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On optimal control problem subject to fractional order discrete time singular systems

Tirumalasetty Chiranjeevi Raj Kumar Biswas Ramesh Devarapalli Naladi Ram Babu Fausto Pedro García Márquez
Archives of Control Sciences | 2021 | vol. 31 | No 4 | 849-863 | DOI: 10.24425/acs.2021.139733
Keywords fractional optimal control problem discrete time singular system fractional derivative Hamiltonian technique
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Abstract

In this work, we present optimal control formulation and numerical algorithm for fractional order discrete time singular system (DTSS) for fixed terminal state and fixed terminal time endpoint condition. The performance index (PI) is in quadratic form, and the system dynamics is in the sense of Riemann-Liouville fractional derivative (RLFD). A coordinate transformation is used to convert the fractional-order DTSS into its equivalent non-singular form, and then the optimal control problem (OCP) is formulated. The Hamiltonian technique is used to derive the necessary conditions. A solution algorithm is presented for solving the OCP. To validate the formulation and the solution algorithm, an example for fixed terminal state and fixed terminal time case is presented.
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Authors and Affiliations

Tirumalasetty Chiranjeevi
1
Raj Kumar Biswas
2
Ramesh Devarapalli
3
ORCID: ORCID
Naladi Ram Babu
2
Fausto Pedro García Márquez
4
  1. Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U. P., India
  2. Department of Electrical Engineering, National Institute of Technology, Silchar, India
  3. Department of Electrical Engineering, BIT Sindri, Dhanbad 828123, Jharkhand, India
  4. Ingenium Research Group, University of Castilla-La Mancha, Spain

Analysis of multiple-area renewable integrated hydro-thermal system considering artificial rabbit optimized PI (FOPD) cascade controller and redox flow battery

Arindita Saha Tirumalasetty Chiranjeevi Ramesh Devarapalli Naladi Ram Babu Puja Dash Fausto Pedro Garcìa Màrquez
Archives of Control Sciences | 2023 | vol. 33 | No 4 | 861-884 | DOI: 10.24425/acs.2023.148885
Keywords solar thermal automatic generation control geothermal artificial rabbit optimization redox flow battery PI(FOPD) controller
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Abstract

The current task explores automatic generation control knowledge under old-style circumstances for a triple-arena scheme. Sources in area-1 are thermal-solar thermal (ST); thermalgeothermal power plant (GPP) in area-2 and thermal-hydro in area-3. An original endeavour has been set out to execute a new performance index named hybrid peak area integral squared error (HPA-ISE) and two-stage controller with amalgamation of proportional-integral and fractional order proportional-derivative, hence named as PI(FOPD). The performance of PI(FOPD) has been compared with varied controllers like proportional-integral (PI), proportional-integralderivative (PID). Various investigation express excellency of PI(FOPD) controller over other controller from outlook regarding lessened level of peak anomalies and time duration for settling. Thus, PI(FOPD) controller’s excellent performance is stated when comparison is undergone for a three-area basic thermal system. The above said controller’s gains and related parameters are developed by the aid of Artificial Rabbit Optimization (ARO). Also, studies with HPA-ISE enhances system dynamics over ISE. Moreover, a study on various area capacity ratios (ACR) suggests that high ACR shows better dynamics. The basic thermal system is united with renewable sources ST in area-1 also GPP in area-2. Also, hydro unit is installed in area-3. The performance of this new combination of system is compared with the basic thermal system using PI(FOPD) controller. It is detected that dynamic presentation of new system is improved. Action in existence of redox flow battery is also examined which provides with noteworthy outcome. PI(FOPD) parameters values at nominal condition are appropriate for higher value of disturbance without need for optimization.
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Authors and Affiliations

Arindita Saha
1
Tirumalasetty Chiranjeevi
2
Ramesh Devarapalli
3
ORCID: ORCID
Naladi Ram Babu
4
Puja Dash
5
Fausto Pedro Garcìa Màrquez
6
  1. Department of Electrical Engineering, RegentEducation & Research Foundation Group of Institutions, Kolkata, West Bengal, India
  2. Department of ElectricalEngineering, Rajkiya Engineering College Sonbhadra, U.P., India
  3. Institute of Chemical Technology, IndianOil Odisha Campus, Bhubaneswar, India
  4. Department of Electrical & Electronics Engineering,Aditya Engineering College, Surampalem, Andhra Pradesh, India
  5. Department of Electrical and Electronics Engineering,Gayatri Vidya Parishad College of Engineering (Autonomous), Visakhapatnam, Andhra Pradesh,India
  6. Ingenium ResearchGroup, University of Castilla-La Mancha, Spain

Real-time validation of an automatic generation control system considering HPA-ISE with crow search algorithm optimized cascade FOPDN-FOPIDN controller

Naladi Ram Babu Tirumalasetty Chiranjeevi Ramesh Devarapalli Łukasz Knypiński Fausto Pedro Garcìa Màrquez
Archives of Control Sciences | 2023 | vol. 33 | No 2 | 371-390 | DOI: 10.24425/acs.2023.146280
Keywords crow search algorithm dish-stirling solar system AGC RT Lab FOPDN-FOPIDN controller
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Abstract

This article validates the application of RT-Lab for the AGC studies of three-area systems. All the areas are employed with thermal-DSTS systems. A new controller named cascade FOPDN-FOPPIDN is employed. Its parameters are optimized using a CSA, subjecting to a new PI named HPA-ISE. The responses of the FOPDN-FOPIDN controller are related and are superior over PIDN and TIDN controllers. Moreover, the dominance of HPA-ISE is verified with ISE, and it performs better in terms of system dynamics. Further, the system performance reliability is analyzed with the AC-HVDC and is better than the AC system. Besides, sensitivity analysis recommends that the proposed FOPDN-FOPIDN at diverse conditions is robust and more reliability.
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Authors and Affiliations

Naladi Ram Babu
1
Tirumalasetty Chiranjeevi
2
Ramesh Devarapalli
3
ORCID: ORCID
Łukasz Knypiński
4
ORCID: ORCID
Fausto Pedro Garcìa Màrquez
5
  1. Department of Electrical and Electronics Engineering, Aditya Engineering College, Surampalem, Andhra Pradesh, India
  2. Department of Electrical Engineering, Rajkiya Engineering College Sonbhadra, U.P., India
  3. Department of Electrical/Electronics and Instrumentation Engineering, Institute of Chemical Technology, Indianoil Odisha Campus, Bhubaneswar751013, India
  4. Faculty of Control, Robotics and Electrical Engineering, Poznan University of Technology, Piotrowo 3A, 60-965 Poznan, Poland
  5. Ingenium Research Group, University of Castilla-La Mancha, Spain

Fixed terminal time fractional optimal control problem for discrete time singular system

Tirumalasetty Chiranjeevi Ramesh Devarapalli Naladi Ram Babu Kiran Babu Vakkapatla R. Gowri Sankara Rao Fausto Pedro Garcìa Màrquez
Archives of Control Sciences | 2022 | vol. 32 | No 3 | 489-506 | DOI: 10.24425/acs.2022.142846
Keywords fractional order differential equation discrete time singular system fractional derivative linear quadratic optimal control problem
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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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