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A modular electric vehicle platform enables ability to integrate different control systems in a flexible way. In this paper, a decentralized cooperative control framework is proposed to achieve the integration of active front steering system (AFS) and active suspension system (ASS) by applying a multi-constrained distributed model predictive control (MDMPC) approach, which aims to improve the vehicle lateral stability, ride comfort and roll safety during path tracking. First, a partly decoupled 6-degree-of-freedom half-vehicle dynamics model is constructed. Then, a multi-agent-system (MAS)-based framework is introduced to coordinate AFS and ASS, which allows for the multi-constraints within the information exchange between agents. Through minimizing linear convex combination of objective functions, the cooperative control strategy is ultimately solved by the Pareto-optimality theory. Moreover, vehicle lateral and roll motion stability region described by the phase plane is employed to bound the controllable limits and achieve the dynamic cooperation between AFS and ASS. The simulation and hardware-in-the-loop (HIL) test results show that the proposed framework is effective for coordinating AFS and ASS, thereby enhancing the vehicle lateral and vertical stability during path tracking.

Hovering is an effective and challenging way for asteroid exploration. In this paper, the adaptive quasi-periodic switching control method for body-fixed hovering of asteroids with low fuel consumption and strong robustness using constant thrust is proposed. By analyzing the active control process and the drift process of the spacecraft in the phase plane, constant thrust control is applied in the appropriate orientation to maintain the desired hovering state above the asteroids. Considering the uncertainty of the dynamic environments near the asteroids, the apex position of drift process in the phase plane is predicted, meanwhile, the compensation conditions and the calculation formula for the constant-thrust engine ignition are given. The simulation results show that the quasi-periodic switching control method can reduce the fuel consumption of the spacecraft compared with other methods, moreover, the adaptive quasi-periodic switching controller can effectively improve the robustness of the system.

形態: カラー図版あり, Physical characteristics: Original contains color illustrations, Accepted: 2020-11-23, 資料番号: PA2110013000

In this paper, a new third-order chaotic system which has extremely multistability is constructed by introducing the boosted control of cosine function. In comparison with other chaotic systems of extremely multistability, the proposed chaotic system can spontaneously generate the infinitely many coexisting attractors towards two directions of the phase plane. It indicates the proposed system can output more chaotic sequences of different amplitudes at the same time. This peculiar physical phenomena is very interesting and worth studying. Relative to original chaotic system, the chaos characteristic of the proposed system is obviously enhanced, the value of max Lyapunov exponent is increased significantly and the complexity value was higher. In particular, many periodic windows of the original chaotic system become chaos. It means the proposed chaotic system has better chaotic characteristics. If the new system is applied to the field of cryptography, it would be a better system model as a pseudo-random signal generator (PRSG). Then, the new image encryption algorithm is designed based on the proposed discrete system, and its safety performance is tested. The experimental results demonstrate the feasibility of its application in the field of cryptography.

We propose a mathematical system capable of exhibiting chaos with a chaotic attractor which is odd symmetrical in the x − y phase plane but even symmetrical in the x − z and y − z phase planes respectively. A hardware implementation of the system is done on a digital FPGA platform for verification. The system is also attractive in the sense that (i) its dynamics are single-parameter controlled and (ii) it inherently generates two chaotic clock signals. As an application, an FPGA design methodology using this oscillator for speech encryption is demonstrated. The security of the proposed encryption scheme is evaluated and results confirm its robustness. Due to the efficient hardware resource utilization, the encrypted system delivers a throughput of 1.3Gbit/sec using a Xilinx Kintex 7.

In this paper authors present the results of a research that had a purpose to develop a method of constructing a neuroregulator model for the case of optimization of the control structure of a technological cycle. The method's implementation is based upon the automation of a production process when a physical controller, that operates the technological process according to a given program, is present. In order to achieve this goal, the artificial neural network approaches were implemented to create a mathematical model of the neuroregulator. The mathematical model of the neuroregulator is based on a physical prototype, and the procedure of a real-time control synthesis (adaptive control) is based on recurrent neural network training. The neural network architecture includes LSTM blocks, which are capable of storing information for long periods of time. A method is proposed for constructing a neuroregulator model for control of a production cycle when solving the task of the optimal trajectory finding on the phase plane of the technological cycle states. In the considered task of the optimal trajectory finding the mathematical model of the neuroregulator receives at each moment of time information about the current system state, the adjacent system states and the movement direction on the phase plane of states. Movement direction is determined by the given control optimization criteria. Based on the research results it was found that recurrent networks with LSTM modules can be used successfully as an approximator for the agent's Q-function to solve the given problem when the partially observed region of system states has a complex structure. The choice of the method of adaptation to the control actions and the external environmental disturbances proposed in the paper satisfies the requirements for the adatation process performance, as well as the requierments for the control processes quality, when there is lack of information about the nature of random control disturbances. The experimental environment, as well as the neural network models was implemented using the Python programming language with TensorFlow library.

