Linear Feedback Control Method Research Articles

Closed-Loop Error Learning Control for Uncertain Nonlinear Systems With Experimental Validation on a Mobile Robot

This paper develops a Closed-Loop Error Learning Control (CLELC) algorithm for feedback linearizable systems with experimental validation on a mobile robot. Traditional feedback and feedforward controllers are designed based on the nominal model by using Feedback Linearization Control (FLC) method. Then, an intelligent controller is designed based on sliding mode learning algorithm that utilizes closed-loop error dynamics to learn the system behavior. The controllers are working in parallel, and the intelligent controller can gradually replace the feedback controller from the control of the system. In addition to the stability of the sliding mode learning algorithm, the closed-loop stability of an $n$th order feedback linearizable system is proven. The simulation results demonstrate that CLELC algorithm can improve control performance (e.g., smaller rise time, settling time and overshoot) in the absence of uncertainties, and also provides robust control performance in the presence of uncertainties as compared to traditional FLC method. To test the efficiency and efficacy of CLELC algorithm, the trajectory tracking problem of a tracked mobile robot is studied in real-time. The experimental results demonstrate that CLELC algorithm ensures high-accurate trajectory tracking performance than traditional FLC method.

Integral Sliding Mode Control for Starting Speed Sensorless Controlled Induction Motor in the Rotating Condition

Starting in the rotating condition is an important technology for induction motor (IM) speed sensorless control. The key of this technology is that the initial speed of the IM in the rotating condition should be estimated quickly and accurately. In this article, an integral sliding mode control method based on the nonlinear model of the rotor back electromotive force is designed to start a speed sensorless controlled IM in the rotating condition. The stability is guaranteed by Lyapunov stability analysis, and the robustness to rotor time constant and disturbance are analyzed. Meanwhile, in comparison with the proposed control method, the existing input–output feedback linearization (IOFL) control method is introduced and the stability and robustness are also analyzed. Compared with the existing IOFL control method, the proposed control method can estimate the initial speed in the rotating condition without overshoot and has better dynamic performance and robustness. In addition, the proposed control method can be applied not only to the restart operation but also to the normal operation. Only a single control strategy is required from the restart operation to the normal operation. The proposed method is verified by simulation and experiments using a 7.5 kW IM.

Synchronisation control for a class of complex-valued fractional-order memristor-based delayed neural networks

In this paper, the problem of drive-response synchronisation of complex-valued fractional-order memristor-based delayed neural networks is discussed via linear feedback control method. By separating complex-valued system into two equivalent real-valued systems, and using the comparison theorem, algebraic criteria are given to ascertain the synchronisation of the considered system with single delay. Meanwhile, for the case of model with multiple delays, the corresponding sufficient conditions are also presented. Because complex-valued system can reduce to real-valued ones when the imaginary part is ignored, the proposed results of this paper generalise existing works on relevant real-valued system. Finally, the effectiveness of the obtained theoretical results is testified by two numerical examples.

A study on load position control and vibration attenuation in crane operation using sub-actuator

The main purpose of any crane system is to move a load to a specified place. Accurate load positioning in the presence of unpredictable external factors is an important issue when operating a crane. Attenuation of load vibration during crane operation is immensely critical in order to satisfy rigorous requirements for safety and efficiency. When a crane is installed and operated on a vessel at sea, work conditions become even more difficult and thus require more stringent attention to load positioning and attenuation of load vibration. At sea, this process is complicated due to factors such as waves and wind, making accurate crane operation nearly impossible. For these reasons, active heave compensation systems have been developed to suppress the effects of disturbances raised from the harsh sea environment including vessel motions. This paper explores the suppression method of unexpected vertical vibration of load. Unlike past research on the topic, this research includes rope dynamics in the control system design for suppressing load vibration. In addition, this research considers uncertain disturbances—vessel motions not controlled by any active force that result in undesirable heave motion of a crane. Load motion is indirectly estimated using a load cell because we do not yet have any useful tool to measure it directly. In the considered crane system, two winches were used, one for moving the load and the other for suppressing residual vibration. To evaluate the proposed control strategy and system performance, several control techniques were applied: proportional–integral–derivative control, sliding mode control, and feedback linearization control methods.

