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We propose new results on input‐to‐state stability (ISS) subject to time delays in the input for compact, invariant sets that contain the origin. First, using nonlinear small‐gain theory, we prove a Razumikhin‐type theorem that ensures ISS for sets in the context of functional differential equations with delayed disturbances. Next we demonstrate that this theorem can be used to ensure set ISS for nonlinear systems with input delays and disturbances. In comparison to the existing research on robustness of set ISS with respect to time delays at the input, our results are more general, retain the ISS gain, and do not impose constraints on time delayed states. The advantages of the method are illustrated through two case‐studies on set‐stability for classes of nonlinear oscillators of practical interest. [ABSTRACT FROM AUTHOR]

A multirotor unmanned aerial vehicle (UAV) slung load system (SLS) is a nonlinear dynamics with eight degrees of freedom and four inputs that can be used for load transportation. The suspended payload can be modelled as a two degree-of-freedom pendulum attached to the UAV. This paper presents a path-following control (PFC) for an SLS. The PFC renders motions along any smooth Jordan curve in $ {\mathbb R}^3 $ R 3 for payload position controlled-invariant. This property has practical benefits over traditional time-based trajectory tracking. Furthermore, the PFC prescribes UAV yaw and a desired payload speed profiles along the path. The PFC adopts dynamic extension and input-output state feedback linearisation. The closed-loop has a 1-dimensional zero-dynamics which is shown to be bounded. Hence, the PFC error dynamics is exponentially stable. Simulations are provided to validate the design. [ABSTRACT FROM AUTHOR]

A microreactor is a chemical reaction device that mixes liquids in a very narrow channel and continuously generates reactions. They are attracting attention as next-generation chemical reaction devices because of their ability to achieve small-scale and highly efficient reactions compared to the conventional badge method. However, the challenge is to design a control system that is tolerant of faults in some of the enormous number of sensors in order to achieve parallel production by numbering up. In a previous study, a simultaneous control system for two different temperatures was proposed in an experimental system that imitated the microreactor cooled by Peltier devices. In addition, a fault-tolerant control system for one area has also been proposed. However, the fault-tolerant control system could not be applied to the control system of two temperatures in the previous study. In this paper, we extend it to a two-input, two-output fault-tolerant control system. We also use a fault detection system that combines ChangeFinder, a time-series data analysis method, and One-Class SVM, an unsupervised learning method. Finally, the effectiveness of the proposed method is confirmed by experiments. [ABSTRACT FROM AUTHOR]

In recent years, vibration control utilizing smart materials has garnered considerable attention. In this paper, we aim to achieve vibration suppression of a plate structure with a tail-fin shape by employing piezoelectric actuators—one of the smart materials. The plate structure is rigorously modeled based on the Kirchhoff–Love plate theory, while the piezoelectric actuators are formulated in accordance with the Prandtl–Ishlinskii model. This research proposed a control system that addresses the interference effects arising during vibration control by dividing multiple piezoelectric elements into two groups and implementing MIMO control. The efficacy of the proposed control method was validated through simulations and experiments. [ABSTRACT FROM AUTHOR]

Wave energy holds significant promise as a renewable energy source due to the consistent and predictable nature of ocean waves. However, optimizing wave energy devices is essential for achieving competitive viability in the energy market. This paper presents the application of a nonlinear model predictive controller (MPC) to enhance the energy extraction of a heaving point absorber. The wave energy converter (WEC) model accounts for the nonlinear dynamics and static Froude–Krylov forces, which are essential in accurately representing the system's behavior. The nonlinear MPC is tested under irregular wave conditions within the power production region, where constraints on displacement and the power take-off (PTO) force are enforced to ensure the WEC's safety while maximizing energy absorption. A comparison is made with a linear MPC, which uses a linear approximation of the Froude–Krylov forces. The study comprehensively compares power performance and computational costs between the linear and nonlinear MPC approaches. Both MPC variants determine the optimal PTO force to maximize energy absorption, utilizing (1) a linear WEC model (LMPC) for state predictions and (2) a nonlinear model (NLMPC) incorporating exact Froude–Krylov forces. Additionally, the study analyzes four controller configurations, varying the MPC prediction horizon and re-optimization time. The results indicate that, in general, the NLMPC achieves higher energy absorption than the LMPC. The nonlinear model also better adheres to system constraints, with the linear model showing some displacement violations. This paper further discusses the computational load and power generation implications of adjusting the prediction horizon and re-optimization time parameters in the NLMPC. [ABSTRACT FROM AUTHOR]

We consider the problem of tracking arbitrary free nutating trajectories of the Lagrange top using linear feedback. The equations of motion of the top are linearised about the desired trajectories. Due to the inherent symmetries, this yields a system of linear equations with periodically varying coefficients governing the error dynamics. It is shown that the higher-order dynamics of the Lagrange top leads to nuances in the implementation of the control. Two different control strategies are implemented in the present work. These are applicable for impulsive and short-duration disturbances, respectively. The control effort is in the form of a body-fixed torque input about the symmetry axis and a vertical space-fixed force input. In both the proposed control strategies, the iterative application of the control effort over multiple periods is shown to stabilise the error. These strategies are shown to work for significantly large errors. [ABSTRACT FROM AUTHOR]

A methodology is presented for the design and implementation of robust controllers that optimise inter-sample performance for a broad range of nonlinear systems operated within a sampled-data environment. The methodology applies to nonlinear continuous-time systems described by state equations, and it allows for modelling uncertainties and constraints on maximal control effort. It is shown that there exist optimal robust state-feedback controllers that minimise inter-sample tracking errors for such systems, as long as an appropriate controllability requirement is met. A relatively simple design and implementation procedure for such controllers is described. [ABSTRACT FROM AUTHOR]

