Peddapullaiah Sannuti

Singular perturbations and order reduction in control theory - An overview

Recent results on singular perturbations are surveyed as a tool for model order reduction and separation of time scales in control system design. Conceptual and computational simplifications of design procedures are examined by a discussion of their basic assumptions. Over 100 references are organized into several problem areas. The content of main theorems is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.

Special coordinate basis for multivariable linear systems—finite and infinite zero structure, squaring down and decoupling

Abstract A special coordinate basis for multivariable linear systems is introduced here. Several fundamental properties of linear systems regarding controllability (stabiliza-bility), observability (detectability), invariant zeros, decoupling zeros, infinite zero structure, effect of feedback on zero structure, squaring down, diagonal and triangular decoupling etc. can be directly displayed in terms of the special coordinate basis. Moreover, connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established.

Control of Linear Systems with Regulation and Input Constraints

From the Publisher: The issue of tracking a desired reference signal in the presence of external disturbances is a classical control problem that resides at the core of control engineering. This is referred to as the output regulation problem. In this book the output regulation problem is examined in depth. New, highly significant dimensions are added to the problem and all pertinent topics associated with it are discussed. These topics include: Analysis and design of controllers for the output regulation problem subject to physical constraints on actuators such as amplitude and rate saturation. Incorporating transient performance requirements into output regulation problem formulation, thus creating an optimal framework for the output regulation problem. Uniting the output regulation problem formulation with other performance requirements of modern control theory such as H2 and Hinfinity optimal and suboptimal performance criteria. Opening up a novel framework of output regulation problem formulation in order to enlarge the class of signals dealt with whilst at the same time adding new possibilities. This book is designed to meet the needs of a variety of readers including practising control engineers, graduate students, and researchers in control engineering.

Fundamental problems in fault detection and identification

A number of different fundamental problems in fault detection and fault identification are formulated in this paper. The fundamental problems include exact, almost, generic and class-wise fault detection and identification. Necessary and sufficient conditions for the solvability of the fundamental problems 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. At the end of the paper, a time domain synthesis procedure based on state-space methods to construct appropriate residual generators is given. Copyright

Observer design for loop transfer recovery and for uncertain dynamical systems

A theory of observer design for exact and approximate loop-transfer recovery (LTR) and for uncertain dynamical systems is given. The method decomposes a given multivariable nominal system into several single-input, single-output subsystems, each of which can be designed separately. Both full-order and reduced-order observer designs can be derived. The design addresses the case when uncertainties are modeled as blocks exterior to the given plant and the case when uncertainties are prescribed structurally in terms of a state-space description. When the uncertainties in a given plant are modeled external to it, the observer design corresponds to a traditional LTR design, When uncertainties are given in terms of a state-space description, observer design can take into account uncertain elements of both linear and nonlinear type. This analysis can be viewed as a contribution to the development of a separation principle under which control system design for an uncertain dynamic system can be decomposed into designing a state feedback law and an observer for implementing the state feedback design. >

Near-optimum design of linear systems by a singular perturbation method

It is shown that the state feedback matrix of a linear system optimal with respect to a quadratic performance index can be expanded in a MacLaurin series in parameters which change the order of the system. The first two terms of this series are employed in a near-optimum design for a high-order plant. The result of the near-optimum design is superior to that achieved by a conventional low-order design, while the amount of computation is considerably less than that required for a high-order design. An example of a second-order design for a fifth-order plant is given.

Squaring down of non-strictly proper systems

In an earlier work, a procedure for squaring down proper systems by static and dynamic compensators has been developed. The compensators designed there have the following properties: (a) they are asymptotically stable; (b) the additional finite zeros induced by them are assignable to the open left half complex plane; and (c) they preserve the fundamental properties such as stabilizability, detectability, infinite zero structure and minimum phase nature of the original system. The earlier design procedure is extended to non-strictly proper systems while retaining all the above-mentioned properties.

Direct singular perturbation analysis of high-gain and cheap control problems

A new and direct approach to the analysis and design of high-gain feedback and cheap control problems is developed. Transformation of such singular problems to singular perturbation models of conventional type early at the onset of analysis or design allows a direct application of the readily available singular perturbation literature. The approach permits a simple characterization of (a) multivariable root loci under a high-gain feedback and (b) asymptotic behavior of optimal closed loop poles, state and control trajectories, performance index and optimal transfer function as the control cost coefficient in the performance index goes to zero.

Brief Paper: Simultaneous External and Internal Stabilization for Continuous and Discrete-Time Critically Unstable Linear Systems with Saturating Actuators

The issues arising in hybrid or simultaneous external as well as internal stabilization of linear systems with saturating actuators are considered. Four different stabilization problems are studied. Roughly, these problems are (1) simultaneous semi-global external as well as semi-global internal stabilization, (2) simultaneous semi-global external as well as global internal stabilization, (3) simultaneous global external as well as semi-global internal stabilization, and (4) simultaneous global external as well as global internal stabilization. As evident from the literature, the requirement of internal stabilization alone either in the global or semi-global sense demands that the linear part of the given system be (a) stabilizable, and (b) has all its poles in the closed left half complex plane for continuous-time systems while it has all its poles inside and/or on the unit circle for discrete-time systems. This implies that the posed simultaneous stabilization problems are solvable at best only under the conditions (a) and (b). Under such conditions, we construct here explicit state as well as measurement feedback controllers for all the four problems in the case of continuous-time systems, and for the problems (1), (2) and (4) in the case of discrete-time systems. The design methodologies used to construct appropriate feedback laws are based on by now familiar low-gain and low-and-high gain design concepts or certain scheduled versions of them.

Theory of LTR for non-minimum phase systems, recoverable target loops, and recovery in a subspace Part 1. Analysis

A complete analysis of loop transfer recovery problem using full order observer based controllers for general not necessarily left invertible and not necessarily minimum phase systems is considered. The analysis here, while showing that neither exact nor asymptotic loop transfer recovery is in general possible, focuses on three fundamental issues. The first issue is concerned with what can and what canot be achieved for a given system and for an arbitrarily specified target loop transfer function, while the second issue is concerned with the development of necessary and/or sufficient conditions a target loop has to satisfy so that it can be either exactly or asymptotically be 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 or not, i.e. to test whether projections of target and achievable sensitivity and complimentary sensitivity functions onto a given subspace match each other or not. Such an...