Applied sciences

Archives of Control Sciences

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Archives of Control Sciences | 2022 | vol. 32 | No 2 |

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Abstract

In the paper, the application of multi-criteria optimization of the parameters of PSS3B system stabilizers to damping electromechanical swings in an extended power system (PS) is presented. The calculations of the power system stabilizer (PSS) parameters were divided into two stages. In the first stage, single-machine systems, generating unit – infinite bus, of generating units critical for the angular stability of the PS were analyzed. Time constants and preliminary values of the PSS gains were calculated. In the second stage, the main one, the main gains on which the effectiveness of operation of PSSs depends the most were calculated by multi-criteria optimization of the extended PS. The calculations were carried out in several variants: for two-dimensional objective functions and the six-dimensional objective function. In multi-criteria optimization, the solution is not one set of PSS parameters, but a set of sets of these parameters, i.e. a set of compromises that were determined for each analyzed case. Additionally, for the six-dimensional compromise set, projections of this set on the planes connected with the quantities of individual generating units and the boundary of these projections on these planes were determined. A genetic algorithm adapted to multi-criteria issues was used to minimize the multivariate objective function. Sample calculations were made for the model of the National (Polish) Power System taking into account 57 selected generating units operating in high and extra high voltage networks (220 and 400 kV). The presented calculations show that the applied multi-criteria optimization of the PSS3B stabilizer parameters allows effectively damping electromechanical swings withoutworsening the voltagewaveforms of generating units in the extended PS.
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Authors and Affiliations

Adrian Nocoń
1
Stefan Paszek
1
Piotr Pruski
1

  1. Faculty of Electrical Engineering, Silesian University of Technology, Akademicka 10, 44-100 Gliwice, Poland
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Abstract

In this paper we deal with the problem of uniform exponential stabilization for a class of distributed bilinear parabolic systems with time delay in a Hilbert space by means of a bounded feedback control. The uniform exponential stabilization problem of such a system reduces to stabilizing only its projection on a suitable finite dimensional subspace. Furthermore, the stabilizing feedback control depends only on the state projection on the finite dimensional subspace. An explicit decay rate estimate of the stabilized state is given provided that a nonstandard weaker observability condition is satisfied. Illustrative examples for partial functional differential equations are displayed.
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Authors and Affiliations

Azzeddine Tsouli
1
Mostafa Ouarit
2

  1. Laboratory of Mathematics and Applications, ENSAM, Hassan II University of Casablanca, Morocco
  2. Laboratory of Fundamental and Applied Mathematics LAMFA, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, Morocco
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Abstract

In this article we focus on optimal control problems involving a nonlinear fractional control system of different orders with Caputo derivatives, associated to a Lagrange cost functional. Based on a lower closure theorem for orientor fields combined with Filippov’s approach, we derive an existence result for at least one optimal solution for such a problem.
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Authors and Affiliations

Rafał Kamocki
1

  1. Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Łódz, Poland
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Abstract

The primary objective of this paper is the custom design of an effective, yet relatively easyto- implement, predictive control algorithm to maintain normoglycemia in patients with type 1 diabetes. The proposed patient-tailorable empirical model featuring the separated feedback dynamics to model the effect of insulin administration and carbohydrate intake was proven to be suitable for the synthesis of a high-performance predictive control algorithm for artificial pancreas.Within the introduced linear model predictive control law, the constraints were applied to the manipulated variable in order to reflect the technical limitations of insulin pumps and the typical nonnegative nature of the insulin administration. Similarly, inequalities constraints for the controlled variable were also assumed while anticipating suppression of hypoglycemia states during the automated insulin treatment. However, the problem of control infeasibility has emerged, especially if one uses too tight constraints of the manipulated and the controlled variable concurrently. To this end, exploiting the Farkas lemma, it was possible to formulate the helper linear programming problem based on the solution of which this infeasibility could be identified and the optimality of the control could be restored by adapting the constraints. This adaptation of constraints is asymmetrical, thus one can force to fully avoid hypoglycemia at the expense of mild hyperglycemia. Finally, a series of comprehensive in-silico experiments were carried out to validate the presented control algorithm and the proposed improvements. These simulations also addressed the control robustness in terms of the intersubject variability and the meal announcements uncertainty.
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Authors and Affiliations

