2022 (vol. 32) - Number 1

*J. Cvejn:*

The magnitude optimum design of the PI controller for plants with complex roots and dead time

*S.F. Al-Azzawi, M.A. Hayali:*

Coexisting of self-excited and hidden attractors in a new 4D hyperchaotic Sprott-S system with a single equilibrium point

*M.A. Hammami, N. El Houda Rettab, F. Delmotte:*

On the state estimation for nonlinear continuous-time fuzzy systems

*M. Ilyas, M.A. Khan, A. Khan, Wei Xie, Y. Khan:*

Observer design estimating the propofol concentration in PKPD model with feedback control of anesthesia administration

*L. Moysis, M. Tripathi, M. Marwan:*

Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs – application to chaos synchronization

*S. Vaidyanathan, K. Benkouider, A. Sambas:*

A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based synchronization design and circuit simulation

*T.T. Tuan, H. Zabiri, M.I.A. Mutalib, Dai-Viet N. Vo:*

Disturbance-Kalman state for linear offset free MPC

*Yuan Xu, Jun Wang:*

A novel multiple attribute decision-making method based on Schweizer-Sklar *t*-norm and *t*-conorm with *q*-rung dual hesitant fuzzy information

*T. Kaczorek:*

Observers of fractional linear continuous-time systems

ACS Abstract:

**2021 (Volume 31)**

Number 1

Novel solutions on model-based and model-free robotic-assisted ankle rehabilitation

J.C. Arceo, C. Armenta, J. Lauber, E. Simoneau-Buessinger(Université Polytechnique Hauts-de-France, Valenciennes, France) | J. Álvarez, M. Bernal(Sonora Institute of Technology, Mexico) |

In this report, ankle rehabilitation routines currently approved by physicians are implemented via novel control algorithms on a recently appeared robotic device known as the motoBOTTE. The physician specifications for gait cycles are translated into robotic trajectories whose tracking is performed twofold depending on the availability of a model: (1) if obtained via the Euler-Lagrange approach along with identification of unknown plant parameters, a new computed-torque control law is proposed; it takes into account the parallel-robot characteristics; (2) if not available, a variation of the active disturbance rejection control technique whose parameters need to be tuned, is employed. A detailed discussion on the advantages and disadvantages of the model-based and model-free results, from the continuous-time simulation to the discrete-time implementation, is included.

**keywords:** active disturbance rejection, computed torque control, differential algebraic, equations, parallel rehabilitation robot, real-time implementation, system identification

On controllability of fractional positive continuous-time linear systems with delay

B. Sikora, N. Matlok(Silesian University of Technology, Poland) |

In the paper positive fractional continuous-time linear systems are considered. Positive fractional systems without delays and positive fractional systems with a single delay in control are studied. New criteria for approximate and exact controllability of systems without delays as well as a relative controllability criterion of systems with delay are established and proved. Numerical examples are presented for different controllability criteria. A practical application is proposed.

**keywords:** fractional systems, positive systems, the Caputo derivative, controllability, delay, the Metzler matrix

Indirect torque observer-based sensor-less efficient control of bearingless switched reluctance motor using global sliding mode and square currents control method

P.N. Rao(Gandhi Institute of Technology and Management, India) | R. Devarapalli(Birsa Institute of Technology Sindri, India) | F.P. García Márquez(University of Castilla-La Mancha, Spain) | G.V. Nagesh Kumar(Jawaharlal Nehru Technological University Anantapur, India) | B. Mohammadi-Ivatloo(University of Tabriz, Iran) |

The Bearingless Switched Reluctance Motor (BSRM) is a new technology motor, which overcomes the problems of maintenances required associated with mechanical contacts and lubrication of rotor shaft effectively. In addition, it also improves the output power developed and rated speed. Hence, the BSRM can achieve high output power and super high speed with less size and cost. It has a considerable ripple in the net-torque due to its critical non-linearity and the salient pole structures of both stator and rotor poles. The resultant torque ripple, especially in these motors, causes the more vibrations and acoustic noises will affects the levitated rotor safety also. Practically at high-speed operations, the accurate measurement of the rotor position is complicated for conventional mechanical sensors. A new square currents control with global sliding mode control based sensorless torque observer is proposed to minimize the torque ripple and achieve a smooth, robust operation without using any mechanical sensors. The proposed controller is designed based on the error between the reference and measured torque values. The sliding mode torque observer measures the torque from the actual phase voltages, currents, and look-up tables. The simulation model has been modelled to validate the proposed methodology. From the simulation outputs, it is clear that the reduction of torque ripple by the proposed method shows improved than the conventional sliding mode controller. The overall system is more robust to the external disturbances, and it also gets efficient torque profile.