Life sciences are devoted to the research of all aspects of living organisms. As the basic unit of a living organism, biological cells are diverse and different. These differences are a direct reflection of their corresponding biological characteristics, so "seeing the cell more clearly" has been the goal of scientists at home and abroad. Based on the principle of coherent imaging, digital holographic quantitative phase microscopy imaging technology adopts digital recording and numerical reconstruction to realize phase retrieval and three-dimensional reconstruction. It has become one of the most promising methods in cellular research with better imaging efficiency, reconstruction accuracy, and stability. However, in the band-pass filtering process, tilt aberrations are often introduced due to manual frame selection of the +1 order spectrum, which is detrimental to the imaging quality of the system. To address this problem, this paper proposes a method to automatically determine the spectral center based on the surface fitting of a two-dimensional Hann window function, which improves the phase retrieval accuracy and imaging quality without reducing the computational speed. A more accurate spectral center can be obtained by conducting the sub-pixel spectral center of surface fitting. In addition, the accuracy is sub-pixel level and requires sub-pixel displacement correction of the tilted phase plane to obtain better quantitative phase retrieval results and imaging quality.

1AbstractTechnical advances in artificial manipulation of neural activity have precipitated a surge in studying the causal contribution of brain circuits to cognition and behavior. However, complexities of neural circuits challenge interpretation of experimental results, necessitating theoretical frameworks for system-atic explorations. Here, we take a step in this direction, using, as a testbed, recurrent neural networks trained to perform a perceptual decision. We show that understanding the computations implemented by network dynamics enables predicting the magnitude of perturbation effects based on changes in the network’s phase plane. Inactivation effects are weaker for distributed network architectures, are more easily discovered with non-discrete behavioral readouts (e.g., reaction times), and vary considerably across multiple tasks implemented by the same circuit. Finally, networks that can “learn” during inactivation recover function quickly, often much faster than the original training time. Our framework explains past empirical observations by clarifying how complex circuits compensate and adapt to perturbations.

The paper deals with bending-torsion coupling response of spur gear system due to its complex excitations. Based on the Bartelmus model, a multi-degrees-of-freedom lumped parameter dynamic model of a one-stage gear system, which includes gear mesh stiffness fluctuations, transmission errors, gear backlash and torque loads, is established. Considering the misalignment of gear root circle and base circle, an improved mesh stiffness model is applied to calculate the time-varying mesh stiffness by simplifying the gear tooth as a cantilever beam on the root circle. Based on these equations of gear system, the dynamic orbits of the bending-torsion coupling system are observed using bifurcation diagrams plotted with the frequency ratio and torsional stiffness as control parameters. Meanwhile the dynamic properties of the gear system are identified from the time domain response diagrams, phase plane diagrams, Poincare maps and amplitude-frequency spectrums of the gear system. The numerical results show that the system exhibits a diverse range of periodic, sub-harmonic, and chaotic motion with the coupling effects of bending and torsional vibrations. The results provide us a further understanding about vibration generation mechanisms and work status of the spur gear system.

Chatter, the vibration between the workpiece and cutting tool, is a common phenomenon during the milling process. Traditionally, the Fourier transform analysis is mainly used to extract the features and determine whether chatter occurs. In this paper, an innovative and practical chatter identification method combining fractional order chaotic system and extension theory is proposed. A lathe spindle with embedded sensors is used in this study. The boundary of chattering state of the lathe spindle is decided by the center of gravity of phase plane of dynamic errors. The boundaries are then fed into extension model and relational function calculation is performed. In this way, chatter identification can be easily achieved based on the position of the chaotic center of gravity. The three chaotic systems, i.e. Lorenz, Chen-Lee, and Sprott, of different fractional orders are used and their results are compared. Compared with the traditional methods, the Fourier transform is time-consuming in terms of mathematical operations and adverse to the establishment of a real-time system. This paper uses the characteristics of the chaotic systems sensitive to input signals in order to more capably detect the boundary state from normal cutting to chattering cutting and more efficiently identify the chatter. The experiment results indicate that the Chen-Lee system (93.5%) exhibits have better chatter diagnosis rate than Lorenz (92.75%) and Sprott (69%) systems. The Chen-Lee system even reaches a diagnosis rate of 100% for orders 0.5 ~ 0.7. Therefore, the method presented in this paper has a very high diagnosis rate and is thus very effective for chatter identification of machine tools.

We present a method to simulate spiking neurons with device nonidealities present in the neuron model. Machine learning algorithms are tested in spiking neural network simulators with an ideal mathematical description of spiking neurons. But silicon implementations of spiking neurons differ significantly from their ideal mathematical models because of device nonidealities and restrictions in the range of device operation. These nonidealites affect the performance of chip implementations of the neuron. We use the dynamical system phase plane of the neuron circuit to produce time domain spiking pattern that is hardware realistic. This way time and cost can be saved by making design changes in the network before sending the chip for manufacturing.

Tire longitudinal forces of electrics vehicle with four in-wheel-motors can be adjusted independently. This provides advantages for its stability control. In this paper, an electric vehicle with four in-wheel-motors is taken as the research object. Considering key factors such as vehicle velocity and road adhesion coefficient, the criterion of vehicle stability is studied, based on phase plane of sideslip angle and sideslip-angle rate. To solve the problem that the sideslip angle of vehicles is difficult to measure, an algorithm for estimating the sideslip angle based on extended Kalman filter is designed. The control method for vehicle yaw moment based on sliding-mode control and the distribution method for wheel driving/braking torque are proposed. The distribution method takes the minimum sum of the square for wheel load rate as the optimization objective. Based on Matlab/Simulink and Carsim, a cosimulation model for the stability control of electric vehicles with four in-wheel-motors is built. The accuracy of the proposed stability criterion, the algorithm for estimating the sideslip angle and the wheel torque control method are verified. The relevant research can provide some reference for the development of the stability control for electric vehicles with four in-wheel-motors.

