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Abstract

Electrical circuits with state-feedbacks are addressed. It is shown that by suitable choice of the gain matrices of state-feedbacks it is possible to obtain the closed-loop system matrices with nilpotency indices equal to two and their state variables are linear functions of time. The considerations are illustrated by linear electrical circuits.

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Authors and Affiliations

Tadeusz Kaczorek
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Abstract

The analysis of the positivity and stability of linear electrical circuits by the use of state-feedbacks is addressed. Generalized Frobenius matrices are proposed and their properties are investigated. It is shown that if the state matrix of an electrical circuit has generalized Frobenius form then the closed-loop system matrix is not positive and asymptotically stable. Different cases of modification of the positivity and stability of linear electrical circuits by state-feedbacks are discussed and necessary conditions for the existence of solutions to the problem are established.

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Authors and Affiliations

Tadeusz Kaczorek
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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
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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
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Abstract

This paper presents an adaptive particle swarm optimization (APSO) based LQR controller for optimal tuning of state feedback controller gains for a class of under actuated system (Inverted pendulum). Normally, the weights of LQR controller are chosen based on trial and error approach to obtain the optimum controller gains, but it is often cumbersome and tedious to tune the controller gains via trial and error method. To address this problem, an intelligent approach employing adaptive PSO (APSO) for optimum tuning of LQR is proposed. In this approach, an adaptive inertia weight factor (AIWF), which adjusts the inertia weight according to the success rate of the particles, is employed to not only speed up the search process but also to increase the accuracy of the algorithm towards obtaining the optimum controller gain. The performance of the proposed approach is tested on a bench mark inverted pendulum system, and the experimental results of APSO are compared with that of the conventional PSO and GA. Experimental results prove that the proposed algorithm remarkably improves the convergence speed and precision of PSO in obtaining the robust trajectory tracking of inverted pendulum.
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Authors and Affiliations

Jovitha Jerome
Kumar E. Vinodh
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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
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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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