Jayanta Pal

System reduction by a mixed method

A mixed method is proposed for deriving reduced order models using the continued-fraction approach and the Routh-Hurwitz array. This method is applicable to a general multivariable system and guarantees stability of the reduced model when the original system is stable.

Simulation based reduced order modeling using a clustering technique

Abstract A new method for reduced order modelling based on clustering the poles and zeros of a high order scalar transfer function is presented. The poles and zeros of the original system in the s -plane are clustered using a newly defined “inverse distance measure”. The reduced order model is identified from the cluster-centres. A tuning factor k is used to minimize the cumulative square of the time response deviations between the original system and the reduced order approximant. The viability of the method is illustrated by some examples from the literature.

An evolutionary computation based approach for reduced order modelling of linear systems

A new model order reduction algorithm taking the advantages of reciprocal transformation and principal pseudo break frequency estimation is presented. The denominator polynomial is constructed using the approximate dominant poles obtained. Ultimately the denominator polynomial formation is based on simple calculations involving high order system characteristic polynomial. Numerator polynomial is then determined using a recently proposed evolutionary computation algorithm-Big Bang Big Crunch algorithm. The method is simple and yields stable reduced order models. Difficulty may arise in finding complex poles in the reduced order model. However a modification in the algorithm by introducing search method to find the imaginary parts of such poles helps in overcoming this.

Large gap control in electromagnetic levitation

This paper describes design and implementation of a single axis dc attraction type electromagnetic suspension system where an electromagnet of 2.6 kg mass is levitated over a large gap under a fixed ferromagnetic guide-way. The electromagnet exhibits nonlinear force-current-distance characteristics, and if controllers are to be designed by using linear analysis, the air-gap is restricted to a small region around the chosen nominal operating point. In this work, an attempt has been made to increase the operating range of an electromagnetic suspension system by using the concept of piecewise linear control where the nonlinear force-current-airgap relationships of the magnetic suspension system have been successively linearized at several operating points with a suitable controller designed for each operating point. A novel analog switching scheme has been designed and implemented to automatically switch to the relevant controller depending on the actual air-gap.

Reduced order modelling of discrete-time systems

Abstract A simple model order reduction technique is proposed for z-transfer functions. This method is based on approximate model matching in the frequency domain. The entire procedure is carried out in the z-domain and the resultant linear algebraic equations are solved to find the unknown parameters of the reduced-order model. An example favorably compares this method with some prevalent techniques.

Nonlinear Analysis of Discretization Effects in a Digital Current Mode Controlled Boost Converter

Digital current mode control finds wide spread application in point of load power converters in DC nano-grid because of its technical benefits. However, finite current-loop sampling effects introduce undesirable sub-harmonic oscillations. This paper presents an analytical framework to investigate such nonlinear phenomena in a digitally current mode controlled boost converter. Discrete-time models for multi-sampled current loops and uniform sample with compensating ramp are derived under continuous conduction mode. We show that the discrete-time maps for such systems are discontinuous in nature. While the error voltage using a proportional-integral controller stays within the zero-error-bin (ZEB), the reference current becomes constant and 1-D maps of the inner current-loop can be used for stability analysis. Uniform sampling may lead to chaos, period doubling or stable period-1 behavior depending on slope of the compensating ramp. Multi-sampled current loop imposes several borders in the discrete parameter space and may eventually lead to high periodic behavior. In a counter-based compensating ramp, staircase effects may lead to sub-harmonic oscillation. Such instability eventually brings the error voltage outside the ZEB and 2-D map models have to be used for further investigating the nonlinear phenomena. A boost converter prototype was made. Digital current mode control is realized using an FPGA device. Test results demonstrate close agreement with the analysis.

Rational approximation of fractional operator — A comparative study

A comparative study of some existing methods for rational approximation of fractional operator (fractional Laplace operator) is presented. The various methods along with their advantages and limitations are described in this paper. Simulation results are shown for different orders of the fractional operator.

A New Method for Model Order Reduction

A new frequency domain method is proposed for reduced order modelling. In addition to using time moments that determine the low frequency matching, consideration of the Markov parameters is required to give better, accurate initial transient response matching and in some cases to provide stable models. We define a new set of parameters called the approximate generalised Markov parameters (AGMPs) and use them in conjunction with the approximate generalised time moments (AGTMs) to obtain reduced order transfer function models for high order systems. The method is applied to some typical examples from the literature.

Digital controller design for systems with transport lag

A new frequency-domain direct method of designing digital controllers for systems with transport lag is proposed. The objective is to design a digital controller such that the response of the resulting closed-loop system approximately matches a specified response. The method uses the principle of approximate model matching and gives a simple controller that, unlike the Smiths predictor method, does not require modelling of the plant or the time-delay term.

Reduced Order Approximation of MIMO Fractional Order Systems

A new two-stage method for reduced integer order approximation of fractional multiple-input, multiple-output (MIMO) systems is proposed. In the first stage, the transfer function matrix (TFM) Gf(s) of the given fractional order MIMO system is obtained and an integer order approximate TFM R(s) is formed by applying an existing approximation method to each fractional order transfer function (FOTF) of Gf(s). In the second stage, a reduced order state space model is formed. The system matrix of the reduced order system is constructed by selecting the dominant poles from the intermediate high integer order model R(s). The input and output matrices are found by matching approximate time moments and Markov parameters of the final reduced order model and the original system. The proposed method has been illustrated by an example.