Optimal Cooperative Secondary Control for Islanded DC Microgrids via a Fully Actuated Approach

DC-DC converter-based multi-bus DC microgrids(MGs) in series have received much attention, where the conflict between voltage recovery and current balancing has been a hot topic. The lack of models that accurately portray the electrical characteristics of actual MGs while is controller design-friendly has kept the issue active. To this end, this paper establishes a large-signal model containing the comprehensive dynamical behavior of the DC MGs based on the theory of high-order fully actuated systems, and proposes distributed optimal control based on this. The proposed secondary control method can achieve the two goals of voltage recovery and current sharing for multi-bus DC MGs. Additionally, the simple structure of the proposed approach is similar to one based on droop control, which allows this control technique to be easily implemented in a variety of modern microgrids with different configurations. In contrast to existing studies, the process of controller design in this paper is closely tied to the actual dynamics of the MGs. It is a prominent feature that enables engineers to customize the performance metrics of the system. In addition, the analysis of the stability of the closed-loop DC microgrid system, as well as the optimality and consensus of current sharing are given. Finally, a scaled-down solar and battery-based microgrid prototype with maximum power point tracking controller is developed in the laboratory to experimentally test the efficacy of the proposed control method.

Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles

This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.

Multivariable Decoupling Control of Civil Turbofan Engines Based on Fully Actuated System Approach

Gas turbine engines must be operated by means of control,and how to achieve multivariable control decoupling with aero-engine control constraints is an open thorny issue attracting increasingly more attention.The paper considers the multivariable decoupling problems of aero-engines by using a compound controller,which originates from the fact that it is impossible to eliminate all the nonlinear dynamics of system to obtain desired constant linear closed-loop system by using full actuated control because of modeling errors and some physical constraints.Two controllers are involved in the compound controller.One is a fully actuated controller and the other is classical feedback controller.In order to use fully actuated control and maintain the accuracy of engine model,a full state scheduling linear parameter-varying(LPV)modeling method is proposed based on fuzzy neural network weights.For a general input matrix of the system,its generalized inverse is applied to design fully actuated controller to result in a pseudolinear system.Combined with a feedback controller and control limiter,the control synthesis is achieved.The simulation shows that the proposed method is possessed of a better decoupling and tracking effect compared with traditional control approach.

Attitude Control of Spherical Liquid-Filled Spacecraft Based on High-Order Fully Actuated System Approaches

The attitude of spherical liquid-filled spacecraft is controlled based on the high-order fully actuated system approaches.The rigid-fluid coupling dynamic equation can be established in terms of the Euler angles of the spacecraft and the angular velocities of the liquid fuel.According to the dynamic equation,three kinds of input selections are presented.In the case of one control input,the dynamic equation is transformed into the third-order or the second-order differential equations of the Euler angle by the high-order fully actuated system approaches.Then a control law is designed to track the target.The effectiveness of the control law is demonstrated by numerical simulations.

Adaptive Control for a Class of Nonlinear Time-Delay System Based on the Fully Actuated System Approaches

This paper focuses on the problem of adaptive control for a class of time-delay systems.First,the strict feedback nonlinear time-delay system is transformed into a fully actuated system by utilizing the fully actuated system theory.Then,the uncertain time-delay terms of the system are bounded by the product of the absolute value of the system state and the non-linear function with the unknown parameters.By following the high order fully actuated system approaches,a continuous adaptive controller is designed for the system.It is proved that the controller can render the system achieve asymptotically stability.Finally,two numerical examples are provided to illustrate the effectiveness of the theoretical results.

