Ganti Prasada Rao

A review of identification in continuous-time systems

This paper aims at taking the reader on a guided tour of the field of identification of continuous-time systems. It presents a birds eye view of the continuous-time related aspects of the greater field of system identification. Continuous-time based contributions to system identification began in the nineteen-fifties but were overshadowed by a ‘go completely digital’ spirit which was spurred by parallel developments in digital computers during the following two decades. The nineteen seventies have witnessed a resurgence of continuous-time spirit and the field of continuous-time system identification has now matured to merit a review as is intended here. This paper is divided into three parts. An overview of the basic techniques of identification of continuous-time systems in a unified framework is presented in Part A. Parts B and C outline some recent developments in the identification of linear systems and nonlinear systems, respectively.

New class of discrete-time models for continuous-time systems

Digital computing in estimation, control or signal processing for continuous-time systems requires the use of discrete-time models. While conventional difference equation or z-transfer function models are widely popular, a class of methods exists that uses discrete approximations of continuous signals and operators, retaining the continuous-time parameters. Some important advantages of this class have been demonstrated in the contexts of parameter estimation, adaptive control and controller design. This paper proposes a new class of discrete-time models that originates from the z transfer function but which is close to continuous-time models in structure and parameters, thereby retaining its advantageous features. The recently proposed ‘delta’ model is seen to be a member of this class. The interrelations among various digital model types are brought out. Better sensitivity properties over z transfer function models are established. Finite word length properties of these models vis-a-vis the z-transfer fu...

Time domain synthesis via Poisson moment functionals

This paper presents a method of time-domain synthesis of dynamical systems treating the process signals as distributions or generalized functions, in the manner originally established by L. Schwartz. The technique of synthesizing the transfer function or the state-space model of a system employs exponentially weighted series of the generalized time derivatives of the impulse distribution, known also as the Poisson moment functional expansion. General algorithms are developed and their application is illustrated in typical eases.

Irreducible model estimation for MIMO systems

Abstract Estimation of the parameters of a reducible (inflated common denominator) model for the transfer function matrix of MIMO systems is well known. However, the reduction of the model to the minimal form by pole-zero cancellation is possible only in the noise-free case. This paper presents an algorithm for the estimation of the minimal continuous-time transfer function matrix model. Monte Carlo simulation results are presented for discrete-time and continuous-time models. Least-squares and generalized least-squares methods have been used in both cases. An asymptotic analysis of convergence has also been provided for these models in the noise-free case. The computation times and space complexities of different variants of the algorithm are compared. The results show that in noisy situations, obtaining a discrete-time model by discretizing an estimated continuous-time model may be a viable proposition

Identification of lumped linear systems in the presence of unknown initial conditions via Poisson moment functionals

This paper presents a method of including the effect, of unknown initial conditions in the general algorithms for transfer function synthesis recently developed by the authors (Saha and Prasada Rao 1979) via Poisson moment functionals. The proposed technique is of considerable practical importance in problems of parameter identification in which input-output data is available on an arbitrary but active interval of time. The technique is tested with process data containing zero mean noise and is found to be remarkably immune to such noise.

Transfer function matrix identification in MIMO systems via Poisson moment functionals

The paper presents a general algorithm for parameter identification in the transfer function matrix of a multi-input multi-output system. The method, whose basis is in the theory of distributions, employs the concept of generalized functions in the manner originally conceived and established by Dirac and Schwartz respectively, while the basis of most of the methods of system identification is to treat the process signals as functions in the ordinary sense with its differentiability limitations. The present method employs exponentially weighted series of the generalized time derivatives of the impulse distribution, known as the Poisson moment functional (PMF) expansion with certain advantages such as infinite differentiability and noise immunity. Some important aspects of identifiability and suitability of input signals in the context of the PMF approach are discussed. The algorithm is capable of treating the practically important case of data on an arbitrary but active period of time implying unknown init...

Structure and parameter identification in linear continuous lumped systems—the Poisson moment functional approach

A method of identifying the structure and the corresponding parameters in a general single-input-single-output lumped continuous linear system from a knowledge of the input-output data is presented in this paper. In the identification of structure indices, such as system order etc., the present technique is found to be superior to the methods which are based on evaluation of rank of certain information matrices. The proposed method is successfully tested with illustrative examples with deterministic and noisy data.

Identification of lumped linear systems in the presence of small unknown delays-the Poisson moment functional approach

Abstract Poisson moment functionals (PMF) of input and output, of a single-input single-output (SISO) system characterized by a linear time-invariant differential equation with a small delay, are used in a general and non-iterative algorithm of parameter identification. The quality of the results may be further improved, if necessary, by an efficient algorithm with iterative sampling of PMFs. The method is a useful extension of the recent algorithms proposed by Saha and Prasada Rao (1979, 1980) for delay-free systems in which process data on an arbitrary but active period of time can be handled.

Identification of lumped systems Identification of lumped linear time-varying parameter systems via Poisson moment functionals

Poisson Moment Functionals (PMF) of input and ouput of a Single-Input-Single-Output (SISO) system characterized by a linear differential equation with time varying coefficients, are used in a general algorithm of parameter identification. The method is a generalized version of certain recent algorithms proposed by Saba and Prasada Rao (1979) for fixed parameter systems. The effect of unknown initial conditions of the process is included in the related operational matrices thereby making the algorithm useful in the important practical situation wherein process data is available over an arbitrary but active length of time.

Parameter identification in lumped linear continuous systems in a noisy environment via Kalman-filtered Poisson moment functionals

Abstract This paper presents a Poisson moment functional (PMF) approach to parameter identification in lumped linear continuous systems in a noisy environment. The method is based on initially Kalman-filtering the PMFs and then employing them in the established general algorithms. This Kalman-filtered Poisson moment Functional (KFPMF) method is shown to be superior to the conventional least squares approach through an illustrative example.