A new robust fault-tolerant controller scheme integrating a main controller and a compensator for the self-repairing flight control system is discussed.The main controller is designed for high performance of the origi...A new robust fault-tolerant controller scheme integrating a main controller and a compensator for the self-repairing flight control system is discussed.The main controller is designed for high performance of the original faultless system.The compensating controller can be seen as a standalone loop added to the system to compensate the effects of fault guaranteeing the stability of the system.A design method is proposed using nonlinear dynamic inverse control as the main controller and nonlinear extended state observer-based compensator.The stability of the whole closed-loop system is analyzed.Feasibility and validity of the new controller is demonstrated with an aircraft simulation example.展开更多
Robust stability for a series of nonlinear systems is presented in this paper. Through different region descriptions, the problem of stability for a complex nonlinear system is transformed into ones of the robust stab...Robust stability for a series of nonlinear systems is presented in this paper. Through different region descriptions, the problem of stability for a complex nonlinear system is transformed into ones of the robust stabilities of several linear time-invariant systems. To get useful robust stability conditions, an expression for interval system is given, and the relationship between the internal stability and low- or supper-bound stability of interval systems is discussed. Thus, the polynomial matrix inequality for the determination of system robust stability is developed. Based on the equivalency transformation of the inequality, the solvable condition of the inequality is obtained. By means of the condition, robust stability theorem for interval systems is presented and a new design method of feedback control for nonlinear system is achieved. Applications to flight controller design show that the new method is efficient for uncertain system design.展开更多
In this paper, a discussion is devoted to the theory and method of a reversed-frame normalization design to robust flight control system. The robust stability theory of the normal transfer function matrix with the sam...In this paper, a discussion is devoted to the theory and method of a reversed-frame normalization design to robust flight control system. The robust stability theory of the normal transfer function matrix with the same characteristic gain loci is proved. An example of flight control system design shows the application and advantage of this method.展开更多
To alleviate the chattering problem, a new type of fuzzy global sliding mode controller (FGSMC) is presented. In this controller, the switching gain is estimated by fuzzy logic system based on the reachable conditio...To alleviate the chattering problem, a new type of fuzzy global sliding mode controller (FGSMC) is presented. In this controller, the switching gain is estimated by fuzzy logic system based on the reachable conditions of sliding mode controller(SMC), and genetic algorithm (GA) is used to optimize scaling factor of the switching gain, thus the switch chattering of SMC can be alleviated. Moreover, global sliding mode is realized by designing an exponential dynamic sliding surface. Simulation and real-time application for flight simulator servo system with Lugre friction are given to indicate that the proposed controller can guarantee high robust performance all the time and can alleviate chattering phenomenon effectively.展开更多
Flight simulator is an important device and a typical high-performance position and speed servo system used in the hardware-in-the-loop simulation of flight control system. Friction is the main nonlinear resistance in...Flight simulator is an important device and a typical high-performance position and speed servo system used in the hardware-in-the-loop simulation of flight control system. Friction is the main nonlinear resistance in the flight simulator servo system, especially in a low-speed state. Based on the description of dynamic and static models of a nonlinear Stribeck friction model, this paper puts forward sliding mode controller to overcome the friction, whose stability is展开更多
With the rapid development of China’s civil aviation industry,the teaching method of operating knowledge of flight principles has changed greatly,which creates a good implementation environment to improve the safety ...With the rapid development of China’s civil aviation industry,the teaching method of operating knowledge of flight principles has changed greatly,which creates a good implementation environment to improve the safety of civil aviation in our country.At present,the main training content of air route transport pilots in China is basic aviation theory,initial flight training,airline modification,etc.The principles of flight control are an important part of basic aviation theoretical knowledge training,which will involve a large number of flight technology training content,instructors will also be based on the pilot type.Teaching flight control theory and practical knowledge requires relatively high theoretical learning ability of students,and the learning effect of this part of theoretical knowledge will directly affect the quality of subsequent learning,but also directly affect the effectiveness of flight training.This paper focuses on the analysis of the basic concepts of flight control,studies the existing problems in the teaching of flight control principles,summarizes the teaching measures of flight control principles,aiming to provide a reference to teaching personnel.展开更多