This work proposes a resource efficient robust control scheme for missile-target engagement scenarios subjected to external disturbances. The robustness is achieved by using an annular event-triggered artificial time-delayed control (ET-TDC) methodology with input saturation. The ET-TDC philosophy uses the TDC strategy through a dynamic predefined triggering mechanism which overcomes the requirement to update the control periodically for every sampling instant, unlike conventional TDC and other robust control schemes. Thus the proposed methodology can tackle uncertainties with minimal a-priori knowledge while significantly reducing the over-utilisation of system resources. In addition, the adopted event-triggered mechanism facilitates further conservation of energy which might be crucial for mid-to-long range engagement scenarios. The closed-loop stability is derived analytically and the simulation results illustrate the efficacy of the proposed guidance framework in comparison with other state-of-art robust control methodologies. [ABSTRACT FROM AUTHOR]

Autonomous vehicles that can reliably operate outside the stable handling limits would have access to a wider range of maneuvers in emergencies, improving overall safety. To that end, this paper presents a novel Nonlinear MPC approach for vehicle control with deeply saturated rear tires. Longitudinal slip management is elevated from the chassis control layer into the optimisation problem by using a coupled-slip tire model, and explicitly including wheelspeed dynamics. Terminal costs on sideslip stability help compensate for the finite horizon, while road bounds and static obstacles are encoded using slack constraints. Experiments on a racetrack with a modified Toyota GR Supra validate the controller's ability to smoothly transition from dynamic, non-equilibrium drifting to grip driving. Further experiments demonstrate robustness to significant longitudinal force and wheelspeed disturbances, and showcase the controller flexibly transitioning in and out of the sliding tire regime to balance slack constraints with tracking objectives. [ABSTRACT FROM AUTHOR]

In this research, we explore a finite horizon optimal stabilization and tracking control scheme for the dynamical model of a 6‐DOF Autonomous Underwater Vehicle (AUV). Dynamical equations of the AUV are represented in a Lie group (SE(3)$$ SE(3) $$) framework, encompassing both translational and rotational motions. Utilizing a left Lie group action on SE(3)$$ SE(3) $$, we define error function for velocities via a right transport map to effectively address optimal trajectory tracking. The optimal control objective is formulated as a trade‐off problem, aiming to minimize both errors and control effort simultaneously. Left action on SE(3)$$ SE(3) $$ yields the left trivialized Hamiltonian function from which the concomitant state and costate dynamical equations are derived using Pontryagin's Minimum Principle (PMP). Consequently, the resulting two‐point boundary value problem is solved to obtain optimal trajectories. We demonstrate the optimality of the resulting solution obtained from the derived control law. For ensuring boundedness in the presence of small disturbances, this study incorporates the effects of internal parametric uncertainties associated with added mass and inertia components, along with the influence of external disturbances induced by ocean currents. Through simulation validations, we confirm the alignment of our results with the theoretical developments, demonstrating that the proposed control law effectively mitigates both parametric uncertainties and ocean current disturbances. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the adaptive saturation prescribed performance control problem for air‐breathing hypersonic vehicles with parameter uncertainties and unknown external disturbances. First of all, different from the traditional performance function, a novel class of performance functions is presented without the initial state information, which does not require to reset parameters even if the initial velocity and altitude change. To ensure the successful design of the velocity controller and altitude controller, the constrained errors are transformed into the unconstrained errors by the projection technique. Secondly, the adaptive neural network and the sliding mode control techniques are combined to design the adaptive neural network sliding mode controllers, which guarantee that the velocity and altitude tracking errors can respectively approach the predetermined regions within the identical preset finite time. Finally, the effectiveness of the designed controllers is verified by an example with comparisons. [ABSTRACT FROM AUTHOR]

This article presents a trajectory‐tracking controller for multi‐rotor unmanned aerial vehicles (UAVs) in scenarios where only the desired position and heading are known without the higher‐order derivatives. The proposed solution modifies the state‐of‐the‐art geometric controller, effectively addressing challenges related to the non‐existence of the desired attitude and ensuring positive total thrust input for all time. We tackle the additional challenge of the non‐availability of the higher derivatives of the trajectory by introducing novel nonlinear filter structures. We formalize theoretically the effect of these filter structures on the system error dynamics. Subsequently, through a rigorous theoretical analysis, we demonstrate that the proposed controller leads to uniformly ultimately bounded system error dynamics. To demonstrate the controller's effectiveness and potential to enhance multi‐rotor performance and reliability in practical applications, we present a simulation study considering two examples with time‐varying trajectories. [ABSTRACT FROM AUTHOR]

In the past decade, there has been much interest in operating quadrotors in uncertain and cluttered environments due to their simplicity. Executing precise agile quadrotor flight maneuvers is an important open research problem for navigating in such environment. Collisions can occur if actuator constraints are not considered in the trajectory tracker design. This paper presents a cascade nonlinear constrained control approach (CNCCA) for trajectory tracking with explicit consideration of actuator constraints, where the output signal of the position controller is converted into the desired command of the attitude controller. The proposed position control loop is shown to be stable and bounded, satisfying the total thrust limits. The proposed attitude tracking control loop is designed as a saturated control law based on a modified geometric controller in SO(3) space. A proof of its stability is provided. The simulation results also show good tracking performance of the proposed approach. [ABSTRACT FROM AUTHOR]

