Nonlinear Feedback Control Research Articles

Symmetric Nonlinear Feedback Control and Machine Learning for Sustainable Spherical Motor Operation

This paper presents a comprehensive evaluation of a new control technique for the sphere motor system, aimed at achieving accurate tracking, robust and dispersion of vibrations. Control methods include the determination of a nonlinear model and the application of feedback linearization, followed by the optimization of the proportional derivative (PD) coefficients through the Adaptive Neuro-Fuzzy Inference System. In addition, the system’s reaction to harsh environments is managed using Long Short-Term Memory. In order to gain a deeper understanding, symmetrical environmental disturbances and trajectories are introduced during the testing phase. The results demonstrate the superior performance of the control strategy, with reduced vibrations, faster recovery and confirmed tracking accuracy. In addition, the control method shows its adaptability and reliability, as evidenced by the significant reduction in CO2 emissions compared to conventional PD control methods. The use of symmetric trajectories and visualizations further emphasizes the behavior of the system under symmetric conditions, strengthening the effectiveness and applicability of the control strategy in real-world scenarios. Overall, this study presents a promising solution for converting complex systems under different conditions and making them potentially applicable in various industrial contexts.

Design of a new multi-wing chaotic system and its application in color image encryption

Due to its chaotic carrier function and pseudorandom nature, chaotic systems are frequently applied in the area of secure communication. To render chaotic signals more complicated, a novel multi-wing chaotic system is developed in this study. Initially, a double-wing attractor generated by a novel 3D Lorenz-like chaotic system that comprises two quadratic terms and four linear terms. By inserting a nonlinear feedback controller, the complex system gets transformed into a multi-wing chaotic system. It is noteworthy that the topological shape of the attractor and the number of equilibrium points can both be altered in the particular multi-wing chaotic system. Secondly, the dynamic features of the multi-wing chaotic system are discussed via employing the bifurcation diagram and the Lyapunov exponential spectrum. According to results from simulation, the system displays widely dispersed chaotic characteristics over a large range of parameters. In addition, the complexity analysis findings of chaotic sequences testify that the chaotic sequences have strong complexity. Therefore, the multi-wing chaotic system will have an excellent effect in image encryption. Finally, a scrambling-diffusion encryption scheme is built using the rich chaotic sequences discussed above. The scheme includes two times scrambling of pixel position and once transform of pixel value by the virtue of Galois field (GF). The proposed algorithm has superior efficiency and excellent security according to the results of the feasibility and security analysis. Moreover, the investigation of the multi-wing chaotic system property and its usage in image encryption additionally broadens the applicability of chaos systems and offers some standards for confidential communication.

Lyapunov stability of cable-driven manipulators with synthetic fibre cables regulated by non-linear full-state feedback controller

Robotic manipulators provide advantages in working environments regarding efficiency and safety, which is further increased in the case of elastic joint manipulators, whose mechanical compliance reduces the energy involved in collisions with workers. Cable-driven manipulators are elastic joint manipulators particularly suitable for industrial inspection thanks to the relocation of actuators outside hostile environments, increasing the manipulator payload-to-weight ratio. Recently, synthetic fibre cables are substituting steel cables due to their better-performing mechanical properties, but their visco-elastic behaviour must be compensated in the controller design. The key novelty of this work is using the four elements model, which includes the viscous behaviour, to design a non-linear full-state feedback controller for cable-driven manipulators. Furthermore, the mathematical proof of the closed-loop Lyapunov stability is provided.

Improved delay-dependent stability of superlinear hybrid stochastic systems with general time-varying delays

In the recent paper (Fei et al., 2019), the study of delay-dependent stability of hybrid stochastic differential delay equations (SDDEs) was generalized to superlinear ones (namely, do not satisfy the usual linear growth condition). However, the theory developed there could not be applied to hybrid SDDEs with non-differentiable time delays, or whose drift coefficients miss the key decomposition in (Fei et al., 2019) (see Assumption 1 below). This paper therefore is to deal with these two challenging problems so that the delay-dependent stability criteria derived in (Fei et al., 2019) could be improved. The decomposition scheme is modified in order to include more general hybrid SDDEs. The differentiability assumption on time-varying delays is replaced by a relatively weaker one. Also the Lyapunov functional used in this paper is modulated to adapt to these new changes. Finally, two interesting examples, an application to mosquito model, and design of nonlinear delay feedback control, respectively, are given to demonstrate the effectiveness of our new theory.

