Linear Feedback Control Method Research Articles

Bifurcation analysis and chaos control of the population model with harvest

In this article, we investigated the dynamic behavior of a discrete-time population model with the harvest. We give numerical simulation and chaos control by using the linear feedback control method.

Feedback Linearization and Maximum Torque per Ampere Control Methods of Cup Rotor Permanent-Magnet Doubly Fed Machine

This paper establishes the state-space model of the cup rotor permanent-magnet doubly fed machine in the synchronous reference frame. The feedback-linearization control method is used to realize the decoupling control of flux and torque. Then, the upper and lower load torque boundaries are solved. Furthermore, to minimize the stator current magnitude of the control machine under a certain torque, the maximum torque per ampere (MTPA) control is derived. Finally, simulation results demonstrate the good decoupling performance of the feedback-linearization control method and the correctness of the load torque boundaries. In addition, the effectiveness and robustness of the proposed control methods are also demonstrated.

SYNTHESIS OF FEEDBACK LINEARIZATION CONTROLLER WITH PARAMETERS OPTIMIZATION BASED ON BAT ALGORITHM FOR A MAGNETIC LEVITATION SYSTEM

In this paper, the method design controller based on the feedback linearization control (FLC) method with optimal parameter for time response thanks to BAT algorithm for magnetic levitation system (MLS). Feedback linearization controller based on equivalent transformations brings a nonlinear system into linear form, then uses the poles-placement method to find parameters for the linear tracking controller. The selected pole does not optimize the controller parameters when the system needs to satisfy a rapid response condition. Therefore, the authors use the BAT algorithm to find linear tracking controller parameters based on ITAE cost function. The controller with optimized parameters is verified through simulation and experiment results. The proposed controller efficiency is compared with the feedback linearization controller through the simulation results.

Adaptive Synchronization Control and Parameters Identification for Chaotic Fractional Neural Networks with Time-Varying Delays

In this paper, the adaptive synchronization control and synchronization-based parameters identification method for time-varying delayed fractional chaotic neural networks are proposed. Based on the adaptive control with suitable update law and linear feedback control, an analytical, rigorous, and simple adaptive control method is given, which can make two coupled fractional-order delayed neural networks achieve synchronization. In addition, the uncertain system parameters can also be identified along with the realization of synchronization. The speed of synchronization and parameter identification can be adjusted by selecting appropriate control parameters. Besides, the proposed method is very easy to accomplish in reality and has strong robustness against external disturbances. Finally, the numerical simulations are put into practice to illustrate the rationality and validity of theoretical analysis.

Disturbance Observer-Based Feedback Linearization Control for a Quadruple-Tank Liquid Level System

A novel input/output feedback linearization control method by utilizing nonlinear disturbance observer (NDOB) is proposed for a quadruple-tank liquid level (QTLL) system in this paper. Firstly, the mathematical model of QTLL system is established by using Bernoulli’s law and mass conservation. Secondly, in view of the nonlinear and coupling characteristics of the QTLL system, a input/output feedback linearization controller is designed. Then, a NDOB is proposed to estimate disturbances and applied to compensation control. Finally, simulation and experimental results show that the proposed strategy has better control performances than PID control and the disturbance observer-based sliding mode control (DOBSMC).

Active fault-tolerant control of a Schon̈flies parallel manipulator based on time delay estimation

Abstract In this paper, a new hybrid fault-tolerant control (FTC) strategy based on nonsingular fast integral-type terminal sliding mode (NFITSM) and time delay estimation (TDE) is proposed for a Schönflies parallel manipulator. In order to detect, isolate, and accommodate actuator faults, TDE is used as an online fault estimation algorithm. Stability analysis of the closed-loop system is performed using Lyapunov theory. The proposed controller performance is compared with conventional sliding mode and feedback linearization control methods. The obtained results reveal the superiority of the proposed FTC based on TDE and NFITSM.

Dynamics and control of a bio-inspired Stewart platform

Collision and strong impacts take place in mission of the on orbit capture of non-cooperative spacecraft. So, it is necessary to design a vibration isolation system with efficient vibration isolation performance. A Stewart vibration isolation platform based on the bio-inspired isolation system is proposed in this paper. The characteristics of the novel bio-inspired Stewart platform realizes the vibration isolation protection of the serving spacecraft during the capture mission. The dynamic model of the vibration isolation platform is established by Lagrange's equations. The fidelity of the established dynamic model is verified via a comparison of the theoretical simulation and the ADAMS simulation. Comparisons between the presently proposed vibration isolation platform and the traditional spring-mass-damper type Stewart vibration isolation platform demonstrates the advantages of the present platform. The effects of system parameters on the isolation performance of the present platform are thoroughly investigated. The feedback linearization control method is used to control the present platform which overcomes the drift motion that occurs in the passive isolation case. The results show that the novel bio-inspired Stewart platform has excellent vibration isolation performance, which provides a promising way for the vibration isolation of the non-orbit capture mission.

