Linear Feedback Control Method Research Articles

Dynamical Behavior Analysis and Control of a Fractional-order Discretized Tumor Model

In this work, we constructed a new fractional-order dynamical model of tumor and apply Euler method to obtain the discrete system. Local stability of the fixed points of the discretized system is studied. Numerical simulations show the chaotic attractor and the richer dynamical behavior of the discretized system. Linear feedback control method is used to control chaos in the considered discretized system. Numerical simulations results show that the controller can control the chaos effectively.

Controlling hyperchaotic Rabinovich system with single state controllers: Comparison of linear feedback, sliding mode, and passive control methods

In this study, the control of hyperchaotic Rabinovich system is applied by using three different single state controllers, namely linear feedback, sliding mode, and passive control. Routh–Hurwitz criterions are used for constructing the sufficient conditions of the linear feedback controller. An appropriate switching surface is designed based on the sliding mode control theory. In order to ensure the global asymptotic stability of the system with the passive controller, a Lyapunov function is used. Simulation results are demonstrated not only to validate all the theoretical analyses but also to compare the effectiveness of proposed control methods. By adding the controllers to the hyperchaotic Rabinovich system, it asymptotically stabilizes towards its zero equilibrium point in the state space. Numerical simulations have also shown that the proposed single state sliding mode controller is more effective than linear feedback and passive controllers on the control of hyperchaotic Rabinovich system.

Research on the Low Voltage Ride-through Control Strategy based on State Feedback Linearization

Based on the analysis of on the dynamic mathematical model of double-fed wind turbines, exact non-linear state feedback linearization control method is adopted to design the control strategy of the LVRT (low voltage ride-through). Firstly, we select the output functions according to control target, and formulate the nonlinear system including input and output. Then, by using linearization the state feedback and using proper coordinate transforming, we convert this nonlinear system to the linear and controllable system. Finally, we finish the control strategy of the control system through the optimized linear control strategy. This control strategy only depend on the parameters of the wind turbines, and strengthen the robust of the parameters of control strategies.

Study on the Inherent Complex Features and Chaos Control of IS–LM Fractional-Order Systems

Based on the traditional IS–LM economic theory, which shows the relationship between interest rates and output in the goods and services market and the money market in macroeconomic. We established a four-dimensional IS–LM model involving four variables. With the Caputo fractional calculus theory, we improved it into a fractional order nonlinear model, analyzed the complexity and stability of the fractional order system. The existences conditions of attractors under different order conditions are compared, and obtain the orders when the system reaches a stable state. Have the detail analysis on the dynamic phenomena, such as the strange attractor, sensitivity to initial values through phase diagram and the power spectral. The order changes in two ways: orders changes synchronously or single order changes. The results show regardless of which the order situation is, the economic system will enter into multiple states, such as strong divergence, strange attractor and the convergence, finally, system will enter into the stable state under a certain order; parameter changes have similar effects on the economic system. Therefore, selecting an appropriate order is significant for an economic system, which guarantees a steady development. Furthermore, this paper construct the chaos control to IS–LM fractional-order macroeconomic model by means of linear feedback control method, by calculating and adjusting the feedback coefficient, we make the system return to the convergence state.

Chaos in PID Controlled Nonlinear Systems

Controlling nonlinear systems with linear feedback control methods can lead to chaotic behaviors. Order increase in system dynamics due to integral control and control parameter variations in PID controlled nonlinear systems are studied for possible chaos regions in the closed-loop system dynamics. The Lur’e form of the feedback systems are analyzed with Routh’s stability criterion and describing function analysis for chaos prediction. Several novel chaotic systems are generated from second-order nonlinear systems including the simplest continuous-time chaotic system. Analytical and numerical results are provided to verify the existence of the chaotic dynamics.

