Linear Feedback Control Method Research Articles

Control Design and Implementation of Autonomous Robotic Lawnmower

This paper presents the trajectory tracking control design and implementation of feedback linearization (FL) and robust feedback linearization (RFL), applicable to a robotic lawnmower with four mecanum driving wheels. The RFL control design additionally includes a robust control law. These two nonlinear control laws are developed to enable the controlled robotic lawnmower to accurately follow any specified trajectory. The simulation outcomes illustrate that the suggested control law based on RFL displays superior trajectory tracking accuracy and resilience compared to the FL control method in the case of a robotic lawnmower operating under demanding conditions. These conditions encompass environmental disturbances and uncertainties in modeling. The RFL control method also exhibits lower energy consumption compared to the FL control method. Finally, using the RFL controller derived from this study, the error in trajectory tracking in computer simulations and the actual mowing performance have demonstrated outstanding results.

Consensus Control of Leader–Follower Multi-Agent Systems with Unknown Parameters and Its Circuit Implementation

With the development and progress of Internet and data technology, the consensus control of multi-agent systems has been an important topic in nonlinear science. How to effectively achieve the consensus of leader–follower multi-agent systems at a low cost is a difficult problem. This paper analyzes the consensus control of complex financial systems. Firstly, the dynamic characteristics of the financial system are analyzed by the equilibrium points, bifurcation diagrams, and Lyapunov exponent spectra. The behavior of the financial system is discussed by different parameter values. Secondly, according to the Lyapunov stability theorem, the consensus of master–slave systems is proposed by linear feedback control, wherein the controllers are simple and low cost. And an adaptive control method for the consensus of master–slave systems is investigated based on financial systems with unknown parameters. In theory, the consensus of the leader–follower multi-agent systems is proved by the parameter identification laws and linear feedback control method. Finally, the effectiveness and reliability of the consensus of leader–follower multi-agent systems are verified through the experimental simulation results and circuit implementation.

Analyzing and Controlling chaos phenomena in fractional chaotic supply chain models

Supply Chain Management (SCM) is a critical business function that involves the planning, coordination, and control of the flow of goods, information, and finances as they move from the manufacturer to the wholesaler to the retailer and finally to the end customer. SCM is a holistic approach to managing the entire process of delivering products or services to consumers. In this study, we will enhance the findings as outlined in Anne et al. (2009). While certain attributes of these systems will have been investigated, numerous aspects of these systems will still require further scrutiny. This calls for additional research studies on these systems. This paper examines a Fractional-Order Supply Chain Management (FOSCM) model utilizing the Adomian Decomposition Method (ADM) and explores qualitative aspects through an approach that addresses existence and uniqueness. By using Arzelà–Ascoli's principle, this system proves that the Caputo FOSCM model has at least one solution. Furthermore, we investigate the dynamics of the system by using the Lyapunov Exponent (LE), Bifurcation Diagram (BD), Complexity Analysis (CA) and 0–1 test. Finally, we introduce the control for FOSCM model using the Linear Feedback Control (LFC) method. We verify the correctness of our analysis by using numerical simulations.

Control of an Energy-Harvesting System Using Sinha’s Theory for the Purpose of Energy Production

The goal of this study was to develop a linear feedback control method to increase the energy produced for a parametrically excited energy-harvesting system. The chosen control design uses state feedback based on the Lyapunov–Floquet transformation to direct the system dynamics toward a previously chosen trajectory. The methodology of this work was based on the studies of Sinha and Butcher. They developed stability and control analysis techniques based on Floquet theory and the approximation of the state transition matrix of systems that have periodic coefficients in time. It was observed that the stability and instability conditions of the system were obtained from the choice of physical parameters related to the parametric excitation force. When the control technique was applied to the system, it was found that the suggested control effectively directed the system’s trajectory in the direction of the predetermined trajectory. The application of control significantly increased the energy generation compared with the uncontrolled system, which was seen when comparing the energy generated by the uncontrolled system and the net energy generated by the controlled system.

Control and Stabilization of Chaotic System Based on Linear Feedback Control Method

In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.

