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Zeroing of state variables in fractional descriptor electrical circuits by state-feedbacks

Tadeusz Kaczorek
Archives of Electrical Engineering | 2014 | vol. 63 | No 3 September | 321-333 | DOI: 10.2478/aee-2014-0024
Keywords fractional descriptor linear electrical circuit state-feedbacks zeroing
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Abstract

The problem of zeroing of the state variables in fractional descriptor electrical circuits by state-feedbacks is formulated and solved. Necessary and sufficient conditions for the existence of gain matrices such that the state variables of closed-loop systems are zero for time greater zero are established. The procedure of choice of the gain matrices is demonstrated on simple descriptor electrical circuits with regular pencils.
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Authors and Affiliations

Tadeusz Kaczorek

PMSM drive with adaptive state feedback speed controller

R. Szczepanski T. Tarczewski L.M. Grzesiak
Bulletin of the Polish Academy of Sciences Technical Sciences | 2020 | 68 | No. 5 (i.a. Special Section on Modern control of drives and power converters) | 1009-1017 | DOI: 10.24425/bpasts.2020.134624
Keywords adaptive control state feedback controller PMSM Widrow-Hoff rule
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Abstract

In this paper, the issue related to control of the plant with nonconstant parameters is addressed. In order to assure the unchanged response of the system, an adaptive state feedback speed controller for permanent magnet synchronous motor is proposed. The model-reference adaptive system is applied while the Widrow-Hoff rule is used as adjustment mechanism of controller’s coefficients. Necessary modifications related to construction of the cost function and formulas responsible for adjustment of state feedback speed controller’s coefficients are depicted. The impact of adaptation gain, which is the only parameter in proposed adjustment mechanism, on system behaviour is experimentally examined. The discussion about computational resources consumption of the proposed adaptation algorithm and implementation issues is included. The proposed approach is utilized in numerous experimental tests on modern SiC based drive with nonconstant moment of inertia. Comparison between adaptive and nonadaptive control schemes is also shown.

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Authors and Affiliations

R. Szczepanski
T. Tarczewski
L.M. Grzesiak

Poles and zeros assignment by state feedbacks in positive linear systems

Tadeusz Kaczorek
Archives of Control Sciences | 2021 | vol. 31 | No 3 | 593-605 | DOI: 10.24425/acs.2021.138693
Keywords assignment pole zero transfer matrix linear positive system state feedback
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Abstract

Poles and zeros assignment problem by state feedbacks in positive continuous-time and discrete-time systems is analyzed. It is shown that in multi-input multi-output positive linear systems by state feedbacks the poles and zeros of the transfer matrices can be assigned in the desired positions. In the positive continuous-time linear systems the feedback gain matrix can be chosen as a monomial matrix so that the poles and zeros of the transfer matrices have the desired values if the input matrix B is monomial. In the positive discrete-time linear systems to solve the problem the matrix B can be chosen monomial if and only if in every row and every column of the n x n system matrix A the sum of n-1 its entries is less than one. Key words: assignment, pole, zero, transfer matrix, linear, positive, system, state feedback
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Bibliography

[1] E. Antsaklis and A. Michel: Linear Systems. Birkhauser, Boston, 2006.
[2] L. Farina and S. Rinaldi: Positive Linear Systems: Theory and Applications. J. Wiley & Sons, New York, 2000.
[3] T. Kaczorek: Linear Control Systems, vol. 2. Research Studies Press LTD., J. Wiley, New York, 1992.
[4] T. Kaczorek: Positive 1D and 2D Systems. London, UK, Springer-Verlag, 2002.
[5] T. Kaczorek: Selected Problems of Fractional Systems Theory. Berlin, Germany, Springer-Verlag, 2011.
[6] T. Kaczorek and K. Rogowski: Fractional Linear Systems and Electrical Circuits, Studies in Systems, Decision and Control, Vol. 13. Springer, 2015.
[7] T. Kailath: Linear systems. Prentice Hall, Englewood Cliffs, New York, 1980.
[8] R.E. Kalman: Mathematical description of linear systems. J. SIAM Control, 1(2), (1963), 152–192, DOI: 10.1137/0301010.
[9] R.E. Kalman: On the general theory of control systems. Proc. First International Congress on Automatic Control, London, UK, Butterworth, (1960), 481–493,
[10] J. Klamka: Controllability of Dynamical Systems. Kluwer, Acadenic Publ., Dordrecht 1991.
[11] H. Rosenbrock: State-Space and Multivariable Theory. New York, USA, J. Wiley, 1970.
[12] S.M. Zak: Systems and Control. New York, Oxford University Press, 2003.
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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID
  1. Białystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland

Sufficient conditions for uniform global asymptotic stabilization of affine discrete-time systems with periodic coefficients

Adam Czornik Evgenii Makarov Michał Niezabitowski Svetlana Popova Vasilii Zaitsev
Archives of Control Sciences | 2021 | vol. 31 | No 1 | 81-98 | DOI: 10.24425/acs.2021.136881
Keywords discrete-time systems periodic systems affine systems uniform global asymptotic stabilization state feedback
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Abstract

Affine discrete-time control periodic systems are considered. The problem of global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has the Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic affine discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Examples of using the obtained results are presented.
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Authors and Affiliations

Adam Czornik
1
Evgenii Makarov
2
Michał Niezabitowski
3
Svetlana Popova
4
Vasilii Zaitsev
4
  1. Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, 44-100 Gliwice, Poland
  2. Institute of Mathematics, National Academy of Sciencesof Belarus, 220072 Minsk, Belarus
  3. Faculty of Automatic Control, Electronics and Computer Science,Silesian University of Technology, 44-100 Gliwice, Poland
  4. Udmurt State University, 426034 Izhevsk, Russia

Fuzzy state feedback with double integrator and anti-windup for the Van de Vusse reaction

C.A. Márquez-Vera M.A. Màrquez-Vera Z. Yakoub A. Ma’arif A.J. Castro-Montoya N.R. Cázarez-Castro
Archives of Control Sciences | 2022 | vol. 32 | No 2 | 383-408 | DOI: 10.24425/acs.2022.141717
Keywords fuzzy state feedback LMIs Van de Vusse reaction double integrator anti-windup
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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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