Control of coexisting attractors and chaos in brushless direct current motor (BLDCM) is investigated in this paper. Using a weak harmonic modulation of a parameter of the BLDCM, the coexisting attractors between chaotic and period-1-oscillations are destroyed and transformed to period-1-oscillations. Moreover, two single controllers are designed to control the chaotic behavior found in BLDCM. Numerical simulations are used to evaluate the performance of the two developed controllers. Finally, the dynamical behaviors found in BLDCM and the physical feasibility of two proposed single controllers are validated through circuit implementations on OrCAD-PSpice software. The robustness of the three controllers is tested by a sensitivity analysis to parametric uncertainties.

Significant amount of energy is consumed in water supply systems resulting in reduced sustainability of these systems. Measures to reduce their energy demand are strongly needed. In this study, an estimation of the intrinsic hydro energy potential of the water supply system of a Cameroon municipality was made in order to propose an energy-potential map useful to identify the most interesting sites where excess energy in the network can be harvested to improve the energy efficiency of the network. A geodatabase to store network data was developed using Geographic Information Systems. The shapefiles resource data were explored and the hydraulic simulator EPANET software was used to create a model. Calculations were performed to determine the energy recovery values at different locations in the network. The resulting digital map presented 18 candidate sites which show a total annual energy potential of 635 MWh, realizable at capacity factor and efficiency of 41 % and 65 % respectively. This potential can offset the energy footprint of the network by about 34 % while 127 tons of carbon-dioxide emission reductions are achieved. The results of this investigation highlight that development of renewable energy resource on water supply network infrastructure is an innovative technology that can contribute significantly to improve the energy efficiency, economic and environmental sustainability of the water supply system.

Genesio–Tesi system with Chua’s diode based on state-controlled cellular neural network is proposed and investigated in this paper. The proposed system can exhibit period doubling bifurcation, periodic attractors, chaotic attractors, multistability and antimonotonicity phenomenon. The results found during numerical simulations are verified in the laboratory experiments in order to confirm the dynamics of the proposed model. A linear augmentation control is used to transform the multistable regime to monostable regime.

The analysis, electronic validation and chaos control of nonsmooth-air-gap brushless direct current motor (BLDCM) running under no loading conditions are investigated in this article. The nonsmooth-air-gap BLDCM is described by a system of three-dimensional autonomous equations. The stability of equilibrium points found is studied. Different dynamical behaviors of nonsmooth-air-gap BLDCM including periodic and chaotic spiking oscillations, monostable and bistable double-scroll chaotic attractors and coexisting attractors are revealed using numerical methods such as two dimensional largest Lyapunov exponents (LLEs) and isospike graphs associated with two parameters of nonsmooth-air-gap BLDCM. Moreover, an analog circuit is designed and implemented in OrCAD-PSpice software to confirm the dynamical behaviors found in nonsmooth-air-gap BLDCM during the numerical simulations. Finally, a simple and single controller is designed and added to the chaotic nonsmooth-air-gap BLDCM in order to suppress chaotic behavior. The performance of the proposed simple and single controller is illustrated by numerical simulations.

Dynamical analysis and chaos control of a synchronous reluctance motor (SynRM) with a constant and sinusoidal load torque are studied in this paper. The SynRM with load vibration perturbation exhibits pitchfork bifurcation, steady state behavior, double-scroll chaotic attractor and coexistence of attractors between steady state behavior and double-scroll chaotic attractors. Furthermore, an analog circuit is designed and implemented in OrCAD-PSpice software to validate the dynamical behaviors found in the SynRM with load vibration perturbation during the numerical simulations. Finally, an adaptive backstepping sliding mode control is used to suppress the chaotic oscillations in the SynRM with load vibration perturbation. Numerical simulations confirm the effectiveness of the proposed controller.

Josephson junction (JJ) with topologically nontrivial barrier is analytically and numerically analyzed in this paper. This system has four, two, or no equilibrium points depending on the external direct current (DC) source and the fractional parameter. The existence of pitchfork bifurcation is established during the stability analysis of the equilibrium points. The inclusion of fractional parameter in JJ leads to an increase in the hysteresis loop of current-voltage characteristics. For a suitable choice of modulation parameters of external current source, JJ with topologically nontrivial barrier can display excitable mode, bistable, periodic and chaotic behaviors.

