Feedback Control Variables Research Articles

Bifurcation in a single-species logistic model with addition Allee effect and fear effect-type feedback control

In this paper, a single-species logistic model with both fear effect-type feedback control and additive Allee effect is developed and investigated using the new coronavirus as a feedback control variable. When the system introduces additive Allee effect and fear effect-type feedback control, more complicated dynamical behavior is obtained. The system can undergo transcritical bifurcation, saddle-node bifurcation, degenerate Hopf bifurcation and Bogdanov–Takens bifurcation. By numerical simulations, the system exhibits homoclinic bifurcation and saddle-node bifurcation of limit cycles as parameters are altered. Remarkably, it is the first time that two limit cycles have been discovered in a single-species logistic model with the Allee effect. Further, stronger Allee effect or stronger fear effect can lead to the extinction of the species population.

Optimal design of an adaptive energy management strategy for a fuel cell tractor operating in ports

As World trade is growing rapidly, the reduction of the environmental impact of in-port operations towards a low or zero-emission scenario is becoming a paramount issue. To this aim, replacing Diesel engines of cargo handling equipment used in port logistics (e.g. reach stackers, forklifts, yard tractors, etc.) with cleaner propulsion alternatives may play a major role. In this study, a robust rule-based energy management strategy is proposed for a newly developed fuel cell/battery hybrid powertrain of a yard tractor used for roll-on and roll-off in-port operations. As typical port operations are characterized by mission profiles that can vary significantly in terms of driving and duty cycles during the same work-shift, the proposed strategy, built upon the observation of the powertrain behavior under the application of an optimal controller, dynamically adapts the operation of fuel cell and battery in order to track a predefined battery state of charge trajectory, while minimizing the hydrogen consumption. The use of an optimal model-based approach as a reference for the design of an online implementable energy management strategy is indeed particularly suitable in the present case: despite their inherent high variability, the yard tractor mission profiles can be regarded as the combination of a set of predictable parameters. Results show that the application of the proposed control strategy allows the hybrid powertrain to achieve excellent performance, by leading its components to run efficiently and across suitable operative conditions. The achieved hydrogen consumption, for the considered missions, is only 2%–3% higher than that of the optimal controller, despite a quite different evolution of the battery state of charge, that is the feedback control variable. By means of this strategy, the transient loading of the fuel cell is prevented, while the battery pack ensures the fulfillment of the peak power requests, with beneficial effects in terms of on-board stored energy exploitation. The key advantage of the developed rule-based approach lies in its robustness, reliability and online applicability in real-time powertrain control.

Design and Experimental Validation of a 3D-Printed Embedded-Sensing Continuum Robot for Neurosurgery.

A minimally-invasive manipulator characterized by hyper-redundant kinematics and embedded sensing modules is presented in this work. The bending angles (tilt and pan) of the robot tip are controlled through tendon-driven actuation; the transmission of the actuation forces to the tip is based on a Bowden-cable solution integrating some channels for optical fibers. The viability of the real-time measurement of the feedback control variables, through optoelectronic acquisition, is evaluated for automated bending of the flexible endoscope and trajectory tracking of the tip angles. Indeed, unlike conventional catheters and cannulae adopted in neurosurgery, the proposed robot can extend the actuation and control of snake-like kinematic chains with embedded sensing solutions, enabling real-time measurement, robust and accurate control of curvature, and tip bending of continuum robots for the manipulation of cannulae and microsurgical instruments in neurosurgical procedures. A prototype of the manipulator with a length of 43 mm and a diameter of 5.5 mm has been realized via 3D printing. Moreover, a multiple regression model has been estimated through a novel experimental setup to predict the tip angles from measured outputs of the optoelectronic modules. The sensing and control performance has also been evaluated during tasks involving tip rotations.

Permanence and Global Attractivity of a Non-autonomous Single Species System with Michaelis-Menten-Type Feedback Control

During the past decade, many scholars have investigated the dynamic behaviors of the ecosystem with Michaelis-Menten-type harvesting; however, most of them assume that the harvesting effort does not change with time. Such an assumption has its drawbacks. Generally speaking, the rate of increase in harvesting effort changes with the density of the species. Inspired by this, we put forth a novel form of single-population feedback control model, in which the feedback control variable is of the Michaelis-Menten-type. Sufficient conditions that ensure the permanence and global attractivity of the system are obtained.