Martin Dodek
1
Eva Miklovicová
1

  1. Institute of Robotics and Cybernetics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Slovakia
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Abstract

In this paper we prove the exact controllability of a time varying semilinear system considering non-instantaneous impulses, delay, and nonlocal conditions occurring simultaneously. It is done by using the Rothe’s fixed point theorem together with some sub-linear conditions on the nonlinear term, the impulsive functions, and the function describing the nonlocal conditions. Furthermore, a control steering the semilinear system from an initial state to a final state is exhibited.
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Authors and Affiliations

Dalia Cabada
1
Katherine Garcia
2
Cristi Guevara
3
Hugo Leiva
2
ORCID: ORCID

  1. School of Mathematical and Statistical Sciences, Arizona State University, United States of America
  2. School of Mathematical Sciences and Information Technology, Yachay Tech University, Ecuador
  3. Arizona Department of Education, United States of America
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Abstract

This paper presents a fault-tolerant control scheme for a 2 DOF helicopter. The 2 DOF helicopter is a higher-order multi-input multi-output system featuring non-linearity, cross-coupling, and unstable behaviour. The impact of sensor, actuator, and component faults on such highly complex systems is enormous. This work employs sliding mode control, which is based on reaching and super-twisting laws, to handle the problem of fault control. Simulation tests are carried out to show the effectiveness of the algorithms. Various performance metrics are analyzed and the results show SMC based on super-twisting law provides better control with less chattering. The stability of the closed-loop system is mathematically assured, in the presence of faults, which is a key contribution of this research.
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Authors and Affiliations

M. Raghappriya
1
S. Kanthalakshmi
2

  1. Department of Electronics and Instrumentation Engineering, Government College of Technology, Coimbatore, India
  2. Department of Electrical and Electronics Engineering, PSG College of Technology, Coimbatore, India
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Abstract

Chemical processes use to be non-minimum phase systems. Thereby, they are a challenge for control applications. In this paper, fuzzy state feedback is applied in the Van de Vusse reaction that has an inverse response. The control design has an integrator to enhance the control performance by eliminating the steady-state error when a step reference is applied. An anti-windup action is used to reduce the undershoot in the system response. In practice, it is not possible to have always access to all the state variables. Thus, a fuzzy state observer is implemented via LMIs. Frequently, the papers that show similar applications present some comments about disturbance rejection. To eliminate the steady-state error when a ramp reference is used, in this work, a second integrator is aggregated. Now, the anti-windup also reduces the overshoot generated due to the usage of two integrators in the final application.
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Authors and Affiliations

C.A. Márquez-Vera
1
M.A. Màrquez-Vera
2
Z. Yakoub
3
A. Ma’arif
4
A.J. Castro-Montoya
5
N.R. Cázarez-Castro
6

  1. Universidad Veracruzana, Prolongación Venustiano Carranza S/N, Col. Revolución, Poza Rica 93390, Veracruz, Mexico
  2. Polytechnic Universityof Pachuca, C. Pachuca-Cd. Sahagún Km 20, Ex-Hacienda de Santa Bárbara, Zempoala 43830, Hgo., Mexico
  3. University of Gabès, National Engineering Schoo lof Gabès, Rue Omar Ibn El Khattab, Zrig Eddakhlania, Gabès 6029, Tunisia
  4. Universitas Ahmad Dahlan, Jl. Kapas No. 9, Semaki, Kec. Umbulharjo, Yogyakarta 55166, Indonesia
  5. Universidad Michoacana de San Nicolás de Hidalgo, Edif. M, Ciudad Universitaria, Morelia 58030, Michoacán, Mexico
  6. Instituto Tecnológico de Tijuana, Calz. Tecnológico S/N, Fracc. Tomás Aquino, Tijuana 22414, BC, Mexico
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Abstract