During the trajectory tracking of robotic manipulators, many factors including dead zones, saturation, and uncertain dynamics, greatly increase the modeling and control difficulty. Aiming for this issue, a nonlinear active disturbance rejection control (NADRC)-based control strategy is proposed for robotic manipulators. In this controller, an extended state observer is introduced on basis of the dynamic model, to observe the extend state of model uncertainties and external disturbances. Then, in combination with the nonlinear feedback control structure, the robust trajectory tracking of robotic manipulators is achieved. Furthermore, to optimize the key parameters of the controller, an improved particle swarm optimization algorithm (IPSO) is designed using chaos theory, which improves the tracking accuracy of the proposed NDRC strategy effectively. Finally, using comparative studies, the effectiveness of the proposed control strategy is demonstrated by comparing with several commonly used controllers. [ABSTRACT FROM AUTHOR]

In this paper, a quick convergence adaptive structure is proposed for trajectory tracking of an articulated type robotic manipulator using the Hardware in the Loop (HIL) simulation technique. A novel Nonlinear Quick Convergence Adaptive Sliding Backstepping Control (QCASBC) algorithm is implemented on a C2000 real-time controller board. The performance of the proposed control algorithm is inspected concerning the sliding mode PID (SM-PID) control technique to estimate its correlation with the proposed algorithm. The experimental part of the HIL simulation tests has been carried out on a simulated model of a three-link serial robot manipulator. A dynamic model of the robotic manipulator has been developed using Matlab Simulink software and its performance is analyzed using the HIL technique via a C2000 real-time controller for tracking the desired trajectory. Results show that the speed of convergence while tracking the desired trajectory of the manipulator is better in the proposed algorithm. It is also estimated that the positional error of the QCASBC algorithm is superior to the SM-PID control algorithm. The observed average angle error is improved by 14% and the average response time error is improved by 11% by using the proposed QCASBC algorithm compared to the SM-PID approach. [ABSTRACT FROM AUTHOR]

The paper describes a novel, simple servo drive position controller, using solely the knowledge about the structure of the nonlinear model and the constraints met by individual components of the model. The desired behavior of the position and velocity signals is obtained by imposing a time-varying constraint on the signal aggregating information about the position and velocity tracking errors. The method allows you to determine the maximum control (servo drive current) necessary to achieve the control goal under the existing initial conditions and the selected reference trajectory. The control is constrained and consists in appropriate reaction when the trajectory approaches the barrier, the shape of which is responsible for the imposed properties of the transient and quasi-steady state tracking error. In addition to the derivation of the control, a discussion of its possible variants and basic properties is presented. Control with time-varying constraints has been introduced, which allows the control objectives to be met with limited conservatism of the imposed constraints. The influence of technical factors related to actual speed and position measurements was discussed and the operation of the real drive on a laboratory stand was presented. [ABSTRACT FROM AUTHOR]

This work proposes a novel method for the real-time identification and nonlinear control of a permanent-magnet synchronous motor (PMSM) based on a Physics-Informed Neural Network (PINN) and the exact feedback linearization approach. The proposed approach is presented in a direct-quadrature framework, where the quadrature current and the rotational speed are selected as outputs and the direct and quadrature voltages are selected as inputs. A nonlinear difference equation is selected to describe the physical dynamics of the PMSM, and a PINN is designed based on the aforementioned structure. A simplified training scheme is designed for the PINN based on a least-squares structure to facilitate online training in real time. A nonlinear controller based on exact feedback linearization is designed by considering the nonlinear model of the system identified based on the PINN. Therefore, the proposed approach involves identification and control in real time, where the PINN is trained online. In order to track the reference for the rotational speed, a nonlinear controller with integral action based on exact feedback linearization is designed based on a linear quadratic regulator. As a result, the proposed approach can be used to identify the system to be controlled in real time, and it is able to track any small change in the real model; in addition, it is robust to both external and internal disturbances, such as variations in torque load and resistance. The proposed approach is evaluated through simulation and using a real PMSM, and the results of reference tracking are evaluated under disturbances. The identification performance is evaluated by using a Taylor diagram under closed-loop and open-loop structures, where ARX and NARX structures are used for comparison. It is thereby verified that this novel proposed control approach involving a PINN-based model can adequately track the dynamics of a PMSM system, where the performance of the proposed nonlinear control is maintained even when using the identified model based on the PINN. [ABSTRACT FROM AUTHOR]

In order to improve the precision of earth pressure balance control and anti‐interference ability of shield sealing chamber, this paper proposes a nonlinear control strategy for the screw conveyor based on disturbance observer and back‐stepping method, so as to ensure the safe and efficient tunneling of the shield machine. According to the hydraulic flow dynamic balance principle of shield machine, the mechanism model of electro‐hydraulic screw conveyor system is established, and the system state space model is derived. The nonlinear controller of the screw conveyor is designed by using the inverse step method and the disturbance observer compensation characteristic, so that the system responds quickly and compensates for the flow disturbance and external force disturbance in real time. At last, the system stability is proven by using the Lyapunov function. The experimental results show that the method has high control accuracy with fast response and strong anti‐interference ability. [ABSTRACT FROM AUTHOR]

Control technology for wheeled mobile robots is one of the core focuses in the current field of robotics research. Within this domain, model-free adaptive control (MFAC) methods, with their advanced data-driven strategies, have garnered widespread attention. The unique characteristic of these methods is their ability to operate without relying on prior model information of the control system, which showcases their exceptional capability in ensuring closed-loop system stability. This paper extensively details three dynamic linearization techniques of MFAC: compact form dynamic linearization, partial form dynamic linearization and full form dynamic linearization. These techniques lay a solid theoretical foundation for MFAC. Subsequently, the article delves into some advanced MFAC schemes, such as dynamic event-triggered MFAC and iterative learning MFAC. These schemes further enhance the efficiency and intelligence level of control systems. In the concluding section, the paper briefly discusses the future development potential and possible research directions of MFAC, aiming to offer references and insights for future innovations in control technology for wheeled mobile robots. [ABSTRACT FROM AUTHOR]