Global asymptotic stability of a basic virus dynamics model with feedback controls

In this paper, a basic virus dynamics model with feedback controls is considered and analyzed to restrain infected cells. The asymptotic stability of the model is investigated by using the Lyapunov stability theorem and numerical experiments. The obtained results show that the feedback control variables are effective to restrain infected cells in the original virus dynamics model. In particular, we propose two effective strategies for selecting the feedback control variables based on the asymptotic stability of the model with the feedback control variables. A set of numerical experiments is performed to confirm the validity of the theoretical results and the effectiveness of the proposed control strategies.

Research on intelligent mobile robot full coverage path planning

Aiming at the full coverage path planning problem of intelligent robot, a local chaos evaluation planning method is proposed. Considering the randomness and unpredictability of the mobile robot, a four-dimensional chaotic system with feedback control variables is designed. The path planning model is established by fusing the system with the robot motion model. At the same time, the coupling control parameters are introduced to adjust the system error. According to the initial coordinates and chaotic initial state parameters of the robot, the moving path points can be calculated by differential discretization. Considering the local optimal solution of the path planning, the mobile space of the robot is meshed, and the dynamic mesh activity value is calculated according to the excitation. The mesh activity is used to divide the mobile path planning, and then the local path and angular displacement changes are obtained. At the same time, the corresponding index evaluation is designed for local path planning to correct the planning results. The simulation results show that the proposed local chaos evaluation planning method has a good effect of full path coverage, and obtains lower path repetition rate, moving distance and path planning time, which effectively improves the mobile efficiency and control stability of the robot.

The effect of delay interval on the feedback control for a turbidostat model

In this paper, we propose a turbidostat model with delay interval on its output using a feedback control law, aiming to investigate how the delay interval affects the feedback control of the model. The delay interval is represented by two parameters, which describe the time delay distributed in a past sub-interval. We first prove the positivity and boundedness of solutions and the permanence of the model. Then, using the input flow rate as a feedback control variable, we discuss the asymptotical stabilization of a given state (i.e., the positive equilibrium) employing the method of Lyapunov functionals. Moreover, we further study the Hopf bifurcations induced by the two delay parameters. Our theoretical and numerical results all show that the delay interval can have a significantly different effect on the dynamics of a turbidostat model from other delay types.

Objective holographic feedbacks linearization control for boost converter with constant power load

As a typical load, the constant power load (CPL) is different from the resistive load and has destabilizing negative impedance characteristics, influencing the system stability. The boost converter with the output voltage as the feedback control variable is a non-minimum phase nonlinear system because its linear approximation has a right-half-plane (RHP) pole. The non– minimum phase system limits the application of control techniques such as input–output linearization (IOL). This paper presents an objective holographic feedbacks linearization control strategy (OHFLC) for DC power systems with constant power loads, bypassing non-minimum phase systems to stabilize the system. The analysis of the proposed method’s pole-zero points indicates that it is based on placing the pole-zero points of the system on their corresponding desired positions through feedback so as to achieve satisfactory dynamic and static performance of the control system. Finally, simulation and experimental verification demonstrate that the presented control approach provides superior dynamic response and robustness than the traditional proportional-integral (PI) control.

Biomechanical design prognosis of two extramedullary fixation devices for subtrochanteric femur fracture: a finite element study.

The design rationale of extramedullary fixation for femur fracture has remained a matter of debate in the orthopaedic community. The present work provides a comparative preclinical assessment between two standard fracture fixation techniques: dynamic hip screw (DHS) and proximal femoral locking plate (PFLP), by employing finite element (FE)-based in silico models. The study attempts to evaluate and compare the two implants on following biomechanical behaviours: (1) stress variation on the femur and implant, (2) axial displacement of the fixated femur constructs, (3) postoperative stress shielding and longer term external remodelling of the host bone. We hypothesised that, of the two implants, PFLP has better biomechanical characteristics when used for subtrochanteric femoral fracture (SFF) fixation considering long-term adaptation. A comminuted fracture, simulated as two-part fracture gap of 20mm, was created in the subtrochanteric region of a femur CAD model. Non-uniform physiological load cases were considered. External bone adaptation was modelled mathematically using stress analysis coupled with a growth model, in which strain energy density (SED) acted as feedback control variable. The computational results predicted lower stress shielding (by ~ 6%) and relatively less cortical thinning beneath the plate for PFLP as compared to DHS. DHS-fixated femur, on the other hand, predicted superior postoperative rigidity. Graphical Abstract FE-based comparative assessment between two extramedullary femur fixation devices-dynamic hip screw (DHS) and proximal femoral locking plate (PFLP).

