Naresh K. Sinha

Modeling and identification of dynamic systems

The problem of identifying system parameters deals with the evaluation of coefficients in the known mathematical model from measured input-output data. Moreover, the identification problem can be reduced to a parameter estimation that uses the tools of estimation theory. According to [2], “identification is the determination, on the basis of input and output, of a system within a specified class of systems, to which the system under test is equivalent.”

Short-Term Load Demand Modeling and Forecasting: A Review

Both the off-line and on-line methods for short-term electric load forecasting are reviewed. Since identifying an adequate model is the most important problem of any forecasting technique, the literature is classified according to the modeling approaches used for representing the load demand. The merits and drawbacks of each approach and how different authors have applied it to the problem under consideration are stressed. Also included is recent work where multivariable identification techniques are used to model the load demand of all the major loading nodes of a large power system. The advantages and the difficulties of applying such techniques are discussed. As a conclusion, directions for future research and future development of available algorithms, which can improve the state of the art, are suggested.

Modified maximum likelihood method for the robust estimation of system parameters from very noisy data

Abstract When experiments are conducted there is always a chance of the occurrence of large measurement errors (outliers). Common identification methods like generalized least squares, maximum likelihood etc. may not converge in these situations due to the presence of outliers. Here we present a method for the robust estimation of system parameters based on the censoring of data and employing the maximum likelihood estimation. Several simulated examples show that the modified maximum likelihood method works well in situations where other methods failed.

Optimum approximation of high-order systems by low-order models†

A method has been proposed for the determination of optimum low-order models for a high-order system which minimize a specified error criterion for a given order of the model. The method is based on the pattern-search algorithm of Hooke and Jeeves. Starting from an approximate first or second-order model, an optimum model of that order is determined, and the process is continued with the order increasing progressively. As an example of the application of the method, optimum second-order models of a seventh-order system have been obtained using a number of different criteria for optimization. A third and a fourth-order optimum model have then been derived for a given criterion.

Identification of continuous-time multivariable systems from sampled data†

Abstract Several approaches to estimating the parameters of a continuous-time model of a multivariable system from samples of input and output observations arc discussed. These include indirect methods where a discrete-time model is first obtained from the input-output data and then transformed into a continuous-time model, as well as direct methods where the continuous-time model is obtained straight from the samples of the observations. An example is used to compare the methods.

A new method for reduction of dynamic systems

A new method has been presented for the determination of a low-order model approximating a high-order system. It is based on the use of the matrix pseudo-inverse to estimate the parameters of the model which minimize the sum of the squares of the errors between the response of the actual system and that of the model at the sampling instants. One of the advantages of this method is that the description of the actual system dynamics need not be known, but only the measurements of the input-output data are required. As the algorithms are iterative, computation is fairly straightforward, and the requirement for storage of input-output data depends only on the order of the assumed model, not on the number of iterations in the interval considered for minimization. An example of the application of the method for the determination of an approximate second-order model of a seventh-order system has been given, and compared with the reduced model obtained using another method.

Digital Measurement of Angular Velocity for Instrumentation and Control

A new approach to digital measurements of angular velocity for control applications is discussed. An optical transducer is described which provides a pulse rate. The pulse period is measured and the division of time is achieved by either a general purpose or a special purpose processor. Since sampling intervals are small, measurements are available in digital form almost immediately. Other advantages include the capability to measure transient angular velocity characteristics and the accurate measurement of angular velocity near zero. With modifications the system can be transformed into an accelerometer.

Brief paper: Recursive estimation of the parameters of linear multivariable systems

A recursive algorithm is proposed for the identification of linear multivariable systems. Utilization of a canonical state space model minimizes the number of parameters to be estimated. The problem of identification in the presence of noise is solved by using a recursive generalized least-squares method.

Some canonical forms for linear multivariable systems

Six different canonical forms for the triple A, B, C of a linear multivariable system are discussed, namely (i) the column-companion form, (ii) the row-companion form, (iii) the output identifiable form, (iv) the input-identifiable form, (v) the controllable canonical form and (vi) the observable canonical form. Simple algorithms for transforming any system into these forms are proposed and illustrated by means of examples. Practical applications of the various forms are discussed.

Efficient algorithm for irreducible realization of a rational matrix

Abstract A computationally efficient algorithm is presented for irreducible realization of a given rational transfer function matrix. It is shown that either the Hankel matrix for the system or a reduced form of it can be systematically transformed to the Hermite normal form using outer products. The dynamical equations then follow immediately. This algorithm requires less computation than the existing algorithms.