A nonlinear hybrid controller for swinging-up and stabilizing the rotary inverted pendulum

In this paper, we propose a new class nonlinear hybrid controller (NHC) for swinging-up and stabilizing the (under-actuated) rotary inverted pendulum system. First, the swing-up controller, which drives the pendulum up towards the desired upright position, is designed based on the feedback linearization and energy control methods. Then, the modified super-twisting sliding mode control is proposed based on the new sliding surface to stabilize both the fully-actuated (the rotary arm) and under-actuated (the pendulum) state variables. In the proposed NHC, around the upright position, the stabilization controller is applied, and in different circumstances aside from the upright position, the swing-up controller is used. We show that with the proposed NHC: (i) in the swing-up stage, the pendulum is able to reach the desired upright position; and (ii) in the stabilization stage, the closed-loop rotary inverted pendulum is asymptotically stable. We demonstrate the effectiveness of the proposed NHC through extensive experiments. In particular, (i) the faster swing-up under the similar control effort is obtained, compared with the existing fuzzy logic swing-up controller; (ii) the better stabilization control performance for the convergence of the angular positions of the rotary arm and pendulum is attained and the chattering is alleviated, compared with the existing sliding mode stabilization controllers; (iii) the better stabilization control accuracy with the faster convergence time and lower peak overshoot is accomplished, compared with the existing Fuzzy-LQR controller; and (iv) the good robustness against sudden external disturbances is achieved.

Trajectory robust control of autonomous quadcopters based on model decoupling and disturbance estimation

In this article, a systematic procedure is given for determining a robust motion control law for autonomous quadcopters, starting from an input–output linearizable model. In particular, the suggested technique can be considered as a robust feedback linearization (FL), where the nonlinear state-feedback terms, which contain the aerodynamic forces and moments and other unknown disturbances, are estimated online by means of extended state observers. Therefore, the control system is made robust against unmodelled dynamics and endogenous as well as exogenous disturbances. The desired closed-loop dynamics is obtained by means of pole assignment. To have a feasible control action, that is, the forces produced by the motors belong to an admissible set of forces, suitable reference signals are generated by means of differentiators supplied by the desired trajectory. The proposed control algorithm is tested by means of simulation experiments on a Raspberry-PI board by means of the hardware-in-the-loop method, showing the effectiveness of the proposed approach. Moreover, it is compared with the standard FL control method, where the above nonlinear terms are computed using nominal parameters and the aerodynamical disturbances are neglected. The comparison shows that the control algorithm based on the online estimation of the above nonlinear state-feedback terms gives better static and dynamic behaviour over the standard FL control method.

An Input–Output Feedback Linearization Control Method Synthesized by Artificial Neural Network for Grid-Tied Packed E-Cell Inverter

In this article, a trained artificial neural network (ANN) input-output feedback linearization (IOFL) control strategy is proposed for a grid-connected nine-level packed E-cell (PEC9) converter under various operating variations. For the first time, a second-order dynamic model in d-q reference frame is developed for PEC9 converter. This model enforces the converter to employ IOFL-based proportional-resonance compensators for accurately contributing to current tracking enhancement, mitigation at the current ripple, and consequently, the capacitors dc voltages ripple. As another contribution, the current tracking ability of the proposed controller is much more promoted by decoupling the d-q dynamic components. Indeed, the effect of each proposed control component is fortified through decoupling feedback coefficients. In addition, as the third contribution, ANN as the complementary controller adapts the proposed IOFL-based controller coefficients to improve efficiency and stability of the whole control loop system, including the PEC9 capacitor voltages in unstable operation of load, grid, and dc source as well as in the presence of parameters mismatch and disturbances. To support the aforementioned contributions with more details, the closed-loop description and the dynamic model of the proposed controller-based PEC9 converter are utilized to present several stability evaluation processes in both time and frequency domains. This assessment process is accurately executed to confirm the stable performance of PEC9 when the errors of the PEC9 converter currents are changed as well as the decoupling feedback coefficients are varied. Finally, comparative dSPACE setup-based experimental and simulation results are attained to further verify the validity of the proposed control strategy under various operating conditions.