**keywords:** bearingless, global sliding mode, efficient: maintenance, safety, torque ripple

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

A. Czornik, M. Niezabitowski(Silesian University of Technology, Poland) | E. Makarov(National Academy of Sciences of Belarus) | S. Popova, V. Zaitsev(Udmurt State University, Izhevsk, Russia) |

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.

**keywords:** discrete-time systems, periodic systems, affine systems, uniform global asymptotic, stabilization, state feedback

A new multistable double-scroll 4-D hyperchaotic system with no equilibrium point, its bifurcation analysis, synchronization and circuit design

S. Vaidyanathan(Vel Tech University, India) | S. He(Central South University, Changsha, China) | A. Sambas(Universitas Muhammadiyah Tasikmalaya, Indonesia) |

In this work, we have developed a new 4-D dynamical system with hyperchaos and hidden attractor. First, by introducing a feedback input control into the 3-D Ma chaos system (2004), we obtain a new 4-D hyperchaos system with no equilibrium point. Thus, we derive a new hyperchaos system with hidden attractor. We carry out an extensive bifurcation analysis of the newhyperchaos model with respect to the three parameters.We also carry out probability density distribution analysis of the new hyperchaotic system. Interestingly, the new nonlinear hyperchaos system exhibits multistability with coexisting attractors.Next,we discuss global hyperchaos selfsynchronization for the newhyperchaos system via Integral Sliding Mode Control (ISMC). As an engineering application, we realize the new 4-D hyperchaos system with an electronic circuit via MultiSim. The outputs of the MultiSim hyperchaos circuit show good match with the numerical MATLAB plots of the hyperchaos model. We also analyze the power spectral density (PSD) of the hyperchaos of the state variables using MultiSim.

**keywords:** hyperchaos, hyperchaotic systems, hidden attractors, multistability, sliding mode control and circuit design

The algorithm of adaptive determination of amplification of the PD filter estimating object state on the basis of signal measurable on-line

T.Kwater, P. Hawro(The State University of Technology and Economics in Jaroslaw, Poland) | J. Bartman(University of Rzeszow, Poland) | D. Mazur(Rzeszow University of Technology, Poland) |

The article presents the algorithm that enables adaptive determination of the amplification coefficient in the filter equation provided by Kalman. The method makes use of an estimation error, which was defined for this purpose, and its derivative to determine the direction of correction changes of the gain vector. This eliminates the necessity to solve Riccati equation, which causes reduction of the method computational complexity. The experimental studies carried out using the proposed approach relate to the estimation of state coordinates describing river pollution using the BOD (biochemical oxygen demand) and DO (dissolved oxygen) indicators).The acquired results indicate that the suggested method does better estimations than the Kalman filter. Two indicators were used to measure the quality of estimates: the Root Mean Squared Error (RMSE) and the Mean Percentage Error (MPE).

**keywords:** estimation, Kalman filter, adaptive PD filter, filter amplification

The Lepschy stability test and its application to fractional-order systems

D. Casagrande, U. Viaro(University of Udine, Italy) | W. Krajewski(Systems Research Institute, Polish Academy of Sciences, Poland) |

It is shown how a stability test, alternative to the classical Routh test, can profitably be applied to check the presence of polynomial roots inside half-planes or even sectors of the complex plane. This result is obtained by exploiting the peculiar symmetries of the root locus in which the basic recursion of the test can be embedded. As is expected, the suggested approach proves useful for testing the stability of fractional-order systems. A pair of examples show how the method operates. It is believed that the suggested geometric approach can also be of some didactic value in introducing basic control-system tools to engineering students.