Nonlinear control design for walking assistance training robotic systems

AbstractIn this paper, the control problem for a novel walking assistance training robot is considered where the main objective is utilizing the robot to control the tilt angle and the position of a user. First, the novel walking assistance training robot together with a user is modeled as a nonlinear dynamical system in state space form with control input where the control input includes two elements standing for pulling forces on two straps which attach to the chest and back, respectively, of the user. Then, based on the nonlinear dynamical system and some results proposed in this paper, a feedback control system is developed, and a nonlinear state feedback control algorithm is designed where the control input includes two parts, namely, a dynamical part and a constant part. By doing this, it is ensured that the feedback control system is stable, and achieves the main objective under some limits for the control input. A simulation example is given to illustrate the effectiveness and performance of the proposed nonlinear state feedback control algorithm.

AlgDiff: an open source toolbox for the design, analysis and discretisation of algebraic differentiators

Abstract Algebraic differentiators have attracted much interest in recent years. Their simple implementation as classical finite impulse response digital filters and systematic tuning guidelines may help to solve challenging problems, including, but not limited to, nonlinear feedback control, model-free control, and fault diagnosis. This contribution introduces the open source toolbox AlgDiff for the design, analysis and discretisation of algebraic differentiators.

Hybrid Dynamical Modeling and Control of Permanent Magnet Synchronous Motors: Hardware-in-the-Loop Verification

The stabilization of a permanent magnet synchronous motor using digital controllers requires the design of both the feedback law and an appropriate sampling frequency. Moreover, the design approach must be robust against existing uncertainties, such as disturbances and parameter variations. In this paper, we develop a stabilizing state feedback nonlinear control scheme for the permanent magnet synchronous motor. Moreover, we consider the case where the feedback signal is transmitted over a digital platform, and we derive the stabilizing sampling frequency, such that the stability of the closed-loop system is maintained. We design the controller by emulation, where the closed-loop stability is first established in continuous time; we then take into account the effect of sampling. The feedback law consists of two parts: feedback linearization and robust linear quadratic regulator for the linearized mode. The robustness is achieved by augmenting the state space model, with additional states representing the tracking errors of the motor speed and the motor current. Then, to cope with sampling, we estimate the maximally allowable sampling interval to reduce the sampling frequency while preserving the closed-loop stability. The overall system is modeled as a hybrid dynamical system, which allows handling both the continuous-time and discrete-time dynamics. The effectiveness of the proposed technique is illustrated by simulation and verified experimentally using a hardware-in-the-loop setup. Upon implementing the proposed approach, the obtained sampling interval was around 91 ms, making it suitable for digital implementation setups.

Robust integral controller design based on composite nonlinear feedback in uncertain systems with constrained inputs and external disturbances

AbstractIn this article, to enhance the transient performances in constrained uncertain systems, a control technique based on linear matrix inequality (LMI) is characterized to the robust integral composite nonlinear feedback (CNF) controller design. To achieve this aim, considering the inputs limitations and the uncertainties, the regulation is transformed into a minimization subjected to several LMIs. Solving an optimization in real‐time, the gains of the controller are calculated. So, the regulation and the disturbance rejection are effectively handled employing the presented control law. Compared with the existing integral methodology, the provided simulations validate the applicability of the robust integral CNF control law in uncertain systems.

Feedback control for fluid mixing via advection

This work is concerned with nonlinear feedback control design for the problem of fluid mixing via advection. The overall dynamics is governed by the transport and Stokes equations in an open bounded and connected domain Ω⊂Rd, with d=2 or d=3. The feedback laws are constructed based on the ideas of instantaneous control as well as a direct approximation of the optimality system derived from an optimal open-loop control problem. It can be shown that under appropriate numerical discretization schemes, two approaches generate the same sub-optimal feedback law. On the other hand, different discretization schemes may result in feedback laws of different regularity, which determine different mixing results. The Sobolev norm of the dual space (H1(Ω))′ of H1(Ω) is used as the mix-norm to quantify mixing based on the known property of weak convergence. The major challenge is encountered in the analysis of the asymptotic behavior of the closed-loop systems due to the absence of diffusion in the transport equation together with its nonlinear coupling with the flow equations. To address these issues, we first establish the decay properties of the velocity, which in turn help obtain the estimates on scalar mixing and its long-time behavior. Finally, mixed continuous Galerkin (CG) and discontinuous Galerkin (DG) methods are employed to discretize the closed-loop system. Numerical experiments are conducted to demonstrate our ideas and compare the effectiveness of different feedback laws.