Stabilization of a Class of Fractional Order Systems With Both Uncertainty and Disturbance

This paper investigates the stabilization problem of fractional order systems with both model uncertainty and external disturbance. By combining the linear feedback control method, the dynamic feedback control method, and the uncertainty and disturbance estimator (UDE)-based control method, respectively, two new UDE-based control methods are developed. Using these methods, the fractional order systems can be stabilized by three steps. In the first step, the linear feedback and dynamic feedback controllers are designed to stabilize the nominal fractional order systems. The second step is to design a UDE-based fractional order controller to estimate the model uncertainty and external disturbance. In the third step, the two controllers are combined into a new controller to realize the stabilization of those fractional order systems. Finally, a numerical example is given to verify the correctness and validity of the proposed methods.

Disturbance Observer and L2-Gain-Based State Error Feedback Linearization Control for the Quadruple-Tank Liquid-Level System

This paper proposes a fresh state error feedback linearization control method with disturbance observer (DOB) and L2 gain for a quadruple-tank liquid-level system. Firstly, in terms of the highly nonlinear and strong coupling characteristics of the quadruple-tank system, a state error feedback linearization technique is employed to design the controller to achieve liquid-level position control and tracking control. Secondly, DOB is purposed to estimate uncertain exogenous disturbances and applied to compensation control. Moreover, an L2-gain disturbance attenuation technology is designed to resolve one class of disturbance problem by uncertain parameter perturbation existing in the quadruple-tank liquid-level system. Finally, compared with the classical proportion integration differentiation (PID) and sliding mode control (SMC) methods, the extensive experimental results validate that the proposed strategy has good position control, tracking control, and disturbance rejection performances.

Fault-tolerant control based on adaptive super-twisting nonsingular integral-type terminal sliding mode for a delta parallel robot

External disturbances, internal uncertainties and actuator faults with an unknown range have detrimental effects on controller performance of industrial robots. In this paper, to deal with such challenges, a new fault-tolerant control (FTC) strategy using a combination of nonsingular integral-type terminal sliding mode (NITSM) and adaptive high-order super-twisting (AST) control is proposed for a delta-type parallel robot. To eliminate the chattering of sliding mode controller as a key ingredient of excessive energy consumption and convergence rate reduction, high-order algorithm is applied. Stability analysis of the closed-loop system is performed using Lyapunov theory. Moreover, to achieve optimal performance, controller parameters are obtained using harmony search algorithm (HSA) by minimizing an objective function consisting of integral time absolute error (ITAE) and control signal rate. The proposed controller performance is compared with conventional sliding mode and feedback linearization control methods. The obtained results reveal the superiority of the proposed AST-NITSM.

Stabilization of a Class of Complex Chaotic Systems by the Dynamic Feedback Control

The stabilization problem of the complex chaotic system is investigated in this paper. First, a systematic method is proposed, by which a given complex chaotic system can be transformed into its equivalent real chaotic system. Then, both simple and physical controller is designed for the corresponding real chaotic system by the dynamic feedback control method, thereby the controller for the original complex chaotic system is obtained. Especially, for some complex system, the controller is obtained by the linear feedback control method. Finally, two illustrative examples with numerical simulations are used to verify the validity and effectiveness of the theoretical results.

Linear Feedback Control of Chaotic Motion in Gear Transmission System

Considering the internal and external excitations such as backlash, time-varying mesh stiffness (TVMS), transmission error and friction force, a lumped mass model of the spur gear system is established. On this basis, the influences of the support stiffness on dynamic response including bifurcation diagrams, time response diagrams, amplitude-frequency spectrums, phase plane diagrams, Poincaré maps are examined by using numerical method. To avoid the system moving in the unstable region, a linear feedback control method (LFCM) in the gear system is realized. Numerical simulations show that the LFCM is effective and feasible, hence the gear system can be controlled from chaotic motion to stable periodic orbits by using the appropriate control parameter.

Synchronization of Butterfly Fractional Order Chaotic System

In this paper, we study the synchronization of a nonlinear fractional system, and analyze its time response and chaotic behaviors. We represent a solution for considered system by employing the Mittag-Leffler matrix function and Jacobian matrix. Thereafter, we prove synchronization of error system between drive-response systems using stability theory and linear feedback control methods. Finally, numerical simulations are presented to show the effectiveness of the theoretical results.