Due to the widespread utilization of composites in structural and machine components, the dynamic analysis of these structures has become very essential for their efficient design. The present work deals with the investigation of the effect of fiber orientation/ lamination scheme on the non-linear forced vibration response of angle-ply laminated composite cylindrical shell. The finite element formulation has been carried out and the geometric nonlinearity has been incorporated. The formulation is based on the kinematics of FSDT and the governing equations have been obtained using Hamilton's principal. The solution procedure employed in the analysis is based on the modified shooting method. The nonlinear steady state frequency response curves have been obtained for different lamination scheme. The differences in the response characteristics for different fiber-angle have been explained through the distribution of strain/stress across the thickness of the laminate. The cyclic variation of the response, its FFT and the phase plane plots are also obtained to explain the nature of the non-linear response.

The development of tidal turbines continues to be carried out by many researchers, including the incorporation of a control system for optimization purposes. This paper attempts to assess the stability of two mechanical systems in a tidal turbine: a propeller harvesting kinetic energy and a d-q diagram system on a permanent-magnet synchronous generator (PMSG). The method employed is the representation of a phase plane profile with a stable eigenvalue. The critical value of the turbine’s rotations per minute provides some points of equilibrium. The effect of the angular velocity singular on the modified system was also investigated. There is no cutoff control for the generator rotational speed in the case of weak currents, according to the results. The combination of the three tidal turbine components results in a shift in the equilibrium point. Although PMSG has an infinite equilibrium point along the line Id = 0, the effect of the rotor angular velocity prevents all of these points from being in equilibrium. Finally, in this study, the rotor angular velocity caused by the speed and type of ocean currents are only the upper and lower limits. The stability of the various wave variations is within this range.

Phase plane control (PPC) method has been widely applied to spacecraft control since the 1970s. However, due to its complex nonlinear nature, the stability analysis problem is usually very difficult and is still not fully tackled to date. In this paper, firstly, the typical applications of the PPC method in the field of spacecraft control are briefly overviewed. Then, the typical nonlinear characteristics of the PPC method and their effects on the stability analysis are clearly pointed out. Further, five common stability analysis methods for the spacecraft PPC system are overviewed and analyzed. Particularly, the framework of computer simulation-based stability analysis proposed in recent related literature is introduced and discussed in detail. Finally, from a systems and control perspective, several challenging problems about the stability analysis of the spacecraft PPC system are formally proposed to provide some further research directions in this field.

The purpose of the article is an improvement of the instruments for automation of the qualitative research of the dynamic system and forecasting parameters values, characterizing the activities of organizations in the field of economics (particularly organizations in the sphere of multitenant apartments management). In the article, the problem of the automation of the analysis of the phase trajectory of the dynamic system is solved (organization in the sphere of multitenant apartments management) using the qualitative theory of the dynamic systems. On the example of the analysis of the phase trajectory, characterizing the activities of the multitenant apartments management organization, are demonstrated opportunities of the software application, which include building of the phase trajectory projections on three phase planes. It is established that in the phase plane, there are no equilibrium states of the “stable node” and “stable focus” types, but there are equilibrium states of the “unstable node”, “unstable focus” and “saddle” types. An example of detecting “attraction area” of the phase trajectory in the phase plane is given. Economic interpretation of “attraction areas” is given.

Time-optimal control of robotic manipulators along specified paths is a well-known problem in robotics. It concerns the minimization of the trajectory-tracking time subject to a constrained path and actuator torque limits. Calculus of variations reveals that time-optimal control is of bang-bang type, meaning that at least one actuator is in saturation for every point on the path. Unfortunately, this rule is broken at singular points, where the enforcement of the maximal and/or minimal torque at the bounding actuator would cause the violation of the path constraint. At these particular points, and, sometimes, at critical ones too, the selection of the torques is cumbersome and may introduce jitters in the control references. In this paper, the time-optimal control is addressed in the phase plane with a genetic approach. Results of calculus of variations are ignored and bang-bang control is re-found for the most of the trajectory, while in the neighborhoods of singular points, torques are automatically selected in order to minimize the trajectory-tracking time. Compared to other techniques, the problem is solved directly, without intermediate steps requiring, for example, the explicit computation of the switching points and the management of torques at critical points. The algorithm is validated in simulation on a canonical 2R planar robot in order to ease the comparison with previous works.