Nonlinear control design of piezoelectric actuators with micro positioning capability

Inherently, piezoelectric actuator is one of the devices equipped with the micrometer positioning capability and characterized by small size, fast response, high stiffness, and large blocking force. These advantages give piezoelectric actuator the possibility of being high-accuracy industrial machineries. However, factors of nonlinear hysteresis, modeling uncertainties, and environmental disturbances result in unacceptable positioning errors and greatly increase the control difficulties. In this paper, a hybrid nonlinear robust control design that integrates a feedback linearization control method and a robust compensator is proposed. It aims to eliminate above-mentioned impacts and tackle the micrometer (μm) positioning design of piezoelectric actuators. The feedback linearization controller is developed for converging of positioning errors exponentially. The robust compensator is used to mitigate the total impact of hysteresis, modeling uncertainties and environmental disturbances and carry out the fine tuning of positioning errors to zero. Simulation results and practical tests reveal that the controlled piezoelectric actuator reaches 1 μm positioning accuracy, and the proposed robust control law delivers promising positioning performance under impacts of hysteresis, modeling uncertainties and environmental disturbances.

Dynamic Analysis and Linear Feedback Control of a Three-Dimensional Energy Price System

Evolution of energy price presents new characteristics in the time of carbon emissions trading. This study sets up a new three-dimensional Energy Price chaotic system based on the interdependent and mutually restricted evolution relationship among carbon price, energy price, and economic growth during a given economic period. The dynamic behavior of the system is studied. All equilibrium points are unstable for the system under certain parameters. Lyapunov exponents spectrum and bifurcation diagram present the existence of chaos, and numerical simulation shows the chaotic behavior of the dissipative system. Then the linear feedback control method is used to control the system to the original unstable equilibrium point. Numerical simulations verify the correctness of the theoretical analysis.

Active vibration control of motorized spindle based on mixed /Kalman filter robust state feedback control

In its working process, a high-speed motorized spindle bearing-rotor system is affected by a variety of vibration excitations, which severely affect the machining precision and reliability. In view of the problems in the active vibration control of current smart-material-based bearing-rotor systems and based on the structural layout of a piezoelectric device and a controlled bearing-rotor system, a bearing was directly connected to a piezoelectric actuator via a sleeve, which improved the working efficiency of the piezoelectric stack actuator. Furthermore, to improve the robustness of the system’s vibration control performance under different external excitations (e.g., cutting force and mass unbalance), uncertainties in internal parameters (changes in bearing stiffness and stiffness nonlinearity of piezoelectric materials), process and measure noises, a mixed state feedback algorithm based on norm optimization and a Kalman filter observer with state disturbance estimation was established. The dynamic and robust performance of the proposed method was compared with that of the linear quadratic Gaussian optimal control methods and output feedback control method through both simulation and experiment by changing the piezoelectric stacks without changing the control program.

Robust Nonlinear Controller Design for Damping of Sub-Synchronous Control Interaction in DFIG-Based Wind Farms

A robust controller taking advantage of feedback linearization control (FLC) and sliding mode control (SMC) is proposed with an objective of mitigating the sub-synchronous control interaction (SSCI) in series-compensated doubly fed induction generator (DFIG)-based wind farms (WFs). FLC method is employed to obtain the reduced-order model of the studied system and, hence, smaller computation burden to controller design. Moreover, unlike linear control methods, FLC enables the controlled system to be independent of the pre-specified operations, which is suitable for highly nonlinear DFIG-based WFs. Considering that the FLC can be sensitive to parameter uncertainties, SMC is combined with the FLC to improve the robustness of the system. To evaluate the performance of the proposed feedback-linearized sliding mode controller (FLSMC) as compared to the conventional sub-synchronous resonance damping controller, the electromagnetic transient simulation and small-signal stability analysis are carried out. The designed FLSMC is observed to demonstrate the effectiveness in SSCI mitigation and robustness against the parameter perturbation at varied operating conditions. The experimental tests are performed to validate the veracity of the simulation results.