This study reviews numerous control approaches utilized to address various issues encountered by unmanned aerial vehicles (UAVs). Specifically, focusing on the quadrotor system. Due to its versatility and compact size, quadrotors have gained popularity as UAVs in recent decades. Quadrotors face challenges such as ambient disturbances, impediments, non-parametric and parametric perturbations while performing tasks. Consequently, a robust and efficient control system is essential for such a system to ensure the stability and enhance their performance. It should be noted that, in this review, we have examined and analyzed the most recent highly cited papers selected from esteemed journals and magazines renowned for their exceptional quality and reputation.

Abstract A novel adaptive tracking controller for magnetic levitation systems (MLS) is developed. The controller is based on a special adaptive control scheme incorporating fuzzy model of electromagnetic acceleration enabling fast and accurate fuzzy inversion. The controller ensures accurate tracking of any smooth desired position signal, despite unknown MLS parameters. The closed-loop system stability, in the sense of uniform ultimate boundedness (UUB) of error trajectories, is proved using Lyapunov approach. The closed-loop system performance is investigated during numerical experiments. Finally the proposed controller is verified by successful implementation on a DSP board controlling a typical magnetic levitation ball system. Performed tests and experiments demonstrate that the proposed control technique is robust against discretization and unknown MLS model parameters, provides high tracking accuracy, is easily implementable, and simple to tune.

Abstract During the trajectory tracking of robotic manipulators, many factors including dead zones, saturation, and uncertain dynamics, greatly increase the modeling and control difficulty. Aiming for this issue, a nonlinear active disturbance rejection control (NADRC)-based control strategy is proposed for robotic manipulators. In this controller, an extended state observer is introduced on basis of the dynamic model, to observe the extend state of model uncertainties and external disturbances. Then, in combination with the nonlinear feedback control structure, the robust trajectory tracking of robotic manipulators is achieved. Furthermore, to optimize the key parameters of the controller, an improved particle swarm optimization algorithm (IPSO) is designed using chaos theory, which improves the tracking accuracy of the proposed NDRC strategy effectively. Finally, using comparative studies, the effectiveness of the proposed control strategy is demonstrated by comparing with several commonly used controllers.

In this paper, a quick convergence adaptive structure is proposed for trajectory tracking of an articulated type robotic manipulator using the Hardware in the Loop (HIL) simulation technique. A novel Nonlinear Quick Convergence Adaptive Sliding Backstepping Control (QCASBC) algorithm is implemented on a C2000 real-time controller board. The performance of the proposed control algorithm is inspected concerning the sliding mode PID (SM-PID) control technique to estimate its correlation with the proposed algorithm. The experimental part of the HIL simulation tests has been carried out on a simulated model of a three-link serial robot manipulator. A dynamic model of the robotic manipulator has been developed using Matlab Simulink software and its performance is analyzed using the HIL technique via a C2000 real-time controller for tracking the desired trajectory. Results show that the speed of convergence while tracking the desired trajectory of the manipulator is better in the proposed algorithm. It is also estimated that the positional error of the QCASBC algorithm is superior to the SM-PID control algorithm. The observed average angle error is improved by 14% and the average response time error is improved by 11% by using the proposed QCASBC algorithm compared to the SM-PID approach.

Mirror therapy is a standard technique of rehabilitation for recovering motor and vision abilities of stroke patients, especially in the case of asymmetric limb function. To enhance traditional mirror therapy, robotic mirror therapy (RMT) has been proposed over the past decade, allowing for assisted bimanual coordination of paretic (affected) and contralateral (healthy) limbs. However, state-of-the-art RMT platforms predominantly target mirrored motions of trajectories, largely limited to 2-D motions. In this paper, an RMT platform is proposed, which can facilitate the patient to practice virtual activities of daily living (ADL) and thus enhance their independence. Two similar (but mirrored) 3D virtual environments are created in which the patients operate robots with both their limbs to complete ADL (such as writing and eating) with the assistance of the therapist. The recovery level of the patient is continuously assessed by monitoring their ability to track assigned trajectories. The patient’s robots are programmed to assist the patient in following these trajectories based on this recovery level. In this paper, the framework to dynamically monitor recovery level and accordingly provide assistance is developed along with the nonlinear controller design to ensure position tracking, force control, and stability. Proof-of-concept studies are conducted with both 3D trajectory tracking and ADL. The results demonstrate the potential use of the proposed system to enhance the recovery of the patients.

This paper deals with the modelling and stabilization of a flexible clamped beam controlled with a piezoelectric actuator in the self-sensing configuration. We derive the model starting from general principles, using the general laws of piezoelectricity. The obtained model is composed by a PDE, describing the flexible deformations dynamics, interconnected with an ODE describing the electric charge dynamics. Firstly, we show that the derived linear model is well-posed and the origin is globally asymptotically stable when a voltage control law, containing the terms estimated in the self-sensing configuration, is applied. Secondly, we make the more realistic assumption of the presence of hysteresis in the electrical domain. Applying a passive control law, we show the well-posedness and the origin's global asymptotic stability of the nonlinear closed-loop system. [ABSTRACT FROM AUTHOR]