Predator–prey interaction system with mutually interfering predator: role of feedback control

In this study, we investigate the global dynamics of non-autonomous and autonomous systems based on the Leslie–Gower type model using the Beddington–DeAngelis functional response (BDFR) with time-independent and time-dependent model parameters. Unpredictable disturbances are introduced in the forms of feedback control variables. BDFR explains the feeding rate of the predator as functions of both the predator and prey densities. The global stability of the unique positive equilibrium solution of the autonomous model is determined by defining an appropriate Lyapunov function. The condition obtained for the global stability of the interior equilibrium ensures that the global stability is free from control variables, which is also a significant issue in the ecological balance control procedure. The autonomous system exhibits complex dynamics via bifurcation scenarios, such as period doubling bifurcation. We prove the existence of a globally stable almost periodic solution of the associated non-autonomous model. The different coefficients of the system are taken as almost periodic functions by generalizing periodic assumptions. The permanence of the non-autonomous system is established by defining upper and lower averages of a function. Our results also explain how the important hypothesis in ecology known as the “intermediate disturbance hypothesis” applies in predator–prey interactions. We show that moderate feedback intensity can make both the ordinary differential equation system and partial differential equation system more robust. The results obtained provide new insights into the protection of populations, where moderate feedback intensity can promote the coexistence of species and adjusting the intensity of the feedback in appropriate regions can control the population biomass while maintaining the stability of the system. Finally, the results obtained from extensive numerical simulations support the analytical results as well as the usefulness of the present study in terms of ecological balance and bio-control problems in agro-ecosystems.

Influence of feedback controls on the global stability of a stochastic predator-prey model with Holling type Ⅱ response and infinite delays

In this work a stochastic Holling-Ⅱ type predator-prey model with infinite delays and feedback controls is investigated. By constructing a Lyapunov function, together with stochastic analysis approach, we obtain that the stochastic controlled predator-prey model admits a unique global positive solution. We then utilize graphical method and stability theorem of stochastic differential equations to investigate the globally asymptotical stability of a unique positive equilibrium for the stochastic controlled predator-prey system. If the stochastic predator-prey system is globally stable, then we show that using suitable feedback controls can alter the position of the unique positive equilibrium and retain the stable property. If the predator-prey system is destabilized by large intensities of white noises, then by choosing the appropriate values of feedback control variables, we can make the system reach a new stable state. Some examples are presented to verify our main results.

Feedback control variables to restrain the Babesiosis disease

In this paper, we complete the study of the dynamics of a recognized continuous‐time model for the Babesiosis disease. The local and global asymptotic stability of the endemic state are established theoretically and experimentally. In addition, to restrain the disease in the original model when the endemic state exists, we propose and study the continuous model with feedback controls. The global stability of the boundary‐equilibrium point of this model is analyzed by means of rigorous mathematical methods. As an important consequence of this result, we propose a strategy to select feedback control variables in order to restrain the disease in the original model. This strategy allows us to make the disease vanish completely. In other words, the feedback controls are specially effective for restraining disease in the model. The validity of the established theoretical result is supported by a set of numerical simulations.

Global Attractivity and Extinction of a Discrete Competitive System with Infinite Delays and Single Feedback Control

A nonautonomous discrete two-species competition system with infinite delays and single feedback control is considered in this paper. Based on the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Then, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that, by choosing some suitable feedback control variable, one of two species will be driven to extinction.

Extinction for a discrete competition system with feedback controls

We consider a nonautonomous discrete competition system with nonlinear interinhibition terms and feedback controls. By constructing a suitable Lyapunov function, we obtain some criteria about the extinction of one of the two species and the corresponding feedback controls varieties. Our conclusions not only supplement but also improve some existing ones. Numerical simulations are used to illustrate our analytic analysis. We show that feedback control variables play an important role in the extinction property of the system.