Feedback linearization control method for hydraulic flight simulation turntable based on variable inertia model compensation

Feedback linearization control method for hydraulic flight simulation turntable based on variable inertia model compensation

A Model-Free Control Scheme for Rehabilitation Robots: Integrating Real-Time Observations with a Deep Neural Network for Enhanced Control and Reliability

Effective control of rehabilitation robots is of paramount importance and requires increased attention to achieve a fully reliable, automated system for practical applications. As the domain of robotic rehabilitation progresses rapidly, the imperative for precise and dependable control mechanisms grows. In this study, we present an innovative control scheme integrating state-of-the-art machine learning algorithms with traditional control techniques. Our approach offers enhanced adaptability to patient-specific needs while ensuring safety and effectiveness. We introduce a model-free feedback linearization control method underpinned by deep neural networks and online observation. While our controller is model-free, and system dynamics are learned during training phases, we employ an online observer to robustly estimate uncertainties that the systems may face in real-time, beyond their training. The proposed technique was tested through different simulations with varying initial conditions and step references, demonstrating the controller’s robustness and adaptability. These simulations, combined with Lyapunov’s stability verification, validate the efficacy of our proposed scheme in effectively controlling the system under diverse conditions.

Stabilizing unstable periodic orbit of unknown fractional-order systems via adaptive delayed feedback control

This article presents an adaptive nonlinear delayed feedback control scheme for stabilizing the unstable periodic orbit of unknown fractional-order chaotic systems. The proposed control framework uses the Lyapunov approach and sliding mode control technique to guarantee that the closed-loop system is asymptotically stable on a periodic trajectory sufficiently close to the unstable periodic orbit of the system. The proposed method has two significant advantages. First, it employs a direct adaptive control method, making it easy to implement this method on systems with unknown parameters. Second, the framework requires only the period of the unstable periodic orbit. The robustness of the closed-loop system against system uncertainties and external disturbances with unknown bounds is guaranteed. Simulations on fractional-order duffing and gyro systems are used to illustrate the effectiveness of the theoretical results. The simulation results demonstrate that our approach outperforms the previously developed linear feedback control method for stabilizing unstable periodic orbits in fractional-order chaotic systems, particularly in reducing steady-state error and achieving faster convergence of tracking error.

An Objective Holographic Feedback Linearization Based on a Sliding Mode Control for a Buck Converter with a Constant Power Load

As a typical load, the constant power load (CPL) has negative impedance characteristics. The stability of the buck converter system with a mixed load of CPL and resistive load is affected by the size of the CPL. When the resistive load is larger than the CPL, the buck converter with the output voltage as an output function is a non-minimum phase nonlinear system, because its linear approximation has a right-half-plane pole. The non-minimum phase characteristic limits the application of many control techniques, but the objective holographic feedback linearization control (OHFLC) method is a good control strategy that can bypass the non-minimum phase system and make the system stable. However, the traditional OHFLC method, in designing the controller, generally uses a linear optimal quadratic design method to obtain a linear feedback control law. It requires a state quantity component with a one-order relative degree to the system. But it is not easy to find such a suitable state quantity with a one-order relative degree to the system. In this paper, an improved OHFLC method is proposed for Buck converters with a mixed loads of CPL and resistive loads, using the sliding mode control (SMC) theory to design the controller, so that the output state quantity components with different relative degrees to the system can be used in the holographic feedback linearization method. Finally, the simulation and experimental results also demonstrate that this method has the same, or even better, dynamic response performance and robustness than the traditional OHFLC method.

Hyperchaos, constraints and its stability control in a 6D hyperchaotic particle motion system

Firstly, a novel six-dimensional (6D) hyperchaotic particle motion system is formulated. The equilibrium points and their characteristics, Poincaré sections, Lyapunov exponents, bifurcations and multi-periodic windows are studied. Secondly, we present two nonholonomic constrained systems. In order to analyze the particle motion trajectories under constraints, the explicit equations for constrained systems are given. Based on Lyapunov exponents, Poincaré maps and bifurcations, we can see that the different hyperchaotic phenomena of the particle motion can be generated by introducing nonholonomic constraints. Finally, the stability control of the 6D hyperchaotic particle motion system is realized by separately using constraint control method and linear feedback control method. Numerical simulations of the dynamical behaviors of the six-dimensional hyperchaotic particle motion system are carried out in order to illustrate the complex phenomena of the systems and verify the analysis results.

A Multiobjective Feedback Linearization Control of a Cuk Converter

Cuk converter is one of the most common power electronic converters, but its controller design has always been a challenging problem due to its fourth-order nonlinear and nonminimum phase characteristics. In order to solve this problem, this paper proposes a multi-objective feedback linearization control method, which selecting the variables of interest to rebuild the output function to linearize the nonlinear system into a combination of a linear subsystem and a nonlinear subsystem. According to the structural characteristics of these two subsystems, the linear optimal control theory is adopted for the control design of the linear subsystem to make the original nonlinear system have a good output performance, while for the nonlinear subsystem, the coefficient of the output function is adjusted to ensure the stability of the original nonlinear system. The results of simulation and experiment show the feasibility and superiority of using the multi- objective feedback linearization control method to design the nonlinear control law of the Cuk converter.