One of several system classes that are frequently encountered in nonlinear and chaos control theory and its applications is the strict feedback form. The dynamics of many nonlinear and chaotic systems can be transformed into the strict feedback form via a change of variables as well. In this paper, a new discrete-time adaptive nonlinear controller is examined for a class of discrete-time high-order nonlinear systems in strict-feedback form. The proposed controller structure consists of a discrete-time controller built on a Lyapunov function, including a positive semi-definite function, and an adaptation mechanism that estimates unknown time-invariant parameters. The contributions of the proposed discrete-time method are twofold. One is that the discrete-time strict-feedback nonlinear systems are re-evaluated by a transformation, which enables us to design a flexible discrete-time controller. An elegant adaptive nonlinear controller is constructed without the complicated design steps, which is one of the main drawbacks encountered in controller design for general strict-feedback nonlinear systems. Owing to the mentioned transformation, computational complexity associated with other examples in the literature is effectively tackled and reduced. Another is that conventional least squares estimation is employed, demonstrating that the closed-loop error dynamics converge to the origin in an uncertain discrete-time internal model. Simulation results on two discrete-time nonlinear systems and a chaotic system verify the contributions of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, an improved self-coupled PI control dual-loop control strategy is proposed for the vector control of permanent magnet synchronous electric speed control system, to improve the poor motor control effect caused by the dead zone of the inverter, the presence of harmonics in the motor magnetic field distribution, and the error in the sampling process of the current. In order to reduce the tracking error of the signal, an acceleration feed-forward method is adopted, and the self-coupled PI controller with an additional Levant differentiator is introduced into the speed loop of the permanent magnet synchronous motor to ensure the accurate derivation of the input signal containing noise to improve the robustness of the system. In addition, this strategy combines the proportional term of the autotuned PI control structure with the standard resonator to form a proportional resonant autotuned PI in the current loop, so that the permanent magnet synchronous motor can better compensate the current in the current loop control to achieve the effect of current harmonic suppression. Finally, the control mechanism of the servo system analyzed, and based on the mathematical model of the controlled object PMSM, the design method of the improved self-coupling PI control structure is given. The experimental results show that the proposed control strategy can reduce the impact of the motor's own parameter changes on the system performance and has a good current harmonic suppression in the low-speed domain, which verifies the effectiveness of the designed improved self-coupled PI controller.

Advanced nonlinear controllers are a desirable solution to rotorcraft flight control as they can solve the system high nonlinear dynamic behavior. However, conventional nonlinear controllers such as Nonlinear Dynamic Inversion (NDI) controller heavily rely on the availability of accurate model knowledge and this can be problematic for rotorcraft. Therefore, incremental control theory can solve the modelling errors sensitivity by relying on the information obtained from the sensors instead. The paper applied the Incremental Nonlinear Dynamic Inversion (INDI) controller to rotorcraft case. It will be demonstrated that, for rotorcraft, the incremental nonlinear controllers depend on the delays introduced in the controller by the rotor dynamics. To correct this behaviour, residualization and synchronization methods need to be applied accordingly in order to remove the effects of rotor flapping (disctilt) dynamics from the controller. These particularities of rotorcraft in dealing with advanced controllers shows that incremental nonlinear controllers can have relatively small stability robustness margin and careful controller design is needed in order to account properly for rotorcraft time delays and unmodelled dynamics.

In this paper, two different active control approaches are proposed for a cascaded interconnection of a boost converter and an input filter. The presence of an Input filter is necessary to connect the DC–DC converter to a DC microgrid through a DC link. This modification results in a challenging design of stabilizing controller in the presence of the input filter. For this reason, a continuous embedded Pulse Width Modulation (PWM) control approach based on the averaged dynamics of the system and duty-cycle manipulation of fixed-frequency PWM control block is proposed, and a nonlinear controller with a simple structure capable of transient response modification is developed. Then, as a secondary approach, the system is presented in the hybrid dynamical system framework, and hybrid control is designed in a time-triggered scheme. The hybrid dynamical model avoids any approximation or use of PWM block, hence control policy is applied via direct switching control resulting in a variable-frequency switching signal capable of controlling chattering frequency at steady-state. Stability analysis and performance investigation are studied for both proposed controllers regarding the required conditions, and control design procedures are extracted. Finally, a comprehensive numerical simulation is evaluated and results are discussed in full detail. [ABSTRACT FROM AUTHOR]

Three-wheeled agricultural robots possess the advantages of high flexibility, strong maneuverability, and low cost. They can adapt to various complex terrains and operational environments, making them highly valuable in the fields of crop planting, harvesting, irrigation, and more. However, the horizontal stability of the three-wheeled agricultural robot chassis is compromised when working in harsh terrain, significantly impacting the overall operational quality and safety. To address this issue, this study designed a leveling system based on active suspension and proposed a stepwise leveling method based on an adaptive dual-loop composite control strategy (ADLCCS-SLM). Firstly, in the overall control of the three-wheeled chassis, a stepwise leveling method (SLM) was introduced. This method allows for rapid leveling by incrementally adjusting one or two suspensions, effectively avoiding the complex interactions between suspension components encountered in traditional methods involving the simultaneous linkage of three suspensions. Next, in terms of suspension actuator control, an adaptive dual-loop composite control strategy (ADLCCS) was proposed. This strategy employs a dual-loop composite control both internally and externally and utilizes an improved adaptive genetic algorithm to adjust critical control parameters. This adaptation optimizes the chassis leveling performance across various road conditions. Finally, the effectiveness of the proposed ADLCCS-SLM was validated through simulation and experimental testing. The test results showed that the control effect of the proposed method was significant. Compared to the traditional multi-suspension linkage leveling method based on PID, the peak values of pitch angle and roll angle were reduced by 31.8% and 33.3%, respectively. [ABSTRACT FROM AUTHOR]