Adaptive Torque and Flux Control of Sensorless IPMSM Drive in the Stator Flux Field Oriented Reference Frame

In this paper, direct torque and flux control of interior permanent magnet synchronous motor has been described in the stator flux field-oriented reference frame based on adaptive input-output feedback linearization (AIOFL) control method. The proposed control method does not need to know the motor two-axis inductances, the rotor permanent magnetic flux linkages, and the rotor position. However, the knowledge of the stator resistance is mandatory and that is estimated by AIOFL method. In practice, the rotor speed is approximately estimated by using the derivation of the stator flux vector angle in the stator stationary reference frame. The experimental and simulation results presented in this paper show the effectiveness and capability of the proposed control approach.

Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two‐degree‐of‐freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.

Dynamics, Chaos Control, and Synchronization in a Fractional-Order Samardzija-Greller Population System with Order Lying in (0, 2)

This paper demonstrates dynamics, chaos control, and synchronization in Samardzija-Greller population model with fractional order between zero and two. The fractional-order case is shown to exhibit rich variety of nonlinear dynamics. Lyapunov exponents are calculated to confirm the existence of wide range of chaotic dynamics in this system. Chaos control in this model is achieved via a novel linear control technique with the fractional order lying in (1, 2). Moreover, a linear feedback control method is used to control the fractional-order model to its steady states when 0<α<2. In addition, the obtained results illustrate the role of fractional parameter on controlling chaos in this model. Furthermore, nonlinear feedback synchronization scheme is also employed to illustrate that the fractional parameter has a stabilizing role on the synchronization process in this system. The analytical results are confirmed by numerical simulations.

Proposed control for wing movement, type flat plate, for ornithopter autonomous robot

The dynamic study and wing control of an ornithopter autonomous robot in level flight was carried out in this work. A rigid flat plate attached to the bird’s body by a spherical joint was adopted as wing model, conferring three degrees of freedom for the system. To model the flight dynamics and wing motion, the hypothesis that the bird was flying at a constant velocity in an horizontal rectilinear trajectory was used. From the definition of the model to be studied, the equations related to kinematics and dynamics of the mechanism were determined. For the control, the feedback linearization control method was used. Based on the results obtained, it can be concluded that the proposed method is able to control the studied system efficiently. The responses of the control system indicate that partial compensation will provide a decrease in the use of computational resources without degrading the desired response. Modeling and all simulations were implemented in MATLAB and Simulink software.

Modeling and Analysis of Variable Frequency One-Cycle Control on High-Power Switched-Capacitor Converters

Switched-capacitor (SC) converter is a type of variable structure systems. SC converters are typically equipped with open-loop control or some linear feedback control methods. However, these approaches provide slow dynamic response speed, small operation region, and large voltage ripple. Some new nonlinear control methods have been proposed in the literature to overcome these barriers. However, such control methods are usually proposed for applications involving low-power SC converters due to the limitations of them. This paper presents a nonlinear constant on-time variable frequency one-cycle control (CVFOCC) strategy based on dynamic capacitor ampere-second balance transient calculation (CASBTC) modeling method and one-cycle control (OCC) technique for high-power SC converters. This method successfully addresses the regulation issue of high-power SC converters. A high-power 3X Two-switch Boosting Switched-Capacitor converter (TBSC) is employed as an example topology. Simulation and experimental results both demonstrate that CVFOCC method could significantly improve the dynamic response speed and achieve excellent line and load regulation for the high-power SC converter in wide operation range.

Controlling Hyperchaotic Finance System with Combining Passive and Feedback Controllers

In this paper, a novel control method that combines passive, linear feedback, and dislocated feedback control methods is proposed and applied to the control of the four-dimensional hyperchaotic finance system which has been introduced and controlled with the linear feedback and speed feedback control methods by Yu, Cai, and Li (2012). The stability of the hyperchaotic finance system at its equilibrium points is ensured on the basis of a Lyapunov function. Computer simulations are used for verifying all the theoretical analyses visually. In the simulations, the proposed control method is also compared with the speed feedback and linear feedback control methods to observe its effectiveness and the results are discussed. DOI: http://dx.doi.org/10.5755/j01.itc.47.1.16898

State Feedback Switching Control of an Underactuated Planar Manipulator with Partial Feedback Linearization

