed and used to evaluate optimal state feedback gain vectors The effect of this optimal feedback on glider performance is observed from computed trajectory simulations An optimal feedback gain vector is selected subject to limitations on angle of attack, elevator deflection angle, and attitude The question of incomplete state variable feedback is considered in the interest of simpler engineering design Using a reduced order system representation, relationships between performance index weights and closed loop poles are established and a sub- optimal system based on feedback of only one state variable is investigated

Abstract: Parseval's theorem gives the possibility of connecting the approximation in the time domain in the sense of least squares with the corresponding approximation in the frequency domain. If the poles of the approximating transfer function are known or preassigned (as it can be in the case of active RC-synthesis) the best location of its zeros can be obtained with the help of the proposed Lagrange-wise ratio. The location of the transfer-function poles can be evaluated, for example, by the decomposition of hyperbolic functions into infinite products; the location of zeros is obtained as the numerator of the above-mentioned ratio at the second stage of the approximation process. The example shows that the combination of these two steps in the frequency domain can give rise to very satisfactory time-domain approximation.

Abstract: A new method of obtaining a minimum state space ( A, B, C, D ) realization of an r \times m proper rational transfer function matrix, P(s) , is presented. D is found in the usual manner. The denominator roots are calculated and the A matrix is formed. An initial estimate of the B and C matrices is assigned and a transfer function matrix is calculated from the estimated state space matrices. The B and C matrices are adjusted by the algorithm until the computed transfer function is "close enough" to the original transfer function matrix.

Abstract: We present here extensions of earlier work [1] on dynamic feedback compensation of infinite dimensional systems The extensions are in two directions: (a) Unstable (in the input-output sense) plans are allowed (b) New classes of irrational transfer functions are being considered (other than meromorphic of bounded type)

Abstract: It is shown that the proper choice of a parameter value in the derivative of the squared magnitude of a function can improve the time-domain behaviour substantially, while preserving the monotonic character of the magnitude function. By means of the well-known root-locus method with a defined parameter acting as a loop transmission constant it is possible to influence the configuration of the transfer function poles in a desired way and to acquire a favourable transient response. The functions described can be advantageously used in pulse networks.

Abstract: Recent papers have established global convergence for a class of adaptive control algorithms for discrete time linear dynamic systems. However, in most cases studied to date it has been assumed that the system is stably invertible. This assumption plays a major role in the proofs of convergence. In this paper we consider the more general case in which it is not assumed that the system is either stable or stably invertible. We establish local convergence for a class of adaptive control algorithms applied to general discrete, deterministic, linear, time-invariant systems. By convergence in this context, we mean that the system inputs and outputs remain bounded for all time and the closed loop poles are effectively assigned in the limit for a given desired trajectory.