Sub-synchronous Oscillation Control of the DFIG System with SVG Based on Feedback Linearization of RSC

To suppress the subsynchronous oscillation in the doubly-fed induction generator (DFIG) system with Static VAR Generator (SVG), a feedback linearization control (FLC) method for rotor-side converter (RSC) is proposed, and its oscillation effect under small disturbances is analyzed and verified. Firstly, a 22-order time-domain model of a DFIG system with SVG is established. Secondly, combined with the principle of feedback linearization, the corresponding control method is designed for RSC inner loop control. Thirdly, the effects of PI control and feedback linearization control FLC on the system stability are compared when different parameters change under small disturbance. The results show the effectiveness of the proposed controller.

Fuzzy Feedback Control for Electro-Hydraulic Actuators

Electro-hydraulic actuators (EHA) have recently played a significant role in modern industrial applications, especially in systems requiring extremely high precision. This can be explained by EHA’s ability to precisely control the position and force through advanced sensors and innovative control algorithms. One of the promising approaches to improve control accuracy for EHA systems is applying classical to modern control algorithms, in which the proportional–integral–derivative (PID) algorithm, fuzzy logic controller, and a hybrid of these methods are popular options. In this paper, we developed a novel version of the fuzzy control algorithm and linear feedback control method, namely fuzzy linear feedback control, to improve the control performance. To achieve the highest performance, we first designed a mathematical EHA model based on the Matlab/Simulink software packages thanks to the selected parameters, which are similar to a real EHA system. Then, we respectively applied PID, fuzzy PID (FPID), and fuzzy linear feedback control (FLFC) before comparing them to have a full view of the outstanding advantages of the proposed algorithm. The simulation results showed that the proposed FLFC algorithm is approximately 99% and 77% superior in performance to the PID and feedback control algorithms, respectively.

Q-learning based model-free input-output feedback linearization control method⋆

Input-output feedback linearization is a nonlinear control method that relies on a precise dynamical model. Combining Q-learning techniques, an input-output feedback linearization correction framework is presented to accomplish model-free feedback linearization of affine nonlinear systems in order to tackle the problem caused by the unknown dynamics model. This framework formulates a model reference tracking control problem that guides the input-output relationship of the nonlinear system into a linear relationship. Due to the two Lie derivative terms present in the feedback linearized controller, the controller is designed as a dual network structure. To overcome the issue of coupling in the dual-network controller, a model-free Q-learning method is presented to solve the unknown controller network weights. The proposed method is experimentally validated on a single-link flexible joint manipulator system, and the resultant linearized system exhibits dynamics similar to the desired linear system in a new tracking task, proving the effectiveness of the proposed method.

Bifurcation, geometric constraint, chaos, and its control in a railway wheelset system

In this paper, an improved railway wheelset system is presented. The dynamical behaviors of the system are investigated, including dissipativity and invariance of the system, stability of zero‐equilibrium point, and the bifurcation characteristics of railway wheelset system at zero equilibrium point. Furthermore, the chaotic behaviors of the motion of railway wheelset and the dynamical behaviors of the railway wheelset system under geometric constraint are studied. It shows that the railway wheelset system has complex dynamical phenomena owing to nonlinear factor and the railway wheelset system may have different complex dynamical behaviors with different nonlinear parameters. In addition, the motion of railway wheelset also has chaotic behaviors under geometric constraint. Finally, the chaos control of the railway wheelset system is achieved by using linear feedback control method. The numerical simulations are carried out in order to analyze the complex phenomena of the railway wheelset system.

A recursive inverse dynamics algorithm for robotic manipulators with elastic joints and its application to control

High-order inverse dynamics is important for the trajectory tracking control of the elastic-joint manipulators. Usually it is undesirable to establish third-order or fourth-order inverse dynamics through the symbolic Lagrangian method, because of its complicated customization and higher computational complexity, which is not suitable for real-time control for multi-joint [Formula: see text] manipulators. Based on the Subsystem of Newton-Euler formulation and the recently proposed elastic joint Newton-Euler algorithm (EJNEA), a novel recursive algorithm (Sub-EJNEA) is proposed in this paper. The Sub-EJNEA obtains a linear complexity [Formula: see text], and has a more compact form and clear physical meaning. Based on the Sub-EJNEA, a recursive control method is proposed, which can be seen as an enhancement of the feedback linearization (FL-E) control method. When facing with friction and external disturbances, a combined controller FL-E-RISE is proposed. Finally, to verify the correctness of the recursive algorithm and the effectiveness of the proposed control schemes, simulation results with the Baxter manipulator are presented.