Composite nonlinear feedback control for cooperative output regulation of linear multi-agent systems by a distributed dynamic compensator

Composite nonlinear feedback control for cooperative output regulation of linear multi-agent systems by a distributed dynamic compensator

Optimization of wind energy extraction for variable speed wind turbines using fuzzy backstepping sliding mode control based on multi objective PSO

This study addresses the problem of designing a nonlinear feedback control strategy for horizontal axis variable speed wind turbines in the below-rated wind speed operating region (whether the wind turbine is offshore or onshore). The objective is to operate the wind turbines to maximum wind energy extraction while reducing the mechanical load. To overcome both issues, a robust nonlinear control strategy based on sliding mode control (SMC) is proposed which tries to seek for an improved performance. The proposed controller has been developed to compensate for negative consequences of external disturbances, measurement noises and unmodeled dynamics. This control strategy exploits a tracking controller that keeps an optimal value for the ratio between the rotor angular speed and the wind speed. For maximum wind energy extraction, the control algorithm employs the sliding mode state output feedback torque controller to provide robustness, combined with backstepping scheme to ensure better performance in the presence of matched and mismatched uncertainties. Next, a fuzzy logic system (FLS) approach is introduced to the backstepping sliding mode controller (BSMC) to achieve better mechanical loads prevention suffered by the transmission shaft by adjusting the parameters of the controller. Finally, multi-objective particle swarm optimization (MOPSO) algorithm is used to find the optimal values for the adjustable parameters of the proposed fuzzy BSMC (FBSMC). To validate the proposed control structure, FAST aeroelastic simulator is used. The obtained results illustrate that the presented control scheme has satisfactory performance.

Inverse cascade based on nonlinear Schrödinger equation analysis with nonlinear feedback control

This paper focuses on the wave inverse cascade instability analysis with self-regulating feedback control for a fixed external potential field and a highly localized finite-amplitude initial pulse. The wave inverse cascade instability analysis is carried out by solving the corresponding two-dimensional generalized nonlinear Schrödinger equation. The wave field firstly suffers from the modulation instability, followed by collapse into turbulence containing the shortest-wavelength modes in the system. This is followed by inverse cascade of the shortest wavelength modes back to the longer-wavelength ones, until a statistical stationary turbulent state is reached. It is found that the inverse cascade is limited to the shorter-wavelength modes with the wavenumber $\left |k\right |\geq 100$ . This shows that the viscous damping $p_i$ acts like a control switch to the inverse cascade, and the feedback control can also regulate the intensity of the inverse cascade mode.

General decay anti-synchronization and [formula omitted] anti-synchronization of coupled reaction-diffusion complex-valued memristive neural networks

This paper studies the general decay anti-synchronization (GDAS) and general decay H∞ anti-synchronization (GDHAS) problems for coupled reaction–diffusion complex-valued memristive neural networks (CRDCVMNNs) without and with time delays. First of all, the concept of GDHAS under the complex-valued case is firstly presented based on the definitions of ψ-type function and ψ-type stability. According to this concept, we further prove a novel lemma which will be used throughout this paper under a new assumption. This lemma is very crucial which gives a new sufficient condition for achieving GDAS of CNNs in complex field. Then, by using the derived lemma and designing a suitable nonlinear feedback controller, some criteria for CRDCVMNNs without and with time delays to realize GDAS and GDHAS are established. At last, two numerical examples are used to verify the effectiveness of the anti-synchronization results.

Global dynamic analysis of a nonlinear state-dependent feedback control SIR model with saturation incidence

Global dynamic analysis of a nonlinear state-dependent feedback control SIR model with saturation incidence

Decentralized robust control of building structures based on sliding mode theory

SummaryIn this paper, a decentralized control algorithm is proposed for actively controlling the response of the flexible tall building structures under earthquake excitations. In the proposed approach, tall building structure was divided into some substructures in the form of state equation. The interaction of the subsystems and external excitations is conducted as bounded generalized force acting on the subsystems. A decentralized control algorithm of tall building structures is established based on the sliding model control theory. The control structure is described based on unit vector control. The control law consists of two parts: a linear control law uL and a nonlinear law uN. The linear control is merely a linear state feedback controller, whereas the nonlinear feedback controller incorporates the discontinuous or continuous nonlinear elements of the control law. Using the advantage of match conditions of sliding mode theory and the bounded feature of generalized force, the overall stability of decentralized control is also investigated. The actuator arrangement and matching conditions are discussed. The effectiveness of the proposed method is demonstrated by the numerical simulation of the decentralized control of a 20‐story benchmark structure under seismic excitations.

Design of the roll and heel reduction controller on ship’s turning motion

When the ship turns, it will heel and exacerbate the roll triggered by the sea waves, ultimately impacting the safe navigation of the ship. A study was conducted on a design method for a roll and heel reduction controller based on nonlinear feedback to mitigate the ship’s roll and heel during turning motion. A mathematical model was established for a ship with four degrees of freedom. Subsequently, a systematic analysis was conducted on the hydrodynamic force, rudder force, fin force and wave disturbance force of the ship. The ship’s roll and heel motion are reduced by controlling the roll reduction force generated by the fin. The roll and heel reduction controller uses a nonlinear PID controller with parameters that vary with the feedback signal. This effectively enhances the dynamic response characteristics of the system. Simulations were performed to analyze the effect of different rudder angles and different fin angles on the performance of the ship’s turning motion. The nonlinear feedback technique is employed to decrease the output of the fin angle, minimize the mechanical wear of fin stabilizer and save energy without compromising the control performance. The study analyzed the effect of a nonlinear feedback based controller in reducing roll and heel during turning motions of a ship. Simulations were conducted and compared with the classical PID controller method. The results indicated that the nonlinear feedback controller had a better performance in reducing roll and heel, validating the effectiveness of the designed method.

