A novel nonlinear controller for enhancement of the transient dynamics performance of a three-wheeled vehicle during different conditions

In this study, a new controller to prevent the yaw instability and rollover of a three-wheeled vehicle has been proposed. This controller offers the most obvious opportunity for affecting the vehicle's lateral dynamics performance on the full range of nonlinearities during various operating boundaries. The active combined controller has been designed based on sliding mode control method using an active roll system and an active braking system to dominate the uncertainties of the nonlinear dynamic model. Firstly, to avoid rollover of the three-wheeled vehicle, the roll angle was considered as the control objective, and the anti-roll bar was employed as an actuator to produce the roll moment. Secondly, to increase the maneuverability and lateral dynamics enhancement, an active braking system was designed. In the control system, the yaw rate and the lateral velocity were regarded as the control variables to track their references. Moreover, to verify the performance of the mentioned combined controller, another control system has been designed using the linearization feedback control method. Then, computer simulation has been carried out with a 12 degrees of freedom dynamic model of the three-wheeled vehicle called the delta. Furthermore, a nonlinear tire model has been utilized to compute the longitudinal and the lateral forces. Next, the comparative simulation results confirmed the effectiveness of the robust control system to raise the vehicle's maneuverability and its rollover stability in comparison with the linearization feedback control method, especially when the three-wheeled vehicle is subjected to critical conditions.

Feedback control method to suppress stick-slip in drill-strings featuring delay and actuation constraints

In this work, performance of a modified-integral resonant controller with integral tracking is investigated numerically under the effects of actuator delay and actuation constraints. Actuation delay and constraints naturally limit controller performance, so much so that it can cause instabilities. A 2-DOF drill-string m with nonlinear bit–rock interactions is analysed. The aforementioned control scheme is implemented on this system and analysed under the effects of actuation delay and constraints and it is found to be highly effective at coping with these limitations. The scheme is then compared to sliding-mode control and shows to be superior in many regimes of operation. Lastly, the scheme is analysed in detail by varying its gains as well as varying system parameters, most notably that of actuation delay.

Complex Dynamics of Mixed Triopoly Game with Quantity and Price Competition

This article investigates the dynamics of a mixed triopoly game in which a state-owned public firm competes against two private firms. In this game, the public firm and private firms are considered to be boundedly rational and naive, respectively. Based on both quantity and price competition, the game’s equilibrium points are calculated, and then the local stability of boundary points and the Nash equilibrium points is analyzed. Numerical simulations are presented to display the dynamic behaviors including bifurcation diagrams, maximal Lyapunov exponent, and sensitive dependence on initial conditions. The chaotic behavior of the two models has been stabilized on the Nash equilibrium point by using the delay feedback control method. The thresholds under price and quantity competition are also compared.

Microcontroller Implementation, Chaos Control, Synchronization and Antisynchronization of Josephson Junction Model

The microcontroller implementation, chaos control, synchronization, and antisynchronization of the nonlinear resistive-capacitive-inductive shunted Josephson junction (NRCISJJ) model are reported in this paper. The dynamical behavior of the NRCISJJ model is performed using phase portraits, and time series. The numerical simulation results reveal that the NRCISJJ model exhibits different shapes of hidden chaotic attractors by varying the parameters. The existence of different shapes of hidden chaotic attractors is confirmed by microcontroller results obtained from the microcontroller implementation of the NRCISJJ model. It is theoretically demonstrated that the two designed single controllers can suppress the hidden chaotic attractors found in the NRCISJJ model. Finally, the synchronization and antisynchronization of unidirectional coupled NRCISJJ models are studied by using the feedback control method. Thanks to the Routh Hurwitz stability criterion, the controllers are designed in order to control chaos in JJ models and achieved synchronization and antisynchronization between coupled NRCISJJ models. Numerical simulations are shown to clarify and confirm the control, synchronization, and antisynchronization.