**keywords:** fractional-order systems, D-stability, recursive algorithms, complex polynomials, root locus, symmetries, control-theory didactics

Approximate controllability of second order infinite dimensional systems

J. Klamka(Silesian University of Technology, Poland) | A.Zh. Khurshudyan(Institute of Mechanics, NAS of Armenia) |

In the paper approximate controllability of second order infinite dimensional system with damping is considered. Applying linear operators in Hilbert spaces general mathematical model of second order dynamical systems with damping is presented. Next, using functional analysis methods and concepts, specially spectral methods and theory of unbounded linear operators, necessary and sufficient conditions for approximate controllability are formulated and proved. General result may be used in approximate controllability verification of second order dynamical system using known conditions for approximate controllability of first order system. As illustrative example using Green function approach approximate controllability of distributed dynamical system is also discussed.

**keywords:** infinite dimensional systems, approximate controllability, Green?s function approach, flexible Kirchhoff?Love plate

The use of synthesis methods in position optimisation and selection of tuned mass damper (TMD) parameters for systems with many degrees of freedom

A. Dymarek, T. Dzitkowski(Silesian University of Technology, Poland) |

The paper formulates and formalises a method for selecting parameters of the tuned mass damper (TMD) for primary systems with many degrees of freedom. The method presented uses the properties of positive rational functions, in particular their decomposition, into simple fractions and continued fractions, which is used in the mixed method of synthesis of vibrating mechanical systems. In order to formulate a method of tuning a TMD, the paper discusses the basic properties of positive rational functions. The main assumptions of the mixed synthesis method is presented, based on which the general method of determining TMD parameters in the case of systems with many degrees of freedom was formulated. It has been shown that a tuned mass damper suppresses the desired resonance zone regardless of where the excitation force is applied. The advantages of the formulated method include the fact of reducing several forms of the object’s free vibration by attaching an additional system with the number of degrees of freedom corresponding to the number of resonant frequencies reduced. In addition, the tuned mass damper determined in the case of excitation force applied at a single point can be attached to any element of the inertial primary system without affecting the reduction conditions in this way. It results directly from the methodology formalised in the paper. As part of the paper, numerical calculations were performed regarding the tuning of the TMD to the first form of free vibration of a system with 3 degrees of freedom. The parameters determined were subjected to analysis and verification of the correctness of the calculations carried out. For the considered case of a system with 3 degrees of freedom together with a TMD, time responses of displacement, from each floor, were generated to excitation induced by a harmonic force equal to the first form of vibration of the basic system. In addition, in the case of the parameters obtained, the response of the inertial element system to which the TMD was attached to random white noise excitation was determined.

**keywords:** structural control system, vibration, simple fractions, synthesis, rational functions, dynamic characteristics

Interval-valued dual hesitant fuzzy prioritized aggregation operators based on Archimedean t-conorm and t-norm and their applications to multi-criteria decision making

A. Sarkar(Heramba Chandra College, India) | A. Biswas(University of Kalyani, India) |

Multi-criteria decision making (MCDM) technique and approach have been a trending topic in decision making and systems engineering to choosing the probable optimal options. The primary purpose of this article is to develop prioritized operators to multi-criteria decision making (MCDM) based on Archimedean t-conorm and t-norms (At-CN&t-Ns) under interval-valued dual hesitant fuzzy (IVDHF) environment. A new score function is defined for finding the rank of alternatives in MCDM problems with IVDHF information based on priority levels of criteria imposed by the decision maker. This paper introduces two aggregation operators: At-CN&t-N-based IVDHF prioritized weighted averaging (AIVDHFPWA), and weighted geometric (AIVDHFPWG) aggregation operators. Some of their desirable properties are also investigated in details. A methodology for prioritization-based MCDM is derived under IVDHF information. An illustrative example concerning MCDM problem about a Chinese university for appointing outstanding oversea teachers to strengthen academic education is considered. The method is also applicable for solving other real-life MCDM problems having IVDHF information.

**keywords:** multi-criteria decision-making, interval-valued dual hesitant fuzzy elements, Archimedean t-conorm and t-norm, prioritized weighted averaging operator, prioritized weighted geometric operator

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