P. Sannuti

Theory of LTR for nonminimum phase systems, recoverable target loops, recovery in a subspace. I. Analysis

A complete analysis of the loop transfer recovery (LTR) problem using full order observer-based controllers for general systems that are not necessarily left invertible and minimum phase is considered. The analysis focuses on three fundamental issues. The first is concerned with what can and cannot be achieved for a given system and for an arbitrarily specified target loop transfer function. The second is concerned with the development of necessary and/or sufficient conditions for a target loop to be either exactly or asymptotically recovered for a given system. The third issue deals with the development of method(s) to test whether recovery is possible in a given subspace of the control space. Such an analysis pinpoints the limitations of the given system for the recovery of arbitrarily specified target loops by observer-based controllers. Furthermore, the analysis discovers a multitude of ways to shape the loops as closely as possible to the target shapes. Also, possible pole-zero cancellations between the eigenvalues of the controller and the input and/or output decoupling zeros of the plant are characterized.<<ETX>>

Explicit expressions for cascade factorization of general nonminimum phase systems

Explicit expressions for two different cascade factorizations of any detectable left invertible nonminimum phase systems are given. The first one is a well known minimum phase/all-pass factorization by which all nonminimum phase zeros of a transfer function G(s) are collected into an all-pass factor V(s), and G(s) is written G/sub m(s)V/

Fundamental problems in fault detection and identification

where G/sub m/s is considered as a minimum phase image of G(s). The second one is a new cascade factorization by which G(s) is rewritten as G/sub M/(s)U(s) where U(s) collects all awkward zeros including all nonminimum phase zeros of G(s). Both G/sub m/(s) and G/sub M/(s) retain the given infinite zero structure of G(s). Further properties of G/sub m/(s), G/sub M/(s), and U(s) are discussed. These factorizations are useful in several applications including loop transfer recovery. >

Analysis, design, and performance limitations of H/sub 2/ optimal filtering in the presence of an additional input with known frequency

For certain fundamental problems in fault detection and identification, the necessary and sufficient conditions for their solvability are derived. These conditions are weaker than the ones found in the literature since we do not assume any particular structure for the residual generator.

Construction and parameterisation of all static and dynamic H/sub 2/-optimal state feedback solutions for discrete time systems

The standard H/sub 2/ optimal filtering problem considers the estimation of a certain output based on the measured output when the input is a zero mean white noise stochastic process of known intensity. In this paper, the inputs are considered to be of two types. The first type of input, as in standard H/sub 2/ optimal filtering, is a zero mean wide sense stationary white noise, while the second type is a linear combination of sinusoidal signals each of which has an unknown amplitude and phase but known frequency. Under such inputs, a generalized H/sub 2/ optimal filtering problem is formulated here. As in the standard H/sub 2/ optimal filtering problem, the generalized H/sub 2/ optimal filtering problem seeks to find a linear stable unbiased filter (called the generalized H/sub 2/ optimal filter) that estimates a desired output while utilizing the measured output such that the H/sub 2/ norm of the transfer matrix from the white noise input to the estimation error is minimized. The analysis, design, and performance limitations of generalized H/sub 2/ optimal filters are presented here.

Constrained output regulation of linear plants

The paper constructs and parameterizes all the static and dynamic H/sub 2/ optimal state feedback solutions. Moreover, all the eigenvalues of an optimal closed-loop system are characterised. All optimal closed-loop systems share a set of eigenvalues which are termed as the optimal fixed modes. Every H/sub 2/ optimal controller must assign among the closed-loop eigenvalues the set of optimal fixed modes. This set of optimal fixed modes includes a act of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and locations of the pole-zero cancellations present in any H/sub 2/ optimal design. It is shown that both the sets of optimal fixed modes and optimal fixed decoupling zeros do not vary depending upon whether the static or the dynamic controllers are used. Most of the results presented are analogous to but not quite the same as those for continuous-time systems.<<ETX>>

Necessary and sufficient conditions for a nonminimum phase plant to have a recoverable target loop-a stable compensator design for LTR

Output regulation of linear systems with state and/or input magnitude constraints is considered. The structural properties of linear plants are identified under which the so called constrained semi-global and global output regulation problems are solvable. An important aspect of our development is a categorization of constraints to show clearly what type of constraints can or cannot be achieved.

On blocking zeros and strong stabilizability of linear multivariable systems

In connection with loop transfer recovery (LTR) of nonminimum phase systems, the authors study the set of recoverable target loops and establish necessary or/and sufficient conditions for a given plant to have at least one recoverable target loop. The authors also show that the compensator structure previously developed by them (Automatica, vol.27, pp.257-280, 1991) for minimum phase systems can recover any recoverable target loop for nonminimum phase systems as well, while retaining all its advantages over conventional observed-based controllers.<<ETX>>

Performance with regulation constraints

A characterization of blocking zeros as related to invariant zeros or transmission zeros and their multiplicity structure is given. This characterization reveals several fundamental properties of blocking zeros. For example, given a multivariable system having a transfer function with normal rank greater than unity, it does not have any blocking zeros and hence is strongly stabilizable whenever all its invariant zeros are distinct. On the other hand, all single input and single output systems and some multivariable systems having the normal rank of their individual transfer functions as unity, always require a certain interlacing property among their invariant zeros and poles in order to be strongly stabilizable.<<ETX>>

Loop transfer recovery for nonstrictly proper plants

We study the problem where we have a regulation (asymptotic tracking) requirement together with a performance requirement. Typically we measure performance by the H/sub 2/ or H/sub /spl infin// norm of a chosen transfer function matrix, although any other norm such as the L/sub 1/ norm could also be used. In the case when the performance is measured by the H/sub 2/ norm, there is no loss in performance due to the regulation constraint. On the other hand, when the performance is measured by the H/sub /spl infin// norm, there exists in general certain loss of performance due to the regulation constraint, and we explicitly characterize such a loss in terms of a static optimization problem.