Experimental Validation of a Fuzzy Adaptive Voltage Controller for Three-Phase PWM Inverter of a Standalone DG Unit

This paper investigates a disturbance observer-based fuzzy adaptive voltage controller for three-phase pulse width modulation (PWM) inverter of a standalone distributed generation (DG) unit in the existence of system uncertainties. The proposed control law includes only a voltage control loop, which has advantages such as a simple control structure and a fast transient response due to the direct control of the output voltage. Next, a disturbance observer is presented to reduce the number of the sensors and improve the control performance. Besides, the proposed strategy is insensitive to any system uncertainties, because it does not require any accurate knowledge about system parameter and load current information. Experimental results on a prototype DG unit with a TMS320F28335 DSP are demonstrated to validate the superior performance of the proposed control scheme over the conventional proportional-derivative (PD) control method and feedback linearization control (FLC) method under sudden load disturbances, system uncertainties, and nonlinear load.

Robust Disturbance Observer-Based Feedback Linearization Control for a Research Reactor Considering a Power Change Rate Constraint

This paper presents a robust disturbance observer-based feedback linearization control method using a fuzzy-based power change rate limiting method for a research reactor. The proposed controller has been designed for a nonlinear model of the reactor. Compared to the conventional control methods, the proposed scheme shows better control performance as it provides effective compensation for the steady-state error, due to a specific type of unmodeled dynamics. To cope with system uncertainties such as parameter uncertainties, unmodeled dynamics, and even external disturbance, we propose a robust disturbance observer-based feedback linearization controller. Moreover, the fuzzy-based power change rate limiting method is proposed, which is practically required for safe operation to limit the power change rate within a pre-designed safety range. In addition, a motor control input is considered and obtained by using the inverse model for the power control system. We show by numerical simulation that the proposed control law guarantees asymptotic stability as well as improved performance even in the presence of disturbance.

Linear Feedback Synchronization Used in the Three-Dimensional Duffing System

It has been realized that synchronization using linear feedback control method is efficient compared to nonlinear feedback control method due to the less computational complexity and the synchronization error. For the problem of feedback synchronization of Duffing chaotic system, in the paper, we firstly established three-dimensional Duffing system by method of variable decomposition and, then, studied the synchronization of Duffing chaotic system and designed the control law based on linear feedback control and Lyapunov stability theory. It is proved theoretically that the two identical integer order chaotic systems are synchronized analytically and numerically.

Chaotic circuit of ion migration memristor and its application in the voice secure communication

A memristor is a nonlinear element of nanoscale size with memory function and when it works as the nonlinear part in a chaotic system, the physical size of the system will be greatly reduced, rich nonlinear curve will be produced, and at the same time, the complexity of the chaotic systems and the randomness of signals will be enhanced. So in this paper, a new chaotic system is designed based on an ion migration memristor. The complex dynamic characteristics of the memristive system are investigated by means of theoretical derivation, numerical simulation, Lyapunov exponent spectrum, power spectrum, and Poincaré map. In addition, the change of system dynamic behaviors with the different parameters are analyzed. Then, a SPICE-based analog circuit is presented. The SPICE simulation results are in conformity with the numerical analysis, and thus verify that the chaotic systems can produce chaos. The linear feedback control structure is simple, economic and easy to realize in engineering practice, so the linear feedback control method has a high application value. At present, most studies focus on memristors' applications in memory and analog neural networks, but little research work is for voice security transmission. Therefore, by using the method of linear feedback control of chaotic synchronization, this paper proves the effectiveness of this method by numerical simulation experiments. As a result, it can achieve secure communication of voice signals. Finally, we conclude that the linear synchronous control method based on memristive chaotic system when applied to the secure communications can achieve the purpose of covering a specific speech. In addition, this method is able to restore the specific speech signal without distortion, which is very meaningful for the promotion of applications of memristor.