In this article, we study the leader‐following formation problem for high‐order nonlinear multi‐agent systems with an uncertain leader system over switching networks. We first divide the uncertain leader system into two types and then design adaptive distributed observers for them respectively. Then, based on our designed observers, we synthesize two adaptive distributed control laws respectively to solve our problem, forcing the errors between the states of the followers and that of the leader to the prescribed time‐varying desired formation vectors. Finally, our main result is illustrated by two examples. [ABSTRACT FROM AUTHOR]

A fault-tolerant control approach is proposed, for a pumping airborne wind energy system (AWES) comprising a tethered fixed-wing aircraft with integrated propellers for vertical take-off and landing (VTOL). First, the flight control design for the traction phase of the system, when the tethered aircraft has to fly in loops using the rudder, is presented. Then, the presence of the propellers, that are normally not used in the traction phase, is exploited to obtain a fault tolerant controller in case of rudder malfunctioning. The approach detects a possible discrete control surface fault and compensates for the loss in actuation by using the VTOL system. A sophisticated model of the system is used to analyse the performance of the proposed technique. The main finding is that the approach is able to handle abrupt rudder faults with high tolerance. [ABSTRACT FROM AUTHOR]

The large flow rate proportional poppet valve (PPV) finds widespread use in high‐power hydraulic systems. However, the indispensable dead‐zone nonlinearity that guarantees the safe shut‐off of the PPV will cause a tracking lag when a command goes outside the dead‐zone. The lag should be properly solved in a controller, which is a highlight of this study. Simultaneously, achieving high tracking precision in a PPV is necessary to meet the demands of advanced hydraulic systems. In this study, a practical nonlinear controller based on an integral separated disturbance observer is proposed to improve the performance of a PPV. In particular, the lag could be alleviated and the high tracking precision achieved simultaneously by enabling or disabling a disturbance observer in the proposed controller. A separation coefficient is proposed for the disturbance observer to detach the integral action from the controller and avert the deep input saturation of the pilot stage. Additionally, the command filtering technology is applied to the nonlinear controller to improve its interference resisting capacity in the industrial environment. The stability and effectiveness of the proposed controller are proved in theory and verified by experiments. [ABSTRACT FROM AUTHOR]

Learning linear and nonlinear dynamical systems from available data is a timely topic in scientific machine learning. Learning must be performed while enforcing the numerical stability of the learned model, the existing knowledge within an informed or augmented setting, or by taking into account the multiscale dynamics—for both linear and nonlinear dynamics. However, when the final objective of such a learned dynamical system is to be used for control purposes, learning transformed dynamics can be advantageous. Therefore, many alternatives exists, and the present paper focuses on two of them: the first based on the discovery and use of the so-called flat control and the second one based on the use of the Koopman theory. The main contributions when addressing the first is the discovery of the flat output transformation by using an original neural framework. Moreover, when using the Koopman theory, this paper proposes an original procedure for learning parametric dynamics in the latent space, which is of particular interest in control-based engineering applications. [ABSTRACT FROM AUTHOR]

This article addresses the bifurcation characteristics and vibration reduction of a 2 -DOF dynamical system simulating the nonlinear oscillation of an asymmetric rotor model subjected to simultaneous multiparametric and external excitations. To suppress the system's vibrations, two 1 / 2 -DOF active dampers are attached to the system in linear and cubic nonlinear forms via a magnetic coupling actuator. The closed-loop system model is derived as two differential equations with multi-control terms, including cubic, quantic, and septic, coupled nonlinearly to two first-order systems. Applying perturbation theory, the system model is solved, and the autonomous system describing the closed-loop slow-flow dynamics is obtained. Through numerical algorithms, the motion bifurcation is analyzed using various tools such as 2D and 3D bifurcation diagrams, two-parameter stability charts, basins of attraction, orbit plots, and time response profiles. The analytical investigations confirm that the uncontrolled model behaves like a hardening Duffing oscillator with multistability characteristics, displaying simultaneous mono-stable, bi-stable, tri-stable, or quadri-stable periodic oscillations depending on both the asymmetric nonlinearities and angular velocity. Subsequently, the influence of different control parameters is analyzed to determine the threshold between mono and multi-stability conditions. Finally, optimal control parameters are designed to eliminate multistability characteristics and achieve minimum and safe vibration levels. [ABSTRACT FROM AUTHOR]

This paper introduces a two-tier feedback control law for the path tracking of a mobile robot equipped with N on-axle trailers. Initially, through a recursive design process, the curvature-tracking challenge is converted into stabilizing the joint angles at predefined reference values. This design approach is straightforward and can be easily extended to configurations with multiple trailers. Using input-to-state stability analysis, we demonstrate the asymptotic stability of the closed-loop system, which is structured in cascade form. Furthermore, we reformulate the path-tracking problem as a curvature-planning challenge and propose an algorithm to determine the desired curvature for the tail trailer. The simulation results validate the effectiveness of this novel algorithm in truck-trailer systems. [ABSTRACT FROM AUTHOR]

This study investigates designing optimal controllers on the dynamics performance of active suspension systems. The study incorporates nonlinearities and actuator saturation in the mathematical model of the suspension system for more reasonable representation of the real system. To improve ride comfort and stability performance in the presence of road disturbances, this study proposes two control frameworks including the Proportional-Integral-Derivative (PID) controller and the State Feedback (SF) controller. The focus of the study is to overcome the limitations of existing approaches in handling the actuator saturation in the controller design. To attain a better performance of the two proposed controllers including the input control constraint, a Grey Wolf Optimization (GWO) has been introduced to improve the searching process for the optimal values of the controllers' adjustable parameters. The simulation results using MATLAB show that the proposed controllers exhibit a good performance in normal operation and in a robustness test involving system parameters' changes. In terms of improving the response of the system, the GWO-PID controller shows a better response than that of the GWO-SF controller. Based on the Integral Square Error (ISE) index, the ISE is reduced by 16.67% using the GWO-PID controller compared to the GWOSF controller. [ABSTRACT FROM AUTHOR]