This paper mainly focuses on control strategy of the regenerative braking system of an electric vehicle under safety critical driving situations. With the aims of guaranteeing the electric vehicle stability in various types of tire-road adhesion conditions, based on the characteristics of an electrified powertrain, a novel control strategy of regenerative braking system is proposed for electric vehicles during anti-lock braking procedures. Firstly, the main construction of the case-study electric car with regenerative braking system is introduced. Next, based on the phase plane theory, the optimal brake torque is calculated for ABS control of an electric vehicle. Then, an allocation control, wherein the required optimal brake torque is divided into two parts that are disposed respectively by the friction and regenerative brakes, is discussed. In addition, two parameters for evaluating regeneration braking energy efficiency contribution while in the deceleration braking process are defined. Furthermore, a novel regenerative braking control strategy named “serial control strategy” is proposed. Finally, the road tests are implemented in four types of tire-road adhesion conditions under safety-critical driving situations. The test results validate the effectiveness and feasibility of the proposed control strategy.

A novel beamforming (BF) method for orbital angular momentum (OAM) index modulation (IM) scheme is proposed in this Letter. Since the OAM wave has an inverted cone-shaped beam structure, only partial phase plane can be received during long distance transmission. Based on this partial phase plane information, an OAM–IM system can be established. Since the receiver is only located on a partial arc of the cone-shaped beam, the energy of the whole beam cannot be fully received. However, by adjusting the combinations of multiple OAM beams, the energy of the cone-shaped beam will be converged to a specific direction where the receiver is located. Compared with the traditional BF method, as a new degree of freedom, the OAM–BF method can not only increase the flexibility of beam steering, but also realise the IM information transmission on the partial receiving phase plane.

A multi-objective active front steering (AFS) control system considering the road adhesion constraint on vehicle stability is developed using the sliding mode control (SMC) method. First, an identi...

In this study, a finite element model of an elastic-support cantilever beam with crack and offset boundary is established by using mixed elements in ANSYS software. In the proposed model, different contact elements are adopted to describe the breathing effect of crack and offset boundary, and spring elements are used to simulate the elastic support, and the model is also validated by comparing the natural frequencies with those in published literatures. Based on the developed model, the combined effects of the crack and offset boundary on the system dynamic characteristics are studied. The results indicate that the amplitude of double frequency component (2fe) firstly decreases and then increases with the offset values when the crack position is on the opposite side of offset boundary. 2fe may disappear when the crack and the offset boundary locate at a certain position. In addition, the more distant the offset boundary is, the more intense the system nonlinearity becomes. The amplitude of 2fe increases with the offset values when the crack position is on the same side of offset boundary under a constant crack depth and location. Moreover, it also shows some complicated frequency components due to the gradually strengthened nonlinearity of the system with the increasing offset values, and the obvious distortion phenomenon in the phase plane portraits can be observed near the super-harmonic resonance region. This study can provide some basis for the diagnosis of beam-like structures with crack.

The article aims to document PhaPl that’s a teaching software to plot and research phase portraits of autonomous systems of 2 differential equations on a plane. Interactive computer teaching materials allow to demonstrate tasks describing large number of states of investigated systems clearly and involving students into solving. Plotting and research of phase portraits of autonomous system of 2 differential equations is an important task in “Differential equations” course and other courses that use dynamic systems. The software allows to visualize phase portraits and to perform analysis easily. Plotting of phase portraits needs a lot of routine computations. The software allows teacher to focus on analytical research of autonomous systems of 2 differential equations. The software supports linear and nonlinear autonomous systems of 2 differential equations. The software differs is very different compared with previously known programs: it has very easy graphical user interface and it gives clarity because it demonstrates all steps of solution. To get the full solution, it is enough to just enter a system to research. Initial conditions to plot phase trajectories are chosen automatically. Graphical representation of the phase plane is interactive and allows user to draw additional trajectories with specified initial conditions by mouse hovering over the phase plane. The software is based on popular Free Software (Maxima, Qt4, LaTeX) and it is Free Software itself, thus it is accessible to wider audience, including online students. The software is portable and works on Windows and Linux operating systems. The article describes advantages, disadvantages and peculiar properties of the software, and some aspects of teaching experience. The software is deployed in Moscow State University of Economics, Statistics, and Informatics (MESI), Lomonosov Moscow State University (MSU) since 2013, and in Plekhanov Russian University of Economics since 2016. Further development will be focused on reduction of binary size of the software, portability improvements, and number of analytical results showed.

Several power system networks exhibit bifurcation, chaos and instability behavior for some specific values of initial conditions and parameters. Angle and voltage instability behavior of power system is prone to such specific values and parameter variation. This paper proposes fractional order proportional integral controller (FOPI) based state feedback for precise and robust control of such undesirable behavior. This paper proposes first ever use of FOPI for precise rotor angle control leading to instability in power system dynamic behavior. FOPI controller is applied on generator connected to IEEE-14 bus benchmark model. The ripple frequency of turbine torque is chosen as one of the cause of instability behavior of power system, which has the potential possibility to push system behavior to chaos and instability mode. The proposed FOPI controller design will inhibit the dynamic behavior of power system to safe and stable bounds. Proposed strategy can be applied to other large power system models as well due to its simplicity in design philosophy. Several phase plane trajectories with and without FOPI controller are used to support the viewpoint.

