Microprocessor-based simulation of sampled data systems with/without a hold device using a set of sample-and-hold functions and Dirac delta functions
01 Jan 2005-Journal of The Franklin Institute-engineering and Applied Mathematics (Pergamon)-Vol. 342, Iss: 1, pp 85-95
TL;DR: The presented method utilizes operational matrices of different orders in the DF and SHF domain to develop different operational transfer functions to aid in identification of control systems with known input and output sequence.
Abstract: In the present work, Dirac delta function (DF) set and sample-and-hold functions (SHF) set are used for microprocessor-based simulation of discrete time as well as sample-and-hold systems. Such simulations are useful for identification of control systems with known input and output sequence. The presented method utilizes operational matrices of different orders in the DF and SHF domain to develop different operational transfer functions. A few open-loop as well as closed-loop systems have been studied and the simulation results obtained are compared with exact solutions derived with the help of z -transform analysis. Experiments have also been carried out to establish the validity of the proposal.
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TL;DR: The present study proposes a new approach for designing stable adaptive fractional-order proportional-integral-derivative (FOPID) controllers, which employs non-sinusoidal orthogonal function (NSOF) domain-based design approach, which simplifies and eliminates the complexity of solving fractiona-order system dynamics.
Abstract: The present study proposes a new approach for designing stable adaptive fractional-order proportional-integral-derivative (FOPID) controllers, which employs non-sinusoidal orthogonal function (NSOF) domain-based design approach. The objective is to design a self-adaptive FOPID controller such that the designed controller can guarantee desired stability and simultaneously it can provide satisfactory transient performance. The proposed design methodology simplifies and eliminates the complexity of solving fractional-order system dynamics by converting it into the algebraic vector-matrix equation with the help of NSOF. The conventional FOPID, NSOF-based FOPID and NSOF-based adaptive FOPID controllers are implemented for benchmark simulation case studies and real-life experimentation and their results demonstrate the usefulness of the proposed approach.
7 citations
References
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Book•
01 Jan 1969
TL;DR: When you read more every page of this transmission of information by orthogonal functions, what you will obtain is something great.
Abstract: Read more and get great! That's what the book enPDFd transmission of information by orthogonal functions will give for every reader to read this book. This is an on-line book provided in this website. Even this book becomes a choice of someone to read, many in the world also loves it so much. As what we talk, when you read more every page of this transmission of information by orthogonal functions, what you will obtain is something great.
366 citations
Book•
01 Jun 1983
TL;DR: In this article, the authors proposed piecewise constant orthogonal basis functions (PCF) for linear and non-linear linear systems, and the optimal control of linear lag-free and time-lag systems.
Abstract: I Piecewise constant orthogonal basis functions.- II Operations on square integrable functions in terms of PCBF spectra.- III Analysis of lumped continuous linear systems.- IV Analysis of time delay systems.- V Solution of functional differential equations.- VI Analysis of non-linear and time-varying systems.- VII Optimal control of linear lag-free systems.- VIII Optimal control of time-lag systems.- IX Solution of partial differential equations (PDE) [W55].- X Identification of continuous lumped parameter systems.- XI Parameter identification in distributed systems.
188 citations
Book•
01 Jan 1992
TL;DR: This research presents a new generation of block pulse operational matrices for integrations that combine nonparametric representations of dynamic systems with state space representations ofynamic systems.
Abstract: Operations of block pulse series.- Block pulse operators.- Block pulse transforms.- Block pulse operational matrices for integrations.- Nonparametric representations of dynamic systems.- Input-output representations of dynamic systems.- State space representations of dynamic systems.- Practical aspects in using block pulse functions.
150 citations
TL;DR: In this paper, a Walsh series is expressed as a series of Walsh functions, and the coefficients of the input series will change, but there will be no new terms not in the original groups.
Abstract: Any well-behaved periodic waveform can be expressed as a series of Walsh functions. If the series is truncated at the end of any group of terms of a given order, the partial sum will be a stairstep approximation to the waveform. The height of each step will be the average value of the waveform over the same interval. If a zero-memory nonlinear transformation is applied to a Walsh series, the output series can be derived by simple algebraic processes. The coefficients of the input series will change, but there will be no new terms not in the original groups. Nonlinear differential and integral equations can be solved as a Walsh series, since the series for the derivatives can always be integrated by simple table lookup. The differential equation is solved for the highest derivative first and the result is then integrated the required number of times to give the solution.
135 citations
TL;DR: In this article, it is shown that block pulse functions (BPFs) are superior to the delayed unit step function (DUSF) proposed by Hwang (1983) due to the most elemental nature of BPFs in comparison to any other PCBF function.
Abstract: It is established that block pulse functions (BPFs) are superior to the delayed unit step function (DUSF) proposed by Hwang (1983). The superiority is mainly due to the most elemental nature of BPFs in comparison to any other PCBF function. It is also proved that the operational matrix for integration in the BPF domain is connected to the integration operational matrix in the DUSF domain by simple linear transformation involving invertible Toeplitz matrices. The transformation appears to be transparent because the integration operational matrices are found to match exactly. The reason for such transparency is explained mathematically. Finally, Hwang claimed superiority of DUSFs compared to Walsh functions in obtaining the solution of functional differential equations using a stretch matrix in the DUSF domain. It is shown that the stretch matrices of Walsh and DUSF domains are also related by linear transformation and use of any of these two matrices leads to exactly the same result. This is supported by a...
49 citations