This study analyses the performances of various path controlling strategies for a 3-degrees of freedom wrist exoskeleton, by comparing key indicators, such as rise time, steady-state error, and implementation difficulty. A model was built to describe both system’s kinematics and dynamics, as well as 3 different controllers (PID, PD¸, and a hybrid force/position controller) that were designed to allow each joint to perform smooth motions within anatomic ranges. The corresponding simulation was run and assessed via Matlab (version 2020a). In addition to the performance comparison, remarkable characteristics could be identified among controllers. PD¸ showed higher response speed than the other controllers (about 4 times), and PID was reinforced as the technique with the easiest implementation due to the smallest matrices. The study also allowed to greater potential of the hybrid controller to interact with its environment, i.e., the robotic device.
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Authors and Affiliations

Valeria Avilés
1
Oscar F. Avilés
1
Jorge Aponte
1
Oscar I. Caldas
1
Mauricio F. Mauledoux
1

  1. Davinci Research Group, Mechatronics Engineering, Militar Nueva Granada University, Cr 11 No 101-80, Bogotá, Colombia
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Abstract

In this paper, an automatic voltage regulator (AVR) embedded with fractional order PID (FOPID) is employed for the alternator terminal voltage control. A novel meta-heuristic technique, a modified version of grey wolf optimizer (mGWO) is proposed to design and optimize the FOPID AVR system. The parameters of FOPID, namely, proportional gain ( Κ Ρ), the integral gain ( Κ I), the derivative gain ( Κ D), λ and μ have been optimally tuned with the proposed mGWO technique using a novel fitness function. The initial values of the Κ Ρ, Κ I , and Κ D of the FOPID controller are obtained using Ziegler-Nichols (ZN) method, whereas the initial values of λ and μ have been chosen as arbitrary values. The proposed algorithm offers more benefits such as easy implementation, fast convergence characteristics, and excellent computational ability for the optimization of functions with more than three variables. Additionally, the hasty tuning of FOPID controller parameters gives a high-quality result, and the proposed controller also improves the robustness of the system during uncertainties in the parameters. The quality of the simulated result of the proposed controller has been validatedby other state-of-the-art techniques in the literature.
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Authors and Affiliations

Santosh Kumar Verma
1
Ramesh Devarapalli
2
ORCID: ORCID

  1. Department of EIE, Assam Energy Institute, Sivasagar (Centre of RGIPT, Jais), Assam–785697, India
  2. Department of EEE, Lendi Institute of Engineering and Technology, Vizianagaram-535005, India
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Abstract

The linguistic q-rung orthopair fuzzy (L q-ROF) set is an important implement in the research area in modelling vague decision information by incorporating the advantages of q- rung orthopair fuzzy sets and linguistic variables. This paper aims to investigate the multicriteria decision group decision making (MCGDM) with L q-ROF information. To do this, utilizing Hamacher t-norm and t-conorm, some L q-ROF prioritized aggregation operators viz., L q- ROF Hamacher prioritized weighted averaging, and L q-ROF Hamacher prioritized weighted geometric operators are developed in this paper. The defined operators can effectively deal with different priority levels of attributes involved in the decision making processes. In addition, Hamacher parameters incorporated with the proposed operators make the information fusion process more flexible. Some prominent characteristics of the developed operators are also wellproven. Then based on the proposed aggregation operators, an MCGDM model with L q-ROF context is framed. A numerical example is illustrated in accordance with the developed model to verify its rationality and applicability. The impacts of Hamacher and rung parameters on the achieved decision results are also analyzed in detail. Afterwards, a comparative study with other representative methods is presented in order to reflect the validity and superiority of the proposed approach.
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Authors and Affiliations

Nayana Deb
1
Arun Sarkar
2
Animesh Biswas
1

  1. Department of Mathematics, University of Kalyani, Kalyani – 741235, India
  2. Department of Mathematics, Heramba Chandra College, Kolkata – 700029, India

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