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Abstract

This paper presents the formulation and numerical simulation for linear quadratic optimal control problem (LQOCP) of free terminal state and fixed terminal time fractional order discrete time singular system (FODSS). System dynamics is expressed in terms of Riemann-Liouville fractional derivative (RLFD), and performance index (PI) in terms of state and costate. Because of its complexity, finding analytical and numerical solutions to singular system (SS) is difficult. As a result, we use coordinate transformation to convert FODSS to its corresponding fractional order discrete time nonsingular system (FODNSS). After that, we obtain the necessary conditions by employing a Hamiltonian approach. The relevant conditions are solved using the general solution approach. For the analysis of formulation and solution algorithm, a numerical example is illustrated. Results are obtained for various �� values. According to state of the art, this is the first time that a formulation and numerical simulation of free terminal state and fixed terminal time optimal control problem (OCP) of FODSS is presented.
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Authors and Affiliations

Tirumalasetty Chiranjeevi
1
Ramesh Devarapalli
2
ORCID: ORCID
Naladi Ram Babu
3
Kiran Babu Vakkapatla
4
R. Gowri Sankara Rao
5
Fausto Pedro Garcìa Màrquez
6

  1. Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U.P., India
  2. Department of EEE, Lendi Institute of Engineering and Technology, Vizianagaram-535005, India
  3. Department of EEE, Aditya Engineering College, Surampalem, Andhra Pradesh, India
  4. Lingayas Institute of Management and Technology Madalavarigudem, A.P., India
  5. Department of EEE, MVGR College of Engineering Vizianagaram, A.P., India
  6. Ingenium Research Group, University of Castilla-La Mancha, Spain
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Abstract

Of the Victorian writers Tolstoy read, Charles Dickens was the most eminent, and his appreciation of the English author was permanent and unchangeable. Tolstoy admired Dickens for the democratic and humanistic qualities in his writings. The theme of social isolation and gradual re‑adaptation into society is explored by Dickens in A Christmas Carol and Tolstoy in Where Love Is, There Is God Also. The story of Scrooge’s mean‑spirited solitude which was later replaced by open‑hearted sociability was not like Martin’s. Scrooge deliberately isolated himself from his family and avoided all human contact. Martin was unable to find a purpose and meaning in life after the death of his wife and children. A series of events and encounters with people lead both protagonists towards the development of a new moral understanding and make life worth living. The moral lesson is to treat all people with compassion. Dickens and Tolstoy took the commonest and simplest sorts of human kindness and showed them intensified. Both stories are also openly didactic, and the main characters are developed through their actions, and good deeds. The details of place, time and people are made very real to the reader. They are intensified through the use of imagery, motifs of light and dark; and cold and heat, which recur throughout A Christmas Carol and Where Love Is, There Is God Also. In Tolstoy’s story there are also many examples of Biblical imagery which are used to add weight to the moral teaching of his story. In the final part of the stories the protagonists no longer desire isolation. Martin helps those in need and is glad to have guests. His every act of kindness is done as an act of charity, and accepted as such. According to Tolstoy, all people are able to do good if they will because man, as a child of the Heavenly Father, is himself good, and the evils of the world are obstructions which prevent him from being himself. What is more, striving towards God means striving for goodness and man’s progress towards his own perfection. In the final part of Dickens’s novel Scrooge visits his nephew Fred, where he has a wonderful time. Being a part of a family is equated for him with happiness. While the backdrop of A Christmas Carol is a Christian festival and moral values underpin the novel in the shape of kindness, generosity and care for others, there is little sense of solemn religious ceremony in the novel. Dickens’s vision of Christmas is largely a secular one. He focuses on secular aspects of Christmas as a joyous holiday with parties and gatherings of friends and family.
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Bibliography

Birns N., The Novel Uncontained: Victorian Fiction, Tolstoy, and the Anglo‑Russian Literary ‘Channel’, [in:] https://www.academia.edu/8566986/The_Novel_Uncontained_Victorian_-Fiction_Tolstoy_and_the_Anglo_Russian_Literary_Channel.

Blumberg E.J., Tolstoy and the English Novel: A Note on “Karenina”, “Slavic Review” 1971, № 30/3.

Dickens C., A Christmas Carol, Waiheke Island 2009.

Jahn G.S., Tolstoy as a writer of popular literature, [in:] D.T. Orwin, ed., The Cambridge Companion to Tolstoy, Cambridge 2002.

Newton A.E., Introduction, [in:] C. Dickens, A Christmas Carol, Boston 1920.

Orwin D.T., Chronology, [in:] D.T. Orwin, ed., The Cambridge Companion to Tolstoy, Cambridge 2002.

Rielly M., Papa Panov’s Special Christmas, [in:] https://clausnet.com/articles/literature/ papa‑panovs‑special‑christmas‑r50/.

Shestov L., Dostoevsky, Tolstoy and Nietzsche, tr. Bernard Martinand and Spencer Roberts, Ohio 1978.

Snow C.P., The Realists. Portraits of Eight Novelists, London 1980.

Tolstoy L., What is Art?, tr. Aylmer Maude, New York 1898.

Tolstoy L., Where Love Is God Is, [in:] Twenty‑three tales, tr. Louise and Aylmer Maude, Oxford 1906.

Tolstoy L.N., Chto takóe iskússtvo? [v:] L.N. Tolstoy, Polnoye sobraniye sochineniy v 90 tomakh, red. V.G. Chertkov, t. 30, Moskva 1928‑1958.

Tolstoy L.N., Gde lyubovʹ, tam i Bog, [v:] L.N. Tolstoy, Polnoye sobraniye sochineniy v 90 tomakh, red. V.G. Chertkov, tom 25, Moskva 1928‑1958.
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Authors and Affiliations

Brygida Pudełko
1
ORCID: ORCID

  1. Opole, Uniwersytet Opolski
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Abstract

Diode neutral point clamped (NPC) three-level converters have been widely used in recent years. Aiming at the problems of the high device failure rate and unstable neutral point potential of NPC three-level converters, an NPC three-level circuit with fourth bridge arm redundancy is proposed based on the traditional NPC three-level converter. The redundant fourth bridge arm is used to realize the function of stabilizing voltage when there is no fault and replacing the fault half-bridge arm to maintain the continuous operation of the converter when there is a fault. By analyzing the working principle of space vector pulse width modulation (SVPWM) and the power loss of the switch, it is of particular significance to the design and control of NPC three-level converters in the future. Matlab/Simulink verifies the feasibility of the fault-tolerant circuit structure.
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Authors and Affiliations

Baoge Zhang
1
ORCID: ORCID
Shanyan Ping
1
Yi Long
1
Yuemin Jiao
1
Boxiang Wu
1

  1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University, China
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Abstract

In this paper, the influence of impact damage to the induction motors on the zero-sequence voltage and its spectrum is presented. The signals detecting the damages result from a detailed analysis of the formula describing this voltage component which is induced in the stator windings due to core magnetic saturation and the discrete displacement of windings. Its course is affected by the operation of both the stator and the rotor. Other fault detection methods, are known and widely applied by analysing the spectrum of stator currents. The presented method may be a complement to other methods because of the ease of measurements of the zero voltage for star connected motors. Additionally, for converter fed motors the zero sequence voltage eliminates higher time harmonics displaced by 120 degrees. The results of the method application are presented through measurements and explained by the use of a mathematical model of the slip-ring induction motor.
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Authors and Affiliations

Piotr Drozdowski
Arkadiusz Duda

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