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The combined effect of fractional filter and Smith Predictor for enhanced closed-loop performanceof integer order time-delay systems: some investigations

Nagarsheth Shaival Hemant, Sharma Shambhu Nath

Archives of Control Sciences

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2020

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Vol. 30, No. 1

47--76

EN

This paper proposes a generalized fractional controller for integer order systems with time delay. The fractional controller structure is so adopted to have a combined effect of fractional filter and Smith predictor. Interestingly, the resulting novel controller can be decomposed into fractional filter cascaded with an integer order PID controller. The method is applied to two practical examples i.e. liquid level system and Shell control fractionator system. The closed-loop responses resulting from the proposed method are compared with that of the available methods in the literature. For quantitative evaluations of the proposed method, Integral Absolute Error (IAE) and Integral Square Control Input (ISCI) performance criteria are employed. The proposed method effectively enhances the closed-loop response by improving the IAE values, reducing the control effort inputs to achieve the desired output. The disturbance rejection and robustness tests are also carried out. The robustness test reveals a significant improvement in the maximum absolute sensitivity measure. That is displayed in numerical simulations of the paper.

2

An application of Plemelj-Smithies formulas to computing generalized inverses of Fredholm operators

Ciecierska G.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 1

13--26

EN

We consider continuous operators S +T in Banach spaces, where S is Fredholm and T is quasinuclear. By referring to the basic result of the Fredholm theory, i.e. to the expression of the resolvent ( I + λT ) −1 of the operator T as a quotient of entire functions of λ , we derive analogous formulas for generalized inverses of operators S +T. We apply the Plemelj-Smithies formulas describing terms of determinant systems for the quasinuclear perturbations of Fredholm operators.

3

A reconstruction method of generalized sampling based on generalized inverse

Zhaoxuan Z., Houjun W., Zhigang W., Hao Z.

Metrology and Measurement Systems

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2010

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Vol. 17, nr 2

163-171

EN

This paper considers the problem of reconstructing a class of generalized sampled signals of which a special case occurs in, e.g., a generalized sampling system due to non-ideal analysis basis functions. To this end, we propose an improved reconstruction system and a reconstruction algorithm based on generalized inverse, which can be viewed as a reconstruction method that reduces reconstruction error as well. The key idea is to add an additional channel into a generalized sampling system and apply the generalized inverse theory to the reconstruction algorithm. Finally, the approach is applied, respectively, to an oscilloscope, which shows the proposed method yields better performance as compared to the existing technique.

4

Throught a generalized inverse

Stępniak C.

Demonstratio Mathematica

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2008

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Vol. 41, nr 2

291-296

EN

Traditionally, the existence of a generalized inverse of a matrix A is derived in an indirect way from the matrix equation AXA = A. We reach this result in a direct and constructive manner, based on spectral decomposition. Moreover, some new results on its characterization and on representation of the entire set of generalized inverses are given. Usefulness of these results is demonstrated in examples.

5

Single stage algorithms for pole placement using static output feedback

Kuźmiński K., Krawiecki M.

Control and Cybernetics

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2007

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Vol. 36, no 4

939-969

EN

Paper presents effective formulae, enabling transfer matrix pole assignment. This is accomplished by the use of generalized matrix inverses and the Kronecker product. All the desired pole distributions are covered - namely simple and multiple, real and complex. On this basis one-stage algorithms were developed, avoiding commonly used reduced orthogonality condition. Computational example of the presented algorithms is given.

6

Spectral properties of generalized inverses

Schmoeger Ch.

Demonstratio Mathematica

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2004

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Vol. 37, nr 1

137--148

EN

Let A denote a unital complex Banach algebra. An element a € A is said to be relatively regular if aba = a for some b 6 A. Then b will be called a generalized inverse of a. In this note we study spectral properties of generalized inverses of a.