Unacceptable vibrations induced by the nonlinear friction in a rotor system seriously affect the health and reliability of the rotating machinery. To find out the basic excitation mechanism and characteristics of the vibrations, a coupled bending and torsional nonlinear dynamic model of rotor system with nonlinear friction is presented. The dynamic friction characteristic is described with a Stribeck curve, which generates nonlinear friction related to relative velocity. The motion equations of unbalance rotor system are established by the Lagrangian approach. Through numerical calculation, the coupled vibration characteristics of a rotor system under nonlinear friction are well investigated. The influence of main system parameters on the behaviors of the system is discussed. The bifurcation diagrams, waterfall plots, the times series, orbit trails, phase plane portraits and Poincare maps are obtained to analyze dynamic characteristics of the rotor system and the results reveal multiform complex nonlinear dynamic responses of rotor system under rubbing. These analysis results of the present paper can effectively provide a theoretical reference for structural design of rotor systems and be used to diagnose selfexcited vibration faults in this kind of rotor systems. The present research could contribute to further understanding on the self-excited vibration and the bending and torsional coupling vibration of the rotor systems with Stribeck friction model.

In this paper, a novel dynamics controller for autonomous vehicle to simultaneously control it to the driving limits and follow the desired path is proposed. The dynamics controller consists of longitudinal and lateral controllers. In longitudinal controller, the G-G diagram is utilized to describe the driving and handling limits of the vehicle. The accurate G-G diagram is obtained based on phase plane approach and a nonlinear vehicle dynamic model with accurate tyre model. In lateral controller, the tyre cornering stiffness is estimated to improve the robustness of the controller. The stability analysis of the closed-looped error dynamics shows that the controller remains stable against parameters uncertainties in extreme condition such as tyre saturation. Finally, an electric autonomous Formula race car developed by the authors is used to validate the proposed controller. The autonomous driving experiment on an oval race track shows the efficiency and robustness of the proposed controller.

Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincare maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

Wear between elements significantly affects the dynamics of a linear guide. Several existing contact stiffness models were used to investigate the dynamic behaviors of linear guide systems. However, the wear of linear guides has been rarely investigated due to difficult prediction of contact load and wear mechanism. To solve this problem, an improved wear prediction method was developed in this study by considering the coupling effects of wear and rolling contact. To ensure the high quality and high precision of long-age service, a final contact stiffness and piecewise-nonlinear dynamic model were established to analyze the dynamic behaviors of a linear guide system. Moreover, the influencing factors in wear rates such as running distance and vertical load were evaluated. To analyze the effects of wear on the dynamics of the system, basic properties such as frequency response, Lyapunov exponents, time histories, phase plane diagram and Poincare mapping were analyzed using numerical simulations.

This paper deals with dynamical behavior and controlled system of a feed-flow-reversal in a RO desalination system, giving inspirations to effective water treatment under large uncertainties, disturbances, and noises. The phase plane and nullclines analyses show an overview of RO nonlinear dynamical behavior around its equilibrium points. From a safety operation perspective, although the process variables still converge to a stable node under parametric variations, the desalination process becomes susceptible to external disturbances and suffers from severe damages due to the random occurrence of water hammering. In turn, the transient pressure has wave profile with maximum value, which can be worsen by CP phenomenon. For controlling purpose, a linear RO system with two inputs and three outputs is realized by the model linearization around the equilibrium points. This model has to be given in state-space parametric uncertainty framework considering the CP phenomenon. Overcoming the various challenges, the robust H ∞ controller has been designed to cope with large parametric variations and unmodeled dynamics uncertainties, and also to regulate the desalination plants under noises and disturbances such as water hammering. Finally, the simulated results show that the presented controller can offer for robust and safe operations of RO dynamical system.

Neurophysiological observations are clarifying how astrocytes can actively participate in information processing and how they can encode information through frequency and amplitude modulation of intracellular Ca2+ signals. Consequently, hardware realization of astrocytes is important for developing the next generation of bio-inspired computing systems. In this paper, astrocytic calcium oscillations and neuronal firing dynamics are presented by De Pittà and IF (Integrated & Fire) models, respectively. Considering highly nonlinear equations of the astrocyte model, linear approximation and single constant multiplication (SCM) techniques are employed for efficient hardware execution while maintaining the dynamic of the original models. This low-cost hardware architecture for the astrocyte model is able to show the essential features of different types of Ca2+ modulation such as amplitude modulation (AM), frequency modulation (FM), or both modes (AFM). To show good agreement between the results of original models simulated in MATLAB and the proposed digital circuits executed on FPGA, quantitative, and qualitative analyses including phase plane are done. This new neuromorphic circuit of astrocyte is able to successfully demonstrate AM/FM/AFM calcium signaling in its real operation on FPGA and has applications in self-repairing systems. It also can be employed as a subsystem for linking biological cells to artificial neuronal networks using astrocytic calcium oscillations in future research

A bivariate time-series analysis based on the phase plane trajectory of feature vectors extracted by principal component analysis is developed for fault detection in a reusable liquid-propellant rocket engine. Static-firing test results of the reusable rocket engine obtained at the Japan Aerospace Exploration Agency are employed for demonstration of the present method. The present method successfully detected temperature sensor failure from 19 firing tests of 62 sensors, even in the deviation of the engine operational sequence between the static-firing tests. The present method was also able to detect the system failure from 23 firing tests. Furthermore, the ability to distinguish the system and sensor failure was demonstrated.