In this paper, position control problem of a two-degree-of-freedom underactuated manipulator is considered and a state feedback control structure with energy-based switching is proposed. The mechanism has two revolute joints that move the two links on horizontal plane. Difficulties in system control arise with the fact that the manipulator has less control input signals than system degrees of freedom, and has complex nonholonomic structure. Furthermore, in horizontal operational conditions, position control of the system is a challenging work since free joint is not affected by the gravity. The system has only one actuator at the shoulder joint and the elbow joint is completely free. Therefore, the system cannot be stabilized around any equilibrium point by a linear state feedback control method. In this study, a control system that utilizes two stabilizing state feedback controllers and an energy-based supervisory switching mechanism is proposed. Stabilizing controllers are obtained utilizing the partial feedback linearization method. Proposed control is tested by computer simulations. First the open-loop plant dynamic model is obtained by Euler-Lagrange formulation and state-space modeling approach. Then, a simulation model of the system in closed loop with proposed control scheme is developed using the dynamic model and control law. Simulation tests are performed with respect to three different initial conditions. Performance of the control system is observed and revealed via simulations.

Stabilization and synchronization of Bose–Einstein condensate systems by single input linear controllers

This paper investigates the control problems of the Bose–Einstein condensate (BEC) system. Firstly, a new linear feedback control method for the control problems of a class of chaotic systems in any dimension based on triangle system structure. Then, based on the obtained method, the stabilization, synchronization, and anti-synchronization of BEC system are investigated extensively, and the corresponding controllers are designed. It should be pointed out that the obtained controllers are single input linear controllers, which are simpler than the existing results. Finally, numerical simulations are given to show the effectiveness and validity of the proposed results.

Controlling roughening processes in the stochastic Kuramoto–Sivashinsky equation

We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strategy is then based on two steps: first, stabilize the zero solution of the deterministic part and, second, control the roughness of the stochastic linear equation. We consider both periodic controls and point actuated ones, observing in all cases that the second moment of the solution evolves in time according to a power-law until it saturates at the desired controlled value.

Fiscal Policy Design in Greece in the Aftermath of the Crisis: An Algorithmic Approach

We present a computational approach to the design of fiscal policy that is based on algorithmic, linear feedback control methods. In particular, in the context of a linear, deterministic macro-model, we develop an algorithmic procedure which allows us to design fiscal policy rules for government expenditures so that desired target-levels for GDP are exactly met (that is, complete tracking is achieved). In order to examine the effectiveness of our method we estimate the model for the Greek economy and run some counterfactual policy experiments. These experiments indicate that, for the Greek economy in the beginning of the crisis in early 2010, expansionary fiscal policy would have been able to stimulate growth and reduce the debt-to-GDP ratio.

Improved resettable integrator control for a bridgeless interleaved AC/DC converter

Plug-in hybrid electric vehicles (PHEVs) consist of a front-end boost rectifier, which incorporates a power factor correction (PFC) circuit for battery charging. Bridgeless interleaved (BLIL) PFC boost converter topology is proved as a standard PFC converter as it has high efficiency, reduced input current ripple, and reduced electromagnetic interference (EMI). This paper proposes a digital nonlinear control technique that employs a resettable integrator to shape the input current of the converter in phase with the input voltage to achieve high input power factor. This control approach rejects power source and load perturbations better than linear feedback control methods. This is accomplished by summing up the sensed input current of a BLIL converter with a fictitious current synthesized with the input voltage. In this work, a BLIL converter is analyzed for its input power factor improvement, voltage stress across the devices, and dynamic response under variable supply and load conditions using simulation. The hardware is tested for a 300 W BLIL boost converter to validate the simulated results. The performance of the proposed controller is compared with that of conventional average current mode control. The experiment and simulation results prove that the resettable integrator controller shows a better performance than the conventional controller.

A gradient descent control for output tracking of a class of non-minimum phase nonlinear systems

In this paper we present a new approach to design the input control to track the output of a non-minimum phase nonlinear system. Therefore, a cascade control scheme that combines input–output feedback linearization and gradient descent control method is proposed. Therein, input–outputfeedback linearization forms the inner loop that compensates the nonlinearities in the input–output behavior, and gradient descent control forms the outer loop that is used to stabilize the internal dynamics. Exponential stability of the cascade-control scheme is provided using singular perturbation theory. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed cascade control scheme.