Chaotic Analysis and Control of Longitudinal Flight Dynamics

AbstractAircraft are considered to be sub‐stable within the flight envelope. This paper presents a chaotic analysis and two kinds of corresponding control methods of aircraft longitudinal flight dynamics. First, the chaotic behavior of the open loop longitudinal flight system is confirmed by the Poincaré section and the Lyapunov exponent. Studies have found that the flight envelope can be divided into a stable area and a sub‐stable area. The probability of instability caused by chaos exists in the sub‐stable area. The definition of the chaotic boundary is also given. Second, based on the chaotic analysis results and considering three different combinations of aircraft mass and elevator deflection, a linear feedback control (LFC) method is implemented to stabilize the chaotic boundary and enlarge the stable area. Third, taking system uncertainties into consideration, an adaptive backstepping sliding mode control (AB‐SMC) method is applied to the trajectory tracking problem of aircraft longitudinal motion, which is based on classic SMC, backstepping and dynamic surface methods. The numerical simulations are given, which can demonstrate the applicability of the proposed control methods.

Combination of Two Nonlinear Techniques Applied to a 3-DOF Helicopter

A combination of two nonlinear control techniques, fractional order sliding mode and feedback linearization control methods, is applied to 3-DOF helicopter model. Increasing of the convergence rate is obtained by using proposed controller without increasing control effort. Because the proposed control law is robust against disturbance, so we only use the upper bound information of disturbance and estimation or measurement of the disturbance is not required. The performance of the proposed control scheme is compared with integer order sliding mode controller and results are justified by the simulation.

2B35 Quaternion-based adaptive attitude control for a winged rocket(The 12th International Conference on Motion and Vibration Control)

Reusable Launch Vehicles (RLVs) are expected to become important transportation systems in future space exploration. RLVs are vehicles which have the ability to be launched into space, carry a payload to orbit and finally landing back on earth without using any expendable rockets. Due to this reason, RLVs are capable to reduce rocket launch operation expenses for space exploration. However, RLVs travel from earth's surface to space in uncertain environments causing the values of the parameters for the RLVs dynamic equations to be inconsistent. Therefore, various researchers have proposed several adaptive control methods to counter this problem. Quaternion is often being used in attitude control system of space vehicles such as rockets and satellites because quaternion has no singular point when the pitch angle approaches ±90[deg], which is a problem for Euler Angles. In this paper, we propose a digital adaptive feedback linearization control method using Quaternion for controlling the attitude of a winged rocket, a type of RLV. The proposed control method is implemented into the control system of a propulsion engine model. The effectiveness of the control system is demonstrated through computer simulations under the condition that the rocket's pitch angle during lift-off is in singularity of Euler angles. Simulation results show that the winged rocket is able to be launched from a vertically upward launch phase, flying into ascending phase and subsequently making a transition into a gliding phase successfully. The simulation results demonstrated the effectiveness of the proposed method in controlling a winged rocket.

선박 자동접안을 위한 순수 횡 이동 모델링 및 제어기 설계

Crabbing motion is the pure sway motion of a ship without surge velocity. Thus, it can be applied to a berthing operation. Crabbing motion is induced by a peculiar operation method called the push-pull mode. The push-pull mode is induced by using a combination of the main propeller and side thruster. Two propellers generating the same amounts of thrust and rotating in opposite directions produce some yawing moment on a vessel but do not induce longitudinal motion. With the additional operation of side thrusters, the push-pull mode is used to induce a large amount of lateral force. In this paper, three-degree-of-freedom equations of motion such as for the surge, sway, and yaw are constructed for the crabbing motion. Based on these equations of motion, a feedback linearization control method is applied to auto-berthing control for a twin-screw ship with side thrusters. The controller can deal with the nonlinearity of a system, which is present in the berthing maneuver of a twin screw ship. A simulation of the auto-berthing of a ship is performed to validate the performance of the designed controller.

Synchronization of chaotic systems using feedback controller: An application to Diffie–Hellman key exchange protocol and ElGamal public key cryptosystem

Abstract In this paper, designing an appropriate linear and nonlinear feedback control, the two identical integer order chaotic systems are synchronized by analytically and numerically. It has been realizing that, synchronization using linear feedback control method is efficient than nonlinear feedback control method due to the less computational complexity and the synchronization error. ElGamal public key cryptosystem is described through the proposed Diffie–Hellman key exchange protocol based on the synchronized chaotic systems using linear feedback control and their security are analyzed. The numerical simulations are given to validate the correctness of the proposed synchronization of chaotic systems and the ElGamal cryptosystem.