The dynamical behaviors and chaos control in Indirect Field Oriented Control (IFOC) of 3-phase induction motor is investigated in the present paper. The IFOC of 3-phase induction motor exhibits steady state behavior, Hopf bifurcation and chaotic behavior through period-doubling. The chaotic behavior is strewed with periodic oscillation. To eliminate the chaotic oscillations in IFOC of 3-phase induction motor, two self-feedback delay controllers are designed: The first is the simple controller and the second controller is with sliding mode method. Numerical simulations are used to show the efficiency of the both controllers. Among the both controllers, the simple self-feedback delay controller gives the better results by comparison to sliding mode self-feedback delay controller. Finally, the physical feasibility of simple self-feedback delay controller applied to IFOC of 3-phase induction motor is validated through electronic circuit’s implementation on OrCAD-PSpice software. The OrCAD-Pspice results are in agreement with the numerical results.

The dynamical characteristics and its applications to random number generator of a fractal Josephson junction with unharmonic current-phase relation (FJJUCPR) described by a linear resistive-capacitive-inductance shunted junction (LRCLSJ) model are investigated in this paper. The dependence of the equilibrium points of the system to the external current source or the unharmonic current-phase relation (UCPR) parameter is revealed and their stability are analysed. The inclusion of unharmonic current-phase relation in an ideal or a fractal Josephson junction leads to transform the spiking, bursting and relaxations oscillations to an excitable mode. While the inclusion of fractal characteristics in insulating layer of Josephson junction leads to an increase of the amplitude of the spiking, bursting and relaxations oscillations. The numerical simulations results also indicate that FJJUCPR exhibits self-excited chaotic attractors and two different shapes of hidden chaotic attractors. The FJJUCPR is implemented in field programmable gate arrays (FPGA) in order to validate the numerical simulations results. In addition, random number generator design is performed using chaotic signals of the FJJUCPR. The random number generator design results are successful in the NIST SP 800-22 test.

The dynamics of indirect field oriented control (IFOC) of 3-phase induction motor is studied in this paper. The dynamical behaviors of the studied system are performed using bifurcation diagrams, maximum Lyapunov exponent plots, phase portraits, and isospike diagram. The numerical simulation results reveal that the IFOC of 3-phase induction motor displays coexistence of attractors for the same set of IFOC of 3-phase induction motor parameters, periodic and chaotic bursting oscillations. Basins of attraction of different competing attractors are plotted showing complex basin boundaries. The numerical simulation finding are validated by the OrCAD-Spice results.

The aim of this paper is to address the problem of the electronic implementation of chaos control using a single controller and synchronization of chaotic permanent magnet synchronous motor (PMSM). Firstly, different dynamical behaviors of the PMSM including steady state, periodic and chaotic behaviors are found using numerical methods such as two-dimensional largest Lyapunov exponents graph associated with two parameters of PMSM. Secondly, two simple and single controllers are designed and added to the chaotic PMSM in order to suppress chaotic behavior. The performance of the two proposed simple and single controllers is illustrated by numerical simulations. Thirdly, controllers are designed to achieve synchronization of unidirectional coupled identical chaotic PMSMs. Numerical simulations are also used to verify the effectiveness of the synchronization. Finally, the existence of chaos in PMSM and the physical feasibility of the proposed two simple and single controllers as well as the chaos synchronization are validated through the circuit implementation on OrCAD-PSpice software. The circuit implementation results comply fairly with those of the numerical simulation results and establish that the existence of chaotic behavior in the PMSM and the achievement of chaos synchronization in unidirectional coupled identical PMSMs designed and the two single controllers designed are effective and successful in suppressing chaotic behavior in PMSM.

In this paper, a simplified nonlinear method is proposed to enhance the transient stability of multimachine power system by using a Static Synchronous Series Compensator (SSSC). The rate of dissipation of transient energy is used to determine the additional damping provided by a SSSC. The proposed algorithm is based on the direct Lyapunov method. The simplicity of the proposed scheme and its robustness with respect to large disturbances constitute the main positive features. Simulation results in the case of 3-machines power system show the effectiveness of the proposed method under large disturbances (3-phase and single phase short-circuits).