The results of detection of periodic signals using the chaos theory based on discrete processing of the Duffing attractor in the Poincare section were considered. A chaotic Duffing system characterized by high sensitivity to periodic signals and a possibility of implementation by means of a relatively simple circuit was chosen for the study. Response of the Duffing system to the periodic influence was analyzed. It was shown that when amplitude of periodic components of the input signal grows at a frequency of driving oscillations, there is a shift of the phase trajectory along the Poincare section which is characterized by fractal geometry. Types of the Duffing attractor changes that result from the influence of a periodic input signal were determined. Control regions for recording types of the phase trajectory dynamics were identified in the phase plane formed by the output signal and its derivative. In accordance with the characteristics of the obtained phase trajectories, a truth table was constructed. It enables estimation of influence of the periodic component with a sufficiently large time sampling increment which is important for ensuring speed of the signal processing devices. Transforms were obtained that describe the process of detecting periodic signals by discrete processing of the Duffing attractor in the Poincare section. Based on the formulated transforms and the truth table, a block diagram of a device for detecting periodic signals in noise was proposed. The proposed device can be used as an input unit to implement the Duffing system based on an analog electric circuit. Values of discrete estimates of amplitude of the periodic component of the input signal according to the shift of the phase trajectory of the Duffing system with respect to the attractor in the Poincare section were obtained. According to the modeling results, the proposed circuit makes it possible to detect periodic signals at low values of the signal-to-noise ratio.

To facilitate the using of 3D-printing process in the design and implementation of microwave components, this paper presents the measurement of the complex dielectric constant of 3D-printing non-magnetic materials. A rectangular waveguide based transmission line method has been used, through which the dielectric constant can be retrieved from the measured $S$ -parameters of the transmission line filled with the 3D-printing material. The calibration of referenced phase plane has been discussed, and two empirical formulas have been introduced to improve the measurement accuracy. The proposed method has been experimentally verified, and a much smoother result has been achieved when comparing with the counterpart result obtained by a commercial software.

This paper contains elements of a comprehensive research devoted to the dynamic behavior of radial ball bearings in real working conditions. The general motivation for this topic comes from the requirements for high performance operation of bearings within complex mechanical systems, defined in many industrial branches during the last decades. The discussion of the fundamental postulates of the approach used for analyzing the vibration response of rolling ball bearings in order to select the optimal working conditions is given. The certain simplifications and reductions used for analyzing the radial ball bearings are explained. The developed procedure can be used for research of influence of different damages and variable operation conditions on the rolling bearings dynamics. The detail analyses of the dynamic behavior of rolling bearings are performed for particular types of radial ball bearings in two case studies: For the damaged outer raceway surface in accordance with real fatigue damage shapes and dimensions and, for variable working temperature. Obtained results are shown by comparative diagrams of vibration and phase plane portraits. Presented results could be a base for more widely research of nonlinear dynamics of radial ball bearings with different damages and for the application of phase plane analysis in order to choose the optimal operation conditions.

Vehicle dynamics control systems play an important role in improving vehicle handling stability performance and passenger safety. Analysis of lateral stability region can further help to arouse the potential of the dynamics control system under critical maneuvers. This paper investigates lateral stability region for lightweight electric vehicle via phase plane approach. Based on the improved cubic formula tire derived from Pacejka model, the nonlinear vehicle dynamic analysis model is built and the particular state-space representation for vehicle phase plane analysis is developed. The lateral stability region is analysed using the band-shaped stability region related to two symmetric saddle points. And the influence of important factors such as road friction coefficient, steering wheel angle and vehicle velocity on the lateral stability of vehicle yaw motion is also discussed and presented, which may provide assist for vehicle dynamics control design.

So far, mobility in fish population has not been given sufficient attention, although movement and spatial heterogeneity can be an important dynamic feature that plays a critical role in their exploitation. Having a qualitative framework to describe and estimate movement and growth based on tagging data is necessary for efficient control and management of the fishing industry. Here, we construct an advection-diffusion-reaction model for the fish population structured to track the population densities of both the tagged fish and the tag-free fish, in which the impulsive tagging practice is incorporated, while continuous tagging is assumed to be done on off springs of trackable tagged fish, or on those in the same swarm as the trackable tagged fish. Using the traveling wave coordinate, we derive analytical expression for the solutions to the model system. We derive the explicit expression for the level of tagged fish which increases in a periodic impulsive fashion. Stability and phase plane analyses are also carried out to determine different behavior permitted by the model system.

Active front steering (AFS), as an effective active technology, can enhance the handling stability of the emergency rescue vehicle. In order to deal with the shortcomings of full AFS intervention for the vehicle, the intervention criterion and control strategy of AFS system for the emergency rescue vehicle are studied deeply. Based on the phase plane theory, the double-line and yaw rate methods are combined to construct the closed polygonal stable area of the vehicle. Depending on whether the vehicle status is outside the closed polygonal stable area, the AFS intervention criterion is proposed. Taking the yaw rate and the sideslip angle of the vehicle as the control targets, a sliding mode control (SMC) controller for the AFS system of the emergency rescue vehicle is designed based on the variable structure theory, and the extended Kalman filter (EKF) state observer is introduced to estimate the vehicle sideslip angle. Based on Matlab/Simulink software, the intervention criterion and control strategy of AFS system are simulated and analyzed. In addition, the self-developed fire rescue prototype vehicle is selected as the experimental vehicle, and the proposed AFS intervention criterion and control strategy is tested. The simulation and experimental results showed that the proposed AFS control strategy with the intervention criterion is reasonable and effective, and it improves the handling stability of the emergency rescue vehicle.