Fully Actuated System Approach for 6DOF Spacecraft Control Based on Extended State Observer

This paper deals with the problem of position and attitude tracking control for a rigid spacecraft.A fully actuated system(FAS)model for the six degree-of-freedom(6DOF)spacecraft motion is derived first from the state-space model by variable elimination.Considering the uncertainties from external disturbance,unknown motion information,and uncertain inertia properties,an extended state observer(ESO)is designed to estimate the total disturbance.Then,a tracking controller based on FAS approach is designed,and this makes the closed-loop system a constant linear one with an arbitrarily assignable eigenstructure.The solution to the parameter matrices of the observer and controller is given subsequently.It is proved via the Lyapunov stability theory that the observer errors and tracking errors both converge into the neighborhood of the origin.Finally,numerical simulation demonstrates the effectiveness of the proposed controller.

Stabilization via Fully Actuated System Approach:A Case Study

In this note,a benchmark example system which is not stabilizable by a smooth state feedback controller is considered with the fully actuated system(FAS)approach.It is shown that a smooth controller exists which drives the trajectories starting from a large domain in the initial value space to the origin exponentially.Such a result brings about a generalization of Lyapunov asymptotical stability,which is termed as global exponential sub-stability.The region of attraction is allowed to be an unbounded open set of the initial values with closure containing the origin.This sub-stability result may be viewed to be superior to some local stability results in the Lyapunov sense because the region of attraction is much larger than any finite ball containing the origin and meanwhile the feasible trajectories are always driven to the origin exponentially.Based on this sub-stabilization result,globally asymptotically stabilizing controllers for the system can be provided in two general ways,one is through combination with existing globally stabilizing controllers,and the other is by using a pre-controller to first move an initial point which is not within the region of attraction into the region of attraction.

Prescribed Error Performance Control for Second-Order Fully Actuated Systems

In this paper,the prescribed error trajectory control is proposed for second-order fully actuated systems.At first,by taking advantage of the full-actuation property,an intermediate control law is designed such that the intermediate closed-loop system is in a very simple form.Then,by utilizing the initial conditions of system states and the prescribed error performance function,the intermediate control law is developed to force the tracking error of the system on the proposed sliding mode surface from the beginning.The overall control law is obtained by combining the aforementioned steps.It is revealed that under the designed control law,the tracking error of the closed-loop system converges to zero along the prescribed error trajectory.Finally,an example is provided to validate the effectiveness of the presented approach.

Fully Actuated System Approach for Linear Systems Control:A Frequency-Domain Solution

This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description(PMD).For a controllable first-order linear state-space system model,by using the right coprime factorization of its transfer function matrix,under the condition that the denominator matrix in the right coprime factorization is column reduced,it is equivalently transformed into a fully actuated PMD model,whose time-domain expression is just a high-order fully actuated(HOFA)system model.This method is a supplement to the previous one in the time-domain,and reveals a connection between the controllability of the first-order linear state-space system model and the fullactuation of its PMD model.Both continuous-time and discrete-time linear systems are considered.Some numerical examples are worked out to illustrate the effectiveness of the proposed approaches.

Adaptive Neural Network Control of Thermoacoustic Instability in Rijke Tube: A Fully Actuated System Approach

Thermoacoustic instability phenomena often encounter in gas turbine combustors,especially for the premixed combustor design,with many possible detrimental results.As a classical experiment,the Rijke tube is the simplest and the most effective illustration to study the thermoacoustic instability.This paper investigates the active control approach of the thermoacoustic instability in a horizontal Rijke tube.What’s more,the radial basis function(RBF)neural network is adopted to estimate the complex unknown continuous nonlinear heat release rate in the Rijke tube.Then,based on the proposed second-order fully actuated system model,the authors present an adaptive neural network controller to guarantee the flow velocity fluctuation and pressure fluctuation to converge to a small region of the origin.Finally,simulation results demonstrate the feasibility of the design method.

A Fully Actuated System Approach for Stabilization of Discrete-Time Multiple-Input Nonlinear Systems with Distinct Input Delays

In this paper,the problem of stabilization is considered for discrete-time multiple-input nonlinear systems with distinct input delays law based on the fully actuated system approach.In order to compensate the input delays,a prediction scheme is presented to predict future states based on the closed-loop linear system.Then,a stabilizing law is constructed for nonlinear delayed systems by replacing the future states in the control law for the corresponding delay-free systems with their prediction.Finally,numerical examples are given to verify the effectiveness of the proposed approach.