Application Methods of Linear Feedback Control on the Modified Lorenz 3D Chaotic System

In this paper we using a linear feedback control methods on the Lorenz modified 3D system. we used the dynamical analysis system to find critical points, eigenvalues, and for stability, the Jacobi matrix, to investigate some dynamical behaviors of the system to find stability regions of the system in all methods used to suppress the originally unstable behavior of this system. The necessary and sufficient condition for suppression of unstable behavior for this system is getting positive feedback coefficient. Theoretical analysis and numerical simulation proved that the results obtained.

Hidden hyperchaotic attractors in a new 4D fractional order system and its synchronization.

The research of finding hidden attractors in nonlinear dynamical systems has attracted much consideration because of its practical and theoretical importance. A new fractional order four-dimensional system, which can exhibit some hidden hyperchaotic attractors, is proposed in this paper. The predictor-corrector method of the Adams-Bashforth-Moulton algorithm and the parameter switching algorithm are used to numerically study this system. It is interesting that three different kinds of hidden hyperchaotic attractors with two positive Lyapunov exponents are found, and the fractional order system can have a line of equilibria, no equilibrium point, or only one stable equilibrium point. Moreover, a self-excited attractor is also recognized with the change of its parameters. Finally, the synchronization behavior is studied by using a linear feedback control method.

Observer based adaptive robust Feedback-linearization control for VVER-1000 nuclear reactors with bounded axial power distribution based on the validated multipoint kinetics reactor model

In nuclear reactor, spatial oscillations in neutron flux distribution resulting from xenon reactivity feedback are a matter of concern. If the oscillations in power distribution are not controlled, power density and rate of change of power at some locations in the reactor core may exceed their respective limits causing the nuclear power plant instability. Therefore, during the design stages of any Pressurized Water Nuclear Reactor (P.W.R), it is necessary to identify the existence of xenon oscillation and to design suitable control strategy for regulating the spatial power distribution. In each nuclear power plant, Load-following control is one of the most important techniques for nuclear reactor regulation. A novel nonlinear controller called observer-based adaptive robust feedback-linearization controller for VVER-1000 nuclear reactors is presented in this paper. This novel control strategy is then applied to the Axial power distribution control during load following operation in the VVER-1000 nuclear reactors.The reactor core is simulated based on the validated four nodes kinetics reactor model and three groups of delayed neutron precursor’s concentration based on the Skinner-Cohen model. Considering the limitations of the xenon concentrations and delayed neutrons precursor’s densities physical measurement, an adaptive sliding mode observer is designed to estimate their values and finally adaptive robust feedback-linearization based on the adaptive sliding mode observer and nodal kinetics reactor model is presented to AO control during load following operation for nuclear reactors. The stability analysis is given by means Lyapunov approach, thus the designed control system is guaranteed to be stable within a large range.Simulation results show that robust control and state estimation with adaptive robust feedback-linearization and adaptive Sliding mode methodologies can be achieved in nuclear plant systems with diverse applications including control and estimation in the presence of model uncertainties and external disturbances. One significant finding to emerge from this paper is that the Observer based Adaptive robust feedback-linearization control method provides a robust, high-performance and automatic control mechanism at all the power ranges of operation for P.W.R control system.

Nonlinear Autopilot Design for Endo- and Exoatmospheric Interceptor With Thrust Vector Control

This paper proposes an autopilot design for an interceptor with thrust vector control that operates in the endo- and exoatmospheric regions. The main objective of the proposed autopilot design is to ensure control performance in both atmospheric regions, without changing the control mechanism. In this paper, the characteristics of the aerodynamic forces in both atmospheric regions are first investigated to examine the issue of the conventional control mechanism at various altitudes. And then, a control mechanism, which can be applied to both atmospheric regions, is determined based on the analysis results. An autopilot design is then followed by utilizing the control mechanism and the feedback linearization control method. Accordingly, the proposed autopilot does not rely on changing the control mechanism depending on flight condition unlike the conventional approach, however it can adjust the control gains automatically according to the changes in flight operating conditions. In this paper, the robustness of the proposed autopilot is investigated through the tracking error analysis and the relative stability analysis in the presence of model uncertainties. The physical meaning of the proposed autopilot is also presented by comparing to the well-known three-loop control structure. Finally, numerical simulations are performed to show the performance of the proposed method.