The paper consists of two parts. First an outline is given of the functions of a tyre as a vehicle component with a discussion of the development of mathematical models describing steady–state cornering behaviour. Also, the concept of effective tyre characteristics are discussed, which represent the combined effects of tyre and elastic suspension and steering properties. The second part considers the motion of the vehicle over a horizontal flat surface with the longitudinal speed constant. After a discussion of steady–state cornering behaviour and the introduction of a handling diagram showing regions of under–steer and over–steer, and regions of stable and unstable motion, the dynamic solution of the plane motion has been studied. In the phase plane, domains of attraction can be indicated beyond which the motion becomes difficult or impossible to control.

This paper presents an elastic solution to the pressure-controlled elliptical cavity expansion problem under the anisotropic stress conditions. The problem is formulated by the assumption that an initial elliptical cavity is expanded under a uniform pressure and subjected to an in-plane initial horizontal pressure Kσ 0 and vertical pressure σ 0 at infinity. A conformal mapping technique is used to map the outer region of the initial elliptical cavity in the physical plane onto the inner region of a unit circle in the phase plane. Using the complex variable theory, the stress functions are derived; hence, the stress and displacement distributions around the elliptical cavity wall can be obtained. Furthermore, a closed-form solution to the pressure-expansion relationship is presented based on the elastic solution to the stress and displacement. Next, the proposed analytical solutions are validated by comparing with the Kirsch’s solution and the finite element method (FEM). The solution to the presented pressure- controlled elliptical cavity expansion can be applied to two cases in practice. One is to employ the solution to the interpretation of the shear modulus of the soil or rocks and the in-situ stress in the pre-bored pressuremeter test under the lateral anisotropic initial stress condition. The other is the interpretation of the membrane expansion of a flat dilatometer test using the pressure-controlled elliptical cavity expansion solution. The two cases in practice confirm the usefulness of the present analytical solution.

This paper presents the analysis of the variety of methods regarding aerial guided bomb control during the ground attack on a moving target. Based on this method there was an earlier research regarding motion control of the three degrees of freedom gyroscope axis [1,2] during space exploration and discovered target tracking. Positive results obtained during that research led to conclusion that the proposed control method will be accurate to establish a control force for aerial bomb guiding. This method is based on the use of phase trajectories control deviations. Switching of the control forces in the particular phase plane points causes the deviations to decrease to zero and facilitates the proper trajectory of the bomb. This paper presents a switching algorithm, equations of kinematics and dynamics of a bomb flight-path and the variety of examples of a numerical simulations. Obtained results were presented in the graphic form.

This paper presents a plane equivalent model of the vehicle and its mathematical model attached. The mathematical model is under a form of four differential equations system of order 1, in order to analyze the dynamic behaviour of the vehicle movement. Its goal is to determine the ranges of speed for that movement is stable or is unstable, or having chaotic character. The authors consider being necessary to know the conditions in which movements occur chaotic movements to avoid them through constructive or functional limitations. Speed ​​values ​​are identified for the behaviour of the system is placed in the quasiperiodic movements field or exceeding these movements trough chaos and are highlighted by the specific instruments: the trajectories in the phase plane, Poincare section and power spectra.

The body of a walking human is an elaborated dynamic system that operates adaptively in various conditions such as fast walking. Due to dynamic redundancies, the individual motor control strategies for speeding up the walking can be different among normal subjects. However, in reality, we see that the pattern of motion is quite similar among people and it is only the profile of hip joint motion along its path which determines the speed. The objective of the current paper is to develop a mathematical framework to investigate time optimal motion of a human during walking. To this end, a nine-link planar biped model is used. The motion is considered to take place in sagittal plane and to follow a normal pattern of motion. The solution is obtained using a phase plane method to solve minimum time problem which is subjected to inequality constraints of variable maximum joint torques and stability conditions. The solution method can be used to find the maximum possible speed of a human with specific body characteristics and to obtain a hip joint trajectory which could produce that speed. The proposed method can be utilized to study quantitative effect of different parameters such as joint strength in fast walking.

Stick-slip vibration presents one of the major causes of drilling problems, such as premature tool failures, low drilling efficiency and poor wellbore quality. The objective of this work is to investigate the influences of rotary table speed (RTS) on stick-slip phenomenon of the drilling system. In this study, the drilling system is treated as a lumped torsional pendulum model of which the bit/rock interaction is regarded as Coulomb friction. By analyzing cases with different RTS, two types of vibrations on the bit are found: stick-slip vibration and uniform motion. With an increase in the RTS, the stick-slip vibration on the drill bit disappears once the RTS arrives at its critical value. For the cases that stick-slip vibrations occur, the phase trajectories converge toward a limit cycle. For the cases that stick-slip vibration does not appear, the drill bit tends to stabilize at a uniform motion and the phase trajectories correspond to contracting spirals observed in the phase plane.

