Analysis and synthesis of time-varying systems via orthogonal hybrid functions (HF) in state space environment
01 Dec 2015-International Journal of Dynamics and Control (Springer Berlin Heidelberg)-Vol. 3, Iss: 4, pp 389-402
TL;DR: In this paper, a set of hybrid functions (HF) formed by a combination of sample-and-hold function (SHF) set and triangular function (TF) set is used for time-varying system analysis.
Abstract: This paper uses a set of hybrid functions (HF) formed by a combination of sample-and-hold function (SHF) set and triangular function (TF) set. The SHF set has been applied for analysing sample-and-hold control systems and the TF set has been proved to be efficient for obtaining piecewise linear solutions of control systems. In the present work, the HF set has been employed for the analysis and synthesis of homogeneous as well as non-homogeneous time-varying control systems in state space. The HF set works with function samples, and is thus useful for building an easier algorithm for time-varying system analysis. After developing necessary theories, a few examples are treated to illustrate the efficiency as well as simplicity of the approach. The results thus obtained are compared with the results obtained via traditional analysis, and relevant tables and graphs are included to justify the case for hybrid functions.
Citations
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01 May 2011
18 citations
01 Jan 2016
TL;DR: This chapter discusses HF domain identification of time varying systems in state space and both homogeneous and non-homogeneous systems are treated.
Abstract: This chapter discusses HF domain identification of time varying systems in state space. Both homogeneous and non-homogeneous systems are treated. Illustration has been provided with the support of three examples, ten figures and two tables.
01 Jan 2016
TL;DR: In this article, a time varying system analysis is presented using state space approach in hybrid function domain, both homogeneous and non-homogeneous systems are treated along with numerical examples.
Abstract: In this chapter, time varying system analysis is presented using state space approach in hybrid function domain. Both homogeneous and non-homogeneous systems are treated along with numerical examples. States and outputs of the systems are solved. Illustration has been provided with the support of five examples, six figures and nine tables.
References
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TL;DR: This book discusses the role of Nonparametric Models in Continuous System Identification, and methods for Obtaining Transfer Functions from nonparametric models using the Frequency-Domain approach.
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239 citations
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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
TL;DR: In this paper, a new technique which employs both Picard iteration and expansion in shifted Chebyshev polynomials is used to symbolically approximate the fundamental solution matrix for linear time-periodic dynamical systems of arbitrary dimension explicitly as a function of the system parameters and time.
105 citations
TL;DR: It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution.
Abstract: The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.
90 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