Transmission Zeros Of Systems Research Articles

QZ-Based Algorithm for System Pole,Transmission Zero, and Residue Derivatives

The QZ algorithm gives a robust way of computing solutions to the generalized eigenvalue problem. The generalized eigenvalue problem is used in linear control theory to find solutions to Ricatti equations, as well as to determine system transmission zeros. In state-space linear system analysis, the system poles and transmission zeros are particularly important for determining system time and frequency response. Here, we embed calculation of the eigenvalue derivatives in the QZ algorithm such that the derivatives of system poles and transmission zeros are computed simultaneously with the poles and zeros themselves. The resulting method is further exercised in finding generalized eigenvalues and their sensitivities required for finding the derivatives of system residues. This technique should open the door to solutions of problems of interest by unconstrained gradient-based methods. Typical numerical results are presented.

Performance limitations in the robust servomechanism problem for discrete-time lti systems

Fundamental limitations for error tracking/regulation are obtained for the robust servomechanism problem (RSP) for a sampled system. In studying this problem, the cheap control problem for a multi-input/multi-output discrete time system is considered, and explicit expressions are obtained for the limiting steady state solution of its associated algebraic Riccati equation (ARE), as the weight on the control energy tends to zero. Application of these results is then made to obtain explicit expressions for the limiting performance costs associated with error tracking/regulation in the RSP. These limitations can be characterized by the system order, the dimension of the outputs, the number of the system's transmission zeros and the location of the system's nonminimum phase transmission zeros.

Limiting performance of optimal linear discrete filters

The limiting variance of the estimation error is obtained for the optimal H 2 filter for discrete time systems when the intensity of the measurement noise tends to zero. In particular, an explicit expression is obtained for the lowest achievable mean-square error when the measurement noise is slowly varying and has intensity which tends to zero. This limitation can be characterized completely by the system order, the dimension of the process noise, the number of the system's transmission zeros, and the location of the system's unstable transmission zeros.

Self-tuning relay control design for MIMO systems with fast convergence

A self-tuning relay control scheme based on the linear quadratic regulator (LQR) method is proposed for MIMO linear systems. It is shown that, by adjusting the control penalty in the LQR solution, the eigenvalues of the relay-controlled system quickly converge to the system transmission zeros. An auxiliary output is then designed to give rise to a set of desired transmission zeros so that fast convergence can be achieved. Simulation results are presented to show the effectiveness of the scheme.

End-point control of a flexible-link manipulator: theory and experiments

This paper focuses on the tip-position control of a single flexible link which rotates in the horizontal plane. The dynamic model is derived using a Lagrangian assumed modes method based on Euler-Bernoulli beam theory. The model is then linearized about an operating point. An output feedback control strategy that uses the principle of transmission zero assignment achieves tracking for this nonminimum phase linear time-invariant system. The control strategy consists essentially of two parts. The first part is an inner (stabilizing) control. Loop that incorporates a feedthrough term to assign the system's transmission zeros at desired locations in the complex plane, and a feedback term to move the system's poles to appropriate positions in the left-half plane. The second part is a feedback servo loop that allows tracking of the desired trajectory. The controller is implemented on an experimental test-bed.

The transmission zeros of systems with delays†

In this paper we study the properties of the zeros of a system with general delays in the input, state and control variables. The main result of this paper shows that the zeros of the transfer function are always zeros of the system matrix, with of at least the same multiplicity moreover, when the system is canonical, the zeros of the system matrix are zeros of the transfer function, with the same multiplicity.

Transmission zeros of linear multivariable systems with parasitics

The transmission zeros of systems with `parasitics´ are computed by solving appropriate separate generalised eigenvalue problems for the `slow´ and `fast´ transmission zeros using powerful QZ techniques.

A design procedure for multivariable regulators

Abstract A computational algorithm is presented for the design of a compensator for linear multivariable regulators. The compensated system is required to be structurally stable, in the sense of preserving output regulation and internal (loop) stability in the face of small parameter variations or uncertainties. The design technique is based on the internal model principle [1]. It is shown that the distance between the system transmission zeros and eigenvalues of the exogenous dynamics may be taken as a measure of the well-conditioning of the algorithm. The design algorithm is demonstrated by application to a two-area power system.

Cascade canonical form for linear multivariable systems

A canonical form is derived for systems described by an m × l transfer-function matrix G(s) and applied to the calculation of system transmission zeros, the feedback control of multivariable second-order-type systems and pole allocation using output feedback.

Properties and calculation of transmission zeros of linear multivariable systems

A new definition of transmission zeros for a linear, multivariable, time-invariant system is made which is shown to be equivalent to previous definitions. Based on this new definition of transmission zeros, new properties of transmission zeros of a system are then obtained; in particular, it is shown that a system with an unequal number of inputs and outputs almost always has no transmission zeros and that a system with an equal number of inputs and outputs almost always has either n−1 or n transmission zeros, where n is the order of the system; transmission zeros of cascade systems are then studied, and it is shown how the transmission zeros of a system relate to the poles of a closed loop system subject to high gain output feedback. An application of transmission zeros to the servomechanism problem is also included. A fast, efficient, numerically stable algorithm is then obtained which enables the transmission zeros of high order multivariable systems to be readily obtained. Some numerical examples for a 9th order system are given to illustrate the algorithm.

Active RC Synthesis for Significant Reduction in Magnitudes of Reactive Elements

Active elements may be used to significantly reduce the total reactance required in a network. This paper presents two active RC synthesis techniques for this purpose. One method employs a negative-impedance-converter to realize any number of system poles and reduces the total required capacitance to any desired extent. The resulting design is, however, very sensitive to active and passive parameter values. The second method also permits any prescribed total capacitance but employs a cascade of isolated second-degree sections. Two such sections are presented and optimized with respect to a figure of merit <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_{t}AS_{A}</tex> , being the product of total capacitance, required active element gain and system sensitivity to the latter. System transmission zeros may be accommodated to a certain extent.