Disturbance Rejection Speed Control Based on Linear Extended State Observer for Isokinetic Muscle Strength Training System

Isokinetic muscle strength training is a type of rehabilitation therapy that can effectively improve the motor dysfunction of limbs and enhance joint muscle strength. In active isokinetic training, how to plan the speed reasonably and improve the performance of speed control to fit individualized needs is the core problem of isokinetic muscle strength training equipment control. In this study, a control strategy for isokinetic muscle strength training equipment is proposed, which identifies the user&#x2019;s motion intention and performs speed planning according to the user&#x2019;s motion participation so that the equipment produces a dynamic damping effect. This ensures active interaction between the user and the equipment and meets the force-speed requirements of elbow joint muscle training. To handle the uncertain disturbance in the training process, a linear extended state observer is used to estimate the disturbance term, and a tracking differentiator and nonlinear error feedback control are used to improve the speed tracking performance. The experimental results show that the proposed control scheme realizes effective speed control in isokinetic muscle strength training. <i>Note to Practitioners</i>&#x2014;The bottleneck of isokinetic muscle strength training equipment control system lies in how to plan the speed according to the patient&#x2019;s movement intention reasonably, and how to improve the performance of speed control in the process of rehabilitation training. This paper designs a speed auto disturbance rejection control strategy for isokinetic muscle strength training system with external interference and model uncertainty in practical application. The experimental results show that the performance of the controller is better than the traditional PI controller, and it can realize isokinetic muscle training. This study provides a method for practitioners interested in developing control systems for isokinetic rehabilitation training equipment.

Statistical Investigation about the SDRE Optimality for Satellites with Nonlinearities

The Attitude Control System (ACS) of a Satellite can be designed with success by linear control theory if the satellite has slow angular motions. However, for fast maneuvers, the linearized models are not able to represent the effects of the nonlinear terms. One candidate technique to design the ACS of the satellite under fast maneuvers is the State-Dependent Riccati Equation (SDRE), which provides an effective algorithm for synthesizing nonlinear feedback control taking into account the nonlinearities. Nonetheless, much criticism has been leveled against the SDRE method since it does not assure global asymptotic stability (GAS), because there are situations in which global asymptotic stability cannot be achieved (e.g., systems with multiple equilibrium points). One way to study the GAS is by estimating the region of attraction (ROA) which in turn is fundamental to investigate the performance of the controller designed by the SDRE method The Brazilian National Institute for Space Research (INPE) is responsible to build a Remote-Sensing Satellites, called Amazonia-1. The ACS of the Amazonia-1 satellite must be stabilized in three axes so that the optical payload can point to the desired target. In this paper, one investigates the performance of the Amazonia-1 ACS using a statistical test (unpaired t-test) that compares the optimality inside the ROA controlled by LQR and SDRE. By several simulations running a full Monte Carlo perturbation satellite model one observes a significant difference between the optimality of the two controllers in favor of SDRE when nonlinearities are accounted for.

Laplace transform and nonlinear control design for quasi‐projective synchronization for Caputo inertial delayed neural networks

The quasi‐projective synchronization problems for Caputo inertial neural networks (INNs) with delays are analyzed in this article. The considered model is transformed into two subsystems by selecting a suitable variable substitution. To realize synchronization, a novel fractional differential inequality is established, and the new lemma is derived via Laplace transform. Applying the given lemmas and inequality techniques, the synchronization conditions are inferred through different nonlinear feedback controllers. From the derivation of the theorems, it can be seen that the designed controllers are more extensive and efficacious. Furthermore, the error bound is validly estimated, and the validity of obtained theorems is illustrated by the numerical simulations.

Chaos synchronization for a class of uncertain chaotic supply chain and its control by ANFIS

In this paper, modelling of a three-level chaotic supply chain network. This model has the uncertainty of the retailer in the manufacturer. An adaptive neural fuzzy method has been proposed to synchronize the two chaotic supply chain networks. To train adaptive neural fuzzy controller, first, a nonlinear feedback control method is designed. Then, using Lyapanov theory, it is proved that the nonlinear feedback controller can reduce the synchronization error to zero in a finite time. The simulation results show that the proposed neural fuzzy controller architecture well controls the synchronization of the two chaotic supply chain networks. In the other part of the simulation, a comparison is made between the performance of the nonlinear controller and the adaptive neural fuzzy. Also, in the simulation results, the controller signal is depicted. This signal indicates that the cost of implementation in the real world is not high and is easily implemented.