Design and remote collaboration control of asymmetric rigid-flexible hybrid-driven lower limb rehabilitation robot

A double-end lower limb rehabilitation robot is introduced in the paper, which can realize the rehabilitation training of the abduction and abduction, internal rotation and external rotation of human lower limb. The kinematics and dynamics of the robot are analyzed. Based on the motion trajectory planning of the lower limb rehabilitation robot, the motion state and dynamic state of the cable are analyzed. In order to realize the good remote cooperative control between the rehabilitation physician terminal and the patient rehabilitation terminal, the bilateral PD control method and the patient terminal force feedback control method based on the absolute stability theory are analyzed by using the dual-port network model. The simulation results show that the performance of the patient terminal force feedback control method is excellent when the force on the moving platform and the external interference force are changed suddenly. The mapping model of double-ended mechanism is established in the SimMechanics. The simulation results show that the mapping model of double-ended mechanism has a good position tracking ability and their workspaces can meet the requirements of trajectory mapping. The remote collaborative rehabilitation training experiment was done on the established experimental platform. The experimental result shows that the experiment system has a good tracking performance under the guidance of the patient terminal force feedback control method. The feasibility and operability of the remote rehabilitation cooperation technology are verified.

ON DYNAMIC BEHAVIOR OF A DISCRETE FRACTIONAL-ORDER NONLINEAR PREY–PREDATOR MODEL

This work is devoted to explore the dynamics of the proposed discrete fractional-order prey–predator model. The model is the generalization of the conventional discrete prey–predator model to its corresponding fractional-order counterpart. The fixed points of the proposed model are first found and their stability analyses are carried out. Then, the nonlinear dynamical behaviors of the model, including quasi-periodicity and chaotic behaviors, are investigated. The influences of fractional order and different parameters in the model are examined using several techniques such as Lyapunov exponents, bifurcation diagrams, phase portraits and [Formula: see text] complexity. The feedback control method is suggested to suppress the chaotic dynamics of the model and stabilize any selected unstable fixed point of the system.

Synchronization of Fractional-Order Chaotic Systems with Model Uncertainty and External Disturbance

This paper is concerned with complete synchronization of fractional-order chaotic systems with both model uncertainty and external disturbance. Firstly, we propose a new dynamic feedback control method for complete synchronization of fractional-order nominal systems (without both uncertainty and disturbance). Then, a new uncertainty and disturbance estimator (UDE)-based dynamic feedback control method for the fractional-order systems with both uncertainty and disturbance is presented, by which the synchronization problem of such fractional-order chaotic systems is realized. Finally, the fractional-order Lorenz system is used to demonstrate the practicability of the proposed results.

Partial Anti-Synchronization of the Fractional-Order Chaotic Systems through Dynamic Feedback Control

This paper investigates the partial anti-synchronization problem of fractional-order chaotic systems through the dynamic feedback control method. Firstly, a necessary and sufficient condition is proposed, by which the existence of the partial anti-synchronization problem is proved. Then, an algorithm is given and used to obtain all solutions of this problem. Moreover, the partial anti-synchronization problem of the fractional-order chaotic systems is realized through the dynamic feedback control method. It is noted that the designed controllers are single-input controllers. Finally, two illustrative examples with numerical simulations are used to verify the correctness and effectiveness of the proposed results.

Modeling and nonlinear energy-based anti-swing control of underactuated dual ship-mounted cranes systems

As the volume and the mass of the payload increases, it is often necessary to use two ship-mounted cranes to jointly transport huge payloads under marine environment. Compared with a single ship-mounted crane, dual ship-mounted cranes contain more state variables, geometric constraints and coupling dynamics, which bring more challenges in kinematic analysis and controller design for such complicated underactuated systems. In order to solve these problems, the dynamic model of the dual ship-mounted cranes systems are established based on Lagrange's method. Considering different practical requirements, two energy-based nonlinear controllers for dual ship-mounted cranes are developed, including a full state feedback control method and an output feedback control method. More preciously, during the control design process, the saturation constraints of the controllers have been fully considered. Meanwhile, the proposed controllers can achieve accurate positioning of the double-constrained derricks as well as effective elimination of payload swing. The stability of the equilibrium point of the closed-loop system is analyzed by using Lyapunov techniques and Lasalle's invariance principle. As far as we know, the modeling and the output feedback controller design of dual ship-mounted cranes are proposed for the first time in this paper. At the same time, the design and analysis process does not need to linearize the complex nonlinear dynamics equations, while the proposed output feedback control method is robust against the situations when the velocity signals are unknown/unavailable. Finally, a series of experiments are carried out to verify the effectiveness of the proposed nonlinear controllers.