The main objective of this research is to expand right coprime factorization based on operator theory in nonlinear systems. A novel method for right coprime factorization is proposed by introducing an operator that can deform the system's response into an arbitrary shape. This enables the design of control systems that are highly effective against noise. As an application, we use a pneumatic stage. The effectiveness of this method is verified through simulations and real-world experiments. [ABSTRACT FROM AUTHOR]

The active suspension systems offer substantial benefits in ride comfort, handling control over traditional passive systems. In this paper, the evaluation of various controllers including the proportional-integral-derivative (PID) controller and the state feedback (SF) controller on the dynamics performance of active suspension systems is presented. Unlike the majority of the previous studies, the nonlinearities and actuator saturation in the mathematical model of the suspension system have been considered for more reasonable representation of the real system. To attain a better performance of the two proposed controllers, a swarm bipolar algorithm (SBA) technique has been introduced to improve the searching process for the optimal values of the controllers' adjustable parameters. The simulation results using MATLAB show that the proposed controllers exhibit a good performance in normal operation and in a robustness test involving system parameters' changes. In terms of improving the response of the system, the SBA-PID controller shows a better response than that of the SBA-SF controller. [ABSTRACT FROM AUTHOR]

Effective nonlinear control of manipulators with dynamically coupled arms, like those with direct drives, is the subject of the paper. Model-based predictive control (MPC) algorithms with nonlinear state-space models and most recent disturbance attenuation technique are proposed. This technique makes controller design and online calculations simpler, avoiding necessity of dynamic modeling of disturbances or resorting to additional techniques like SMC. The core of the paper are computationally effective MPC-NPL (Nonlinear Prediction and Linearization) algorithms, where computations at every sample are divided into two parts: prediction of initial trajectories using nonlinear model, then optimization using simplified linearized model. For a comparison, a known CTC-PID algorithm, which is also model-based, is considered. It is applied in standard form and also proposed in more advanced CTC-PID2dof version. For all algorithms a comprehensive comparative simulation study is performed, for a direct drive manipulator under disturbances. Additional contribution of the paper is investigation of influence of sampling period and of computational delay time on performance of the algorithms, which is practically important when using model-based algorithms with fast sampling. [ABSTRACT FROM AUTHOR]

This article introduces a novel strategy for devising an optimal Static Synchronous Compensator (STATCOM) controller via Hamiltonian function method in mitigating the transient stability of a multimachine power system. The STATCOM, a second generation shunt type FACTS device, is popularly employed for power system control. To test the applicability of the Hamiltonian function approach, an IEEE Type WSCC 9-bus system is taken under study. An appropriate Hamiltonian functional has been framed using the parameters of the test system, which is applied to optimize the preferred performance index. The performance of the proposed nonlinear controller is judged against a regular state feedback based STATCOM controller. The parameters of this traditional controller are computed via dynamical Games of the Nash Equilibrium method. The proposed method is beneficial in terms of mathematical complexity as needed in estimating relative degree and coordinate transformation in the feedback linearization method. A detailed investigation of the results reveals that the proposed controller is effective and efficient to a greater degree than the traditional STATCOM controller in a multimachine system, even at some point in serve eventualities like earth fault scenarios. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability analysis of the static output‐feedback polynomial fuzzy‐model‐based (SOF PFMB) control systems through designing a novel membership grade integration (MGI) approach. The nonconvex problems of the SOF PFMB control systems are convexificated into the convex conditions by introducing block diagonal positive‐definite Lyapunov matrix and nonsingular transformation matrix. We proposed new approximate membership functions, that is, Lagrange membership functions (LMFs), which can be introduced into the stabilization process to relieve the conservativeness of stability results. The LMFs are general representations of piecewise‐linear membership functions, which makes the number of stability conditions not limited by the number of sample points. In a fixed subdomain, arbitrary sample points can be employed by the LMFs method and achieve higher approximation capability by increasing more sample points so that membership grades can be incorporated into the system analysis. Furthermore, a novel MGI approach, including the information of premise variables and LMFs, is proposed making the stability conditions more relaxed. Finally, two simulation examples show the merits of the developed techniques. [ABSTRACT FROM AUTHOR]

Incremental control strategies such as Incremental Nonlinear Dynamics Inversion (INDI) and Incremental Backstepping (IBKS) provide undeniable advantages for controlling Uncrewed Aerial Vehicles (UAVs) due to their reduced model dependency and accurate tracking capacities, which is of particular relevance for tail-sitters as these perform complex, hard to model manoeuvres when transitioning to and from aerodynamic flight. In this research article, a quaternion-based form of IBKS is originally deduced and applied to the stabilization of a tail-sitter in vertical flight, which is then implemented in a flight controller and validated in a Hardware-in-the-Loop simulation, which is also made for the INDI controller. Experimental validation with indoor flight tests of both INDI and IBKS controllers follows, evaluating their performance in stabilizing the tail-sitter prototype in vertical flight. Lastly, the tracking results obtained from the experimental trials are analysed, allowing an objective comparison to be drawn between these controllers, evaluating their respective advantages and limitations. From the successfully conducted flight tests, it was found that both incremental solutions are suited to control a tail-sitter in vertical flight, providing accurate tracking capabilities with smooth actuation, and only requiring the actuation model. Furthermore, it was found that the IBKS is significantly more computationally demanding than the INDI, although having a global proof of stability that is of interest in aircraft control. [ABSTRACT FROM AUTHOR]