Hyperchaotic Oscillation and Multistability in a Fourth Order Smooth Chua System with Implementation Using No Analog Multipliers

Abundant dynamical behaviors and succinct realization forms are of great significance for nonlinear circuits and systems. Hyperchaos represents more complex oscillation mode compared with chaos, while multistability means more complex essential features compared with robustness. And the coexistence of the two is rare but interesting. Based on the classic Chua model, a fourth order smooth Chua system is constructed through utilizing linear feedback control method in this article. The introduction of hyperbolic sine nonlinearity remarkably simplifies the physical realization form for the new system. The two interesting nonlinear phenomena of hyperchaotic oscillation and multistability are discovered by adjusting system parameters. Dynamic analyses including bifurcation diagrams and Lyapunov exponent spectra comprehensively reveal the evolution of oscillatory behaviors brought by the variation of system parameters, whereupon more attractors such as periodic attractors, chaotic attractors in different oscillation scales, coexisting quasi-periodic attractors, coexisting multiple attractors and coexisting periodic attractors are found. And the attractor morphologies of this system are rare and significantly different from those in the reported Chua circuits and systems. Hardware circuit experiments without using analog multipliers are performed from a four-layer printed circuit board, which efficiently verify the simulated dynamical behaviors within the acceptable deviation.

Nonlinearity compensation based robust tracking control of nonlinear nonminimum phase hypersonic flight vehicles

This paper introduces a nonlinearity compensation based robust tracking controller for hypersonic flight vehicles. The controller focuses on robust control design with respect to the nonminimum phase feature and system uncertainties for the control-oriented model. Firstly, following the principle of decomposing the complex control problem into two simpler problems, the original robust tracking problem for nonlinear nonminimum phase hypersonic flight vehicles is decomposed into a simpler robust tracking problem for a linear nonminimum phase system with disturbances and a stabilization problem for a nonlinear system without disturbances. After the problem decomposition, a proportional–integral tracking controller and a feedback linearization controller are designed for the linear system and the nonlinear system, respectively. Then, the addition of the two designed controllers gives the final controller. By compensating for the system nonlinearity using the secondary system and its controller, the proposed control method can satisfy the robust tracking control requirements for nonlinear nonminimum phase hypersonic flight vehicles. The simulation results show, compared with a feedback linearization control method and a composite neural learning control method, the proposed method has superior tracking accuracy and robustness against system uncertainties and external disturbances.

Synchronization of Incommensurate Fractional-Order Chaotic Systems Based on Linear Feedback Control

The dynamics and synchronization of fractional-order (FO) chaotic systems have received much attention in recent years. However, the research are focused mostly on FO commensurate systems. This paper addresses the synchronization of incommensurate FO (IFO) chaotic systems. By employing the comparison principle for FO systems with multi-order and the linear feedback control method, a sufficient condition for ensuring the synchronization of IFO chaotic systems is developed in terms of linear matrix inequalities (LMIs). Such synchronization condition relies just on the system parameters, and is easily verify and implemented. Two typical FO chaotic systems, named the IFO Genesio-Tesi system and Hopfied neural networks are selected to demonstrate the effectiveness and feasibility of the proposed method.

Burden of cytokines storm on prognosis of SARS-CoV-2 infection through immune response: dynamic analysis and optimal control with immunomodulatory therapy.

Immune responses have a crucial role to play against SARS-CoV-2 virus as the adaptive and innate immune systems of the human body help restoring the body to a healthy stage by annihilating this deadly viral infection. Cytokines also play a significant role in modulating a balance between innate and adaptive immune responses but excess of it can have a detrimental affect on critically ill patients. Therefore, this paper is a novel attempt to formulate a within-host mathematical model showing the impact of cytokines storm on healthy cells. The dynamics of the system is analysed which involves basic reproduction number, steady state solutions and global dynamics for disease-free point and endemic equilibrium using geometric approach. Further, an optimal control problem is discussed considering immunomodulatory therapy (targeting cytokines signaling) as control using linear feedback control method to increase the level of healthy cells, which provides vitality for our system. Through numerical simulations, analytic solutions are validated followed by the curve-fit for the cytokines using real data and an optimization algorithm for optimal fit. Finally, sensitivity analysis for the basic reproduction number and the rate of change of healthy cells using Latin Hypercube Sampling method (LHS) is performed. Our finding suggests that immunomodulatory therapy (tocilizumab) can act as a key component to control cytokines storm for critically ill patients to restore the body to a healthy state.