Controlling Rucklidge chaotic system with a single controller using linear feedback and passive control methods

In this paper, the control of chaos with a single controller, which provides simplicity in implementation, is investigated in continuous time nonlinear Rucklidge system. For this purpose, a linear feedback controller and a passive controller are constructed and added to the Rucklidge chaotic system. Lyapunov function is used to realize that the controller ensures the global asymptotic stability of the system. Owing to the controller, Rucklidge chaotic system can be regulated to its equilibrium points. Numerical simulations of the proposed methods and local relay control method have been demonstrated, compared and discussed.

CHAOS MULTISCALE-SYNCHRONIZATION BETWEEN TWO DIFFERENT FRACTIONAL-ORDER HYPERCHAOTIC SYSTEMS BASED ON FEEDBACK CONTROL

In this paper, the chaos multiscale-synchronization between two different Fractional-order Hyperchaotic System (FOHCS)s have been investigated. The Lü-like and its FOHCS are also studied. The Lü-like FOHCS is controlled to be multiscale-synchronization with Liu FOHCS and new Lorenz FOHCS, respectively. The analytical conditions for the multiscale-synchronization of these pairs of different FOHCSs are derived by utilizing Laplace transform. Furthermore, multiscale-synchronization between two different FOHCSs is achieved by utilizing the different linear and nonlinear feedback control method in a short period and both remain in chaotic states. Numerical simulations are used to verify the theoretical analysis using different values of the fractional-order parameter and the different linear and nonlinear control functions.

역보행 제어 형태의 궤환 선형화를 이용한 양방향 플래툰 제어

This paper proposes a bidirectional platoon control law using a coupled distance error based on the backstepping-like feedback linearization control method for an interconnected mobile agent system with a string structure. Unlike the previous results where the single agent was controlled using the only own information without other agents, the proposed control law cannot show the only distance error convergence of each agent, but also the string stability of the whole system. Also, the control performances are improved by the proposed control law in spite of low performance of bidirectional control strategy in the previous results. The proposed bidirectional platoon control algorithm is based on the backstepping-like feedback linearization control method. The position errors between each agent and the preceding and the behind agents are coupled by weighted summation. By the proposed control law, the distance error of each agent can converge to zero while the string stability is guaranteed when the coupled errors can converge to zero. To this end, the back-stepping control method is employed. The pseudo velocity input is determined considering the kinematic relationship between agents and the string stability. Then, the actual dynamic control input is determined to make the actual velocity converge to the pseudo velocity input. The stability analysis and the simulation results of the proposed method are included in order to demonstrate the practical application of the proposed algorithm.

Pinning synchronization of complex network with non-derivative and derivative coupling

This paper investigates synchronization of a complex network with non-derivative and derivative coupling. For achieving the pinning synchronization, the corresponding controllers are designed and applied to only a small fraction of nodes. Both linear and adaptive feedback control methods are used to design controllers. Based on Lyapunov stability theory, several simple and useful criteria for pinning synchronization are derived. Finally, numerical simulations are given to verify the effectiveness of the derived results.

Dynamics and Feedback Control for a New Hyperchaotic System

In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verify the theoretical results. Keywords—Feedback control, Hopf bifurcation, hyperchaotic system, stability.

Linear Feedback Control Research on Hopf Bifurcation in Wind Power System

Hopf bifurcation frequently results in periodical oscillation instability in the nonlinear system. For Hopf bifurcation at equilibrium point in the wind power system, Hopf bifurcation point of the wind power system with static var compensator is calculated based on the continuation method. The analysis shows that the increase of reactive power will lead to Hopf bifurcation, static var compensation can delay Hopf bifurcation and improve voltage stability region via reactive power compensation, in order to eliminate Hopf bifurcation, a unified and simple linear feedback control method is adopted. The results indicate that the method put forward in the research is effective to eliminate Hopf bifurcation in the wind power system