Variable-Time-Domain Online Neighboring Optimal Trajectory Modification for Hypersonic Interceptors

The predicted impact point (PIP) of hypersonic interception changes continually; therefore the midcourse guidance law must have the ability of online trajectory optimization. In this paper, an online trajectory generation algorithm is designed based on neighboring optimal control (NOC) theory and improved indirect Radau pseudospectral method (IRPM). A trajectory optimization model is designed according to the features of operations in near space. Two-point boundary value problems (TPBVPs) are obtained based on NOC theory. The second-order linear form of transversality conditions is deduced backward to express the modifications of terminal states, costates, and flight time in terms of current state errors and terminal constraints modifications. By treating the current states and the optimal costates modifications as initial constraints and perturbations, the feedback control variables are obtained based on improved IRPM and nominal trajectory information. The simulation results show that when the changes of terminal constraints are not relatively large, this method can generate a modified trajectory effectively with high precision of terminal modifications. The design concept can provide a reference for the design of the online trajectory generation system of hypersonic vehicles.

Global dynamics of autonomous and nonautonomous SI epidemic models with nonlinear incidence rate and feedback controls

This paper discusses autonomous and nonautonomous epidemic models with nonlinear incidence rate of saturated mass action and feedback controls. The global asymptotic stability of disease-free equilibrium and the endemic equilibrium of the autonomous system is established using suitable Lyapunov functional. It is shown that by choosing suitable values of feedback control variables, one can make the disease endemic or extinct as time evolves. Moreover, the effect of coefficient of inhibition on the persistence of disease is also discussed. We discuss the permanence, existence, uniqueness and asymptotic stability of an almost periodic solution of the model. The analytical results obtained in this paper are illustrated with the help of numerical examples.

Global stability of May cooperative system with feedback controls

In this paper, a May cooperative system with feedback controls is proposed and studied. The dynamic behaviors of the system are discussed by using the Lyapunov function method. If $b_{i}\neq0$ , $i=1,2$ , we show that feedback control variables have no influence on the global stability of the unique positive equilibrium of the system, which means that feedback control variables only change the position of the positive equilibrium and retain its global stability property. If $b_{i}= 0$ , $i=1,2$ , we can make the system which has a unique globally stable equilibrium or has unboundedly large solutions become globally stable. Some examples are given to illustrate the feasibility of the main results.

Global stability of disease-free equilibria in a two-group SI model with feedback control

In this letter, a two-group SI epidemic model is tackled with an eye to population mobility. Using the method of Lyapunov functions, global stability of the disease-free equilibria with respect to one group as well as both groups is investigated. We find that the disease outbreak can be effectively controlled through adjusting the feedback control variables. Examples are worked out to illustrate the theoretical results.

Influence of single feedback control variable on an autonomous Holling-II type cooperative system

An autonomous two-species Holling-II type cooperative system with single feedback control is considered in this paper. Firstly, by applying the comparison theorem of differential equation, sufficient conditions which ensure the permanence of the system are obtained. Secondly, by constructing some suitable Lyapunov function and using the average Inequality, some sufficient conditions for the globally asymptotical stability and extinction of the system are obtained. Our results show that by choosing suitable values of feedback control variables, stable species could become extinct, or still keep the property of globally stable.

Adaptive current compensation with nonlinear disturbance observer for single-sided linear induction motor considering dynamic eddy-effect

An adaptive current compensation control for a single-sided linear induction motor (SLIM) with nonlinear disturbance observer was developed. First, to maintain t-axis secondary component flux constant with consideration of the specially dynamic eddy-effect (DEE) of the SLIM, a instantaneously tracing compensation of m-axis current component was analyzed. Second, adaptive current compensation based on Taylor-discretization algorithm was proposed. Third, an effective kind of nonlinear disturbance observer (NDOB) was employed to estimate and compensate the undesired load vibrations, then the robustness of the control system could be guaranteed. Experimental verification of the feasibility of the proposed method for an SLIM control system was performed, and it showed that the proposed adaptive compensation scheme with NDOB could significantly promote speed dynamical response and minimize speed ripple under the conditions of external load coupled vibrations and unavoidable feedback control variables measured errors, i.e., current and speed.