The attitude tracking control problem for a satellite with parameter uncertainties and external disturbances is considered in this paper. For this class of multi-input multi-output uncertain nonlinear systems, a desig...The attitude tracking control problem for a satellite with parameter uncertainties and external disturbances is considered in this paper. For this class of multi-input multi-output uncertain nonlinear systems, a design method of robust output tracking controllers is proposed based on the upper-bounds of the uncertainties. Using the input/output feedback linearization approach and Lyapunov method, a control law is designed, which guarantees that the system output exponentially tracks the given desired output. The proposed controller is easy to compute and complement. Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties in the system.展开更多
A dynamic model of a remotely operated vehicle(ROV)is developed.The hydrodynamic damping coefficients are estimated using a semi-predictive approach and computational fluid dynamic software ANSYS-CFX?and WAMIT?.A slid...A dynamic model of a remotely operated vehicle(ROV)is developed.The hydrodynamic damping coefficients are estimated using a semi-predictive approach and computational fluid dynamic software ANSYS-CFX?and WAMIT?.A sliding-mode controller(SMC)is then designed for the ROV model.The controller is subsequently robustified against modeling uncertainties,disturbances,and measurement errors.It is shown that when the system is subjected to bounded uncertainties,the SMC will preserve stability and tracking response.The paper ends with simulation results for a variety of conditions such as disturbances and parametric uncertainties.展开更多
The robust bounded flight control scheme is developed for the uncertain longitudinal flight dynamics of the fighter with control input saturation invoking the backstepping technique. To enhance the disturbance rejecti...The robust bounded flight control scheme is developed for the uncertain longitudinal flight dynamics of the fighter with control input saturation invoking the backstepping technique. To enhance the disturbance rejection ability of the robust flight control for fighters, the sliding mode disturbance observer is designed to estimate the compounded disturbance including the unknown external disturbance and the effect of the control input saturation. Based on the backstepping technique and the compounded disturbance estimated output, the robust bounded flight control scheme is proposed for the fighter with the unknown external disturbance and the control input saturation. The closed-loop system stability under the developed robust bounded flight control scheme is rigorously proved using the Lyapunov method and the uniformly asymptotical convergences of all closed-loop signals are guaranteed. Finally, simulation results are presented to show the effectiveness of the proposed robust bounded flight control scheme for the uncertain longitudinal flight dynamics of the fighter.展开更多
The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are...The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are bounded, but the upper bounds are incompletely known. This paper can be viewed as an extension of the work in reference [1]. To compensate the uncertainties, an adaptive robust controller based on Lyapunov method is proposed and the design algorithm is also suggested. Compared with some previous controllers which can only ensure ultimate uniform boundedness of the systems, the controller given in the paper can make sure that the obtained closed-loop system is asymptotically stable in the large. Simulations show that the method presented is available and effective.展开更多
Using the future desired input value, zero phase error controller enables the overall system's frequency response exhibit zero phase shift for all frequencies and a small gain error at low frequency range, and based ...Using the future desired input value, zero phase error controller enables the overall system's frequency response exhibit zero phase shift for all frequencies and a small gain error at low frequency range, and based on this, a new algorithm is presented to design the feedforward controller. However, zero phase error controller is only suitable for certain linear system. To reduce the tracking error and improve robustness, the design of the proposed feedforward controller uses a neural compensation based on diagonal recurrent neural network. Simulation and real-time control results for flight simulator servo system show the effectiveness of the proposed approach.展开更多
This paper aims to provide a parametric design for robust flight controller of the model-scale helicopter. The main contributions lie in two aspects. Firstly,under near-hovering condition,a procedure is presented for ...This paper aims to provide a parametric design for robust flight controller of the model-scale helicopter. The main contributions lie in two aspects. Firstly,under near-hovering condition,a procedure is presented for simplification of the highly nonlinear and under-actuated model of the model-scale helicopter. This nonlinear system is linearized around the trim values of the chosen flight mode,followed by decomposing this high-order linear model into three lower-order subsystems according to the coupling properties among channels.After decomposition,the three subsystems are obtained which include the coupling subsystem between the roll( pitch) motion and the lateral( longitudinal) motion,the subsystem of the yaw motion and the subsystem of the vertical motion. Secondly,by using eigenstructure assignment,the problem of flight controller design can be converted into solving two optimization problems and the linear robust controllers of these subsystems are designed through solving these optimization problems. Besides, this paper contrasts and analyzed the performances of the LQR controller and the parametric controller. The results demonstrate the effectiveness and the robustness against the parametric perturbations of the parametric controller.展开更多