Trajectory tracking control of input-constrained systems is an essential problem in many control applications, including robotics. In this paper, we propose a constrained tracking controller for input affine nonlinear systems with convex input constraints based on tracking control Lyapunov functions (TCLFs). To deal with general convex input constraints, we first solve a convex optimization problem that minimizes the time derivative of TCLFs subject to convex input constraints; we refer to its optimal solution as minimizing input. Then, the proposed trajectory tracking is constructed by using the minimizing input and an appropriate scaling function. We prove that the proposed controller locally achieves trajectory tracking and satisfies the given convex input constraints. Finally, we demonstrate the effectiveness of the proposed controller by numerical simulations of a wheeled mobile robot. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a new control approach to be applied to a variable rotor speed wind turbine at a low wind velocity zone. The aim is to reduce dynamic mechanical loads and optimize energy production by acting on the generator torque through a new hybrid adaptive controller. This combines two well-known nonlinear methods: nonlinear control based on Radial Basis Function Neural Networks used to estimate the nonlinear part of the wind turbine system and Integral Sliding Mode Control to tackle system uncertainties. Lyapunov’s approach has been applied to assess the stability of this new controller. Then, simulations were carried out using the Matlab/Simulink software package. The obtained results demonstrated the superior performance of the hybrid controller compared to each controller taken alone. [ABSTRACT FROM AUTHOR]

Nonlinear, imbalanced, and constant power loads pose significant technical and power quality challenges in both AC and DC microgrids. Hybrid AC/DC microgrids further compound these complexities. In response, this paper presents a novel hierarchical control scheme comprising primary and secondary layers for such microgrids. The proposed scheme introduces innovative cooperative voltage and frequency secondary control methods, complementing conventional droop-based primary controllers. This hierarchical structure aims to provide acceptable voltage and frequency regulations, as well as power sharing in both AC and DC sub-grids, mitigating issues arising from various loads. Specifically, the DC sub-grid maintains its stability in the presence of constant power loads, while the AC bus output voltages maintain sinusoidal waveforms. Finally, we conduct digital time-domain simulation studies on a test microgrid system using the MATLAB/Simulink environment to assess the performance of the proposed control strategy. We compare the results with previously reported methods. The results demonstrate that the proposed methods effectively share power with reduced overshoot and faster convergence toward desired values compared to conventional controllers. Simulation analyses validate the superiority and efficacy of the proposed control scheme.

IntroductionIsokinetic exercise can improve joint muscle strength and stability, making it suitable for early rehabilitation of stroke patients. However, traditional isokinetic equipment is bulky and costly, and cannot effectively avoid external environmental interference.MethodsThis paper designed a lightweight upper limb joint isokinetic rehabilitation training equipment, with a control system that includes a speed planning strategy and speed control with disturbance rejection. Based on the established human-machine kinematic closed-loop model between the equipment and the user, a dynamic evaluation method of torque at the joint level was proposed.ResultsTo validate the effectiveness of the equipment, experiments were conducted by manually applying random disturbances to the equipment operated at an isokinetic speed. The results showed that the root mean square error between the observed torque curve of the second-order linear extended state observer used in this paper and the actual disturbance curve was 0.52, and the maximum speed tracking error of the speed control algorithm was 1.27%. In fast and slow sinusoidal speed curve tracking experiments, the root mean square errors of the speed tracking results for this algorithm were 9.65 and 5.27, respectively, while the tracking errors for the PID speed control algorithm under the same environment were 19.94 and 12.11.DiscussionThe research results indicate that compared with traditional PID control method, the proposed control strategy demonstrates superior performance in achieving isokinetic control and suppressing external disturbances, thereby exhibiting significant potential in promoting upper limb rehabilitation among patients.

This article presents the complete design of a nonlinear control system for multiple stationary bikes connected to a mechanical energy conversion system equipped with squirrel cage induction generators (SIGs) linked to AC/DC converters. The primary objective of this study is to investigate the feasibility of powering multiple treadmills using the DC bus via DC/AC converters. The novelty of our approach lies in the integration of a new strategy of control system to achieve multiple control objectives within a gym microgrid environment, and an energy management algorithm to ensure the energy flow between intermittent generation and the considered, somewhat random, demand. The system is composed of several subsystems: i) stationary bikes connected to the DC bus via inverters acting as intermittent power sources; ii) a Li-ion battery-based energy storage system interfaced through a Buck-Boost converter; iii) electromechanical loads, including treadmills, powered by DC/AC converters, in addition to other DC loads. The main control objectives are as follows: a) each stationary bike extracts energy from the DC network by regulating the torque applied by the athlete, ensuring that the torque follows the reference torque; b) the treadmill’s speed must follow the reference generated based on the athlete’s condition; c) ensuring the protection of the energy storage system by monitoring its current and voltage; d) all mentioned objectives are achieved while maintaining the DC bus voltage at a reference value. To achieve these objectives, a nonlinear control approach based on Lyapunov theory is used to design the controllers. A formal analysis is conducted to assess the performance of the studied system. The system’s performance is demonstrated using the MATLAB/Simulink environment. Numerous simulations demonstrate that every control objective is achieved. Specifically, the system maintained the DC bus voltage at 500 V with a maximum deviation of 1 V, and the treadmill speed followed the reference within a margin of 0.1 m/s.