On the Role of Zeros in the Pole Assignment of Scalar High-Order Fully Actuated Linear Systems

It is well known that for a linear system in state space form,controllability is equivalent to arbitrary pole assignment by state feedback.This brief points out that for a scalar high-order fully actuated linear system,the pole assignment problem is solvable if and only if the desired pole set of the closed-loop system should not include the zero set of the open-loop system if the implementation issue of the controller is taken into account,that is,controllability cannot guarantee arbitrary pole assignment by state feedback.

Predictive Control of High-Order Fully Actuated Nonlinear Systems with Time-Varying Delays

This paper investigates the control problem of high-order fully actuated nonlinear systems with time-varying delays in the discrete-time domain.To make the compensation for time-varying delays concise,active and universal,a novel nonlinear predictive control method is proposed.The designed nonlinear predictive controller can achieve the same expected control performance as the nonlinear systems without delays.At the same time,the necessary and sufficient conditions for the stability of the closed-loop nonlinear predictive control systems are derived.Numerical examples show that the proposed nonlinear predictive controller design method can completely compensate for the time-varying delays of nonlinear systems.

Almost Disturbance Decoupling for HOFA Nonlinear Systems with Strict-Feedback Form

The article is devoted to the almost disturbance decoupling problem for high-order fully actuated(HOFA)nonlinear systems with strict-feedback form.Using the full-actuation feature of high-order fully actuated systems and Lyapunov stability theory,a state feedback control law and virtual control laws are designed.The unknown disturbances are handled by almost disturbance decoupling(ADD)method.Finally,the effectiveness of the control strategy is verified by stability analysis and simulation.

Brockett's Second Example:A FAS Approach Treatment

In this paper,several equivalent forms of the well-known Brockett's second example system are firstly presented.The stabilization of the system is then treated in the fully actuated system approach.A simple continuous time-invariant sub-stabilizing controller is designed,and the corresponding region of attraction is characterized.As a result,all trajectories of the system starting from the characterized region of attraction are driven exponentially to the origin.Since the region of attraction is very large,the designed sub-stabilizing controller can be directly useful in many practical situations.In cases where the initial values are indeed needed to be chosen out of the region of attraction,extremely simple pre-controllers can be designed,which drive the system trajectories into the designed region of attraction.A simulation of the designed control system is carried out to show the effect of the proposed approach.

An Optimal FASA Approach for UAV Trajectory Tracking Control

In this paper,a fully actuated system approach(FASA)-based control scheme is proposed for the trajectory tracking of a quadrotor unmanned aerial vehicle(UAV).System uncertainty,external disturbance and actuator constraint are all considered,which make the problem challenging.Inspired by the active disturbance rejection control(ADRC),tracking di®erentiator(TD)and extended state observer(ESO)are introduced for handling the uncertainties and generating the feedback signals.With the proposed feedback control law,the performance of the resulted closed loop system is related to its eigenstructure-eigenvalue and eigenvectors.Based on a type of control parametrization method,the parametrized eigenstructure of the closed loop system are optimized.A better performance is observed by comparative numerical simulation.

Brockett’s First Example: An FAS Approach Treatment

In this note,the well-known Brockett’s first example system is treated with the fully actuated system(FAS)approach.Firstly,it is shown that the system can be exponentially substabilized by a smooth controller in the sense that,except those starting from initial values on the z0-axis of the initial value space,all trajectories of the designed system as well as the control signals decay to zero exponentially.Secondly,global stabilization is realized through a way of enabling the trajectories starting from initial values on the z0-axis also to go to the origin.The idea is to firstly move an initial point on the z0-axis away from the axis using a pre-controller,and then to take over by the designed exponentially sub-stabilizing controller.