The analytical approach is presented to study the nonlinear vibration of W-Cu sandwich shell containing heavy water surrounded by an elastic foundation under thermo-mechanical loads. The cylindrical shell is assumed to be made of Tungsten and Copper, continuously graded in the thickness direction. The fluid in the shell is heavy water which is assumed to non-viscous and incompressible. The nonlinear vibration of the full-filled fluid shell using Flugge-Lur'e-Bryrne theory is investigated through the Galerkin method. The natural frequencies, the dynamical responses as time history and phase plane graphs, Poincare map are given in detail. The obtained results that are validated with other studies, have the valuable applications in nuclear reactors, rocket shells, fusion reactor vessels.

In this work we applied a Hamiltonian formalism to simplify the equations of non-degenerate nonlinear four-wave mixing to the one-degree-of-freedom Hamiltonian equations with a three-parameter Hamiltonian. Thereby, a problem of signal amplification in a phase-sensitive double-pumped parametric fiber amplifier with pump depletion was reduced to a geometrical study of the phase portraits of the one-degree-of-freedom Hamiltonian system. For a symmetric case of equal pump powers and equal signal and idler powers at the fiber input, it has been shown that the theoretical maximum gain occurs on the extremal trajectories. However, to reduce the nonlinear interaction of waves, we proposed to choose the separatrix as the optimal trajectory on the phase plane. Analytical expressions were found for the maximum amplification, as well as the length of optical fiber and the relative phase of interacting waves allowing this amplification. Using the proposed approach, we optimized of the phase-sensitive parametric amplifier. As a result, the optimal parameters of the phase-sensitive amplifier were found and the maximum possible signal amplification was realized in a broad range of signal wavelengths.

This paper addresses the yaw stability analysis of articulated vehicles using the phase trajectory method. The goal of this work is to ascertain the dynamic conditions that the articulated vehicle can assume without the occurrence of instability events such as jackknife and rollover. The study focuses on the vehicle configuration composed by one tractor unit and a driven unit such as, for instance, a tractor semi-trailer combination. The system consists of a nonlinear tire model and a nonlinear articulated bicycle model with four degrees of freedom. The analysis presented in this paper illustrates the convergence regions of equilibrium points obtained through numerical integration of the equations of motion of the model for different initial conditions in the phase plane. In addition, the changes in the obtained regions are presented as a function of the tractor speed and the position of the articulation point between the two units.

In this paper, the dynamic model of an 8-degree-of-freedom hypoid gear pair model with time-varying stiffness, comprehensive gear error and the nonlinearity backlash is established. The numerical integration method is applied to solve the dynamic responses. With help of bifurcation diagrams, time history, phase plane, frequency spectrum and Poincare maps, the effects exaction frequency, load coefficient and support damping are investigated by using the numerical integration method. The results reveal that system exhibits a diverse range of one-period responses, multi-periodic responses, bifurcation and chaotic responses when the parameters are changed. Some results presented in this study provide some useful reference to dynamic design and vibration control of the gear transmission system.

A transient stability control system for the electric power system composed of a prediction method and a control method is proposed based on trajectory information. This system, which is independent of system parameters and models, can detect the transient stability of the electric power system quickly and provide the control law when the system is unstable. Firstly, system instability is detected by the characteristic concave or convex shape of the trajectory. Secondly, the control method is proposed based on the analysis of the slope of the state plane trajectory when the power system is unstable. Two control objectives are provided according to the methods of acquiring the far end point: one is the minimal cost to restore the system to a stable state, the other one is the minimal cost to limit the maximum swing angle. The simulation indicates that the mentioned transient stability control system is efficient.

This paper presents LabVIEW based Graphical User Interface (GUI) tool called as ‘nonlintool’. The tool provides much needed user friendly computational platform for nonlinear control system as there are very few endeavours found on computer aided tool for analysis and design of nonlinear control system. The tool is useful for analysis and design of nonlinear control system. The tool offers user friendly computational platform for the study of nonlinear control system. It has capability to carry the analysis and design for almost all type of discrete (or discontinuous) and continues nonlinearities. It aims to provide quick and effective means for the understanding of behaviour of nonlinear systems. The different modules integrated in the tool to analyse the discrete type nonlinearity with phase plane trajectory and continuous type nonlinearity with linearization. The tool enables the user to investigate the stability of the system and help to proceed for the design of nonlinear control system. The tool is converted in to executable file to make it open source package. © 2015 Wiley Periodicals, Inc. Comput. Appl. Eng. Educ. 9999:1–7, 2015; View this article online at wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.21697

The paper suggests a design procedure for fuzzy cascade control. The expert knowledge based tuning procedure is supported by investigation the phase plane of the reference tracking. The plant is a one degree of freedom helicopter model with highly non-linear dynamics in a hardware-in-the-loop arrangement. Starting from a common fuzzy-PI controller in the outer loop and classic PI-controller in the inner loop, the presented tuning procedure enables to obtain fuzzy-adaptive parameter settings of the inner-loop and a heuristic modified rule base in the outer loop. The developed control strategy proves to be very successful: both the settling times and overshoots have become well regulated.