An investigation into the aircraft flight simulation and control system is presented in this paper. The study was firstly focused on the establishment of an integrated hardware-in-the-loop(HITL) platform for aircraf...An investigation into the aircraft flight simulation and control system is presented in this paper. The study was firstly focused on the establishment of an integrated hardware-in-the-loop(HITL) platform for aircraft flight simulation based on MATLAB/Simulink + dSPACE. The platform combines the abundant software and hardware resources of dSPACE simulation platform to simulate the flight attitude of an aircraft in six-DOF ( degree of freedom) motion. Based on the platform, the study was then focused on the flight numerical simulation by taking a loitering aerial vehicle as an example. An aircraft mathematical model was created for a modular design and off-line numerical simulation based on MATLAB/Simulink. Finally, the study was focused on the control system design of the loitering aerial vehicle and conduct of an HITL simulation experiment for the vehicle pitch control. The experiment verifies the system design and control effectiveness. Research results show that the dSPACE simulation system provides a real time good experimental platform to improve the efficiency of study and development of a flight control system.展开更多
In this paper, sensitivity approaches are taken to analyze and design an integrated flight propulsion control system where the interaction between subsystems direitly affects the stability property and handling perfor...In this paper, sensitivity approaches are taken to analyze and design an integrated flight propulsion control system where the interaction between subsystems direitly affects the stability property and handling performances of the aircraft. The eigenvalue sen sitivity approach is employed to study the effect of coupling parameters on system stability and gain sensitivity approach is used to direct the reduced states feedback suboptimal control system design. Simulation results show that the integrated flight propulsion control system designed by sensitivity approaches is of good performance.展开更多
There is proposed an adaptive sliding controller in task space on the base of the linear Newton-Euler dynamic equation of motion platform in a six-DOF flight simulator. The uncertain parameters are divided into two gr...There is proposed an adaptive sliding controller in task space on the base of the linear Newton-Euler dynamic equation of motion platform in a six-DOF flight simulator. The uncertain parameters are divided into two groups: the constant and the time-varying. The controller identifies constant uncertain parameters using nonlinear adaptive controller associated with elimination of the influences of time-varying uncertain parameters and compensation of the external disturbance using sliding control. The results of numerical simulation attest to the capability of this control scheme not only to, with deadly accuracy, identify parameters of motion platform such as load, inertia moments and mass center, but also effectively improve the robustness of the system.展开更多
Based on nominal model, a novel global sliding mode controller (GSMC) with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is th...Based on nominal model, a novel global sliding mode controller (GSMC) with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is the global sliding mode controller for practical plant, the other is the integral backstepping controller for nominal model. Modeling error between practical plant and nominal model is used to design GSMC. The steady-state control accuracy can be guaranteed by the integral backstepping control law, and the global robustness can be obtained by GSMC. The stability of the proposed controller is proved according to the Lyapunov approach. The simulation results both of sine signal and step signal tracking for 3-axis flight table are investigated to show good position tracking performance and high robustness with respect to large and parameter changes over all the response time.展开更多
The super-maneuver flight performance has a very high tactical value, and the development of this tactical value has great significance. A discussion is devoted to the study of intelligent control methods and technolo...The super-maneuver flight performance has a very high tactical value, and the development of this tactical value has great significance. A discussion is devoted to the study of intelligent control methods and technologies of real-time distributed 3-dimensional animation simulation for the super-maneuverable attack of new generational fighter in this paper. A flight control system of super-maneuver is reconstructed by adopting three layers BP neural networks of number 3, and the fire/flight coupler is designed by introducing a fuzzy control rule whose universe of discourse and gain are regulated adaptively on the line. Furthermore, a new method of real-time distributed 3-dimensional animation simulation is put forward, and a real-time distributed 3-dimensional animation simulation tool platform is constructed in this paper. The simulation result is lifelike, perceivable directly and useful.展开更多
This work investigates the problem of controller design for the inverters in an islanded microgrid.Robust-synthesis controllers and local droop controllers are designed to regulate the output voltages of inverters and...This work investigates the problem of controller design for the inverters in an islanded microgrid.Robust-synthesis controllers and local droop controllers are designed to regulate the output voltages of inverters and share power among them,respectively.The designed controllers alleviate the need for additional sensors to measure the states of the system by relying only on output feedback.It is shown that the designed-synthesis controller properly damps resonant oscillations,and its performance is robust to the control-loop time delay and parameter uncertainties.The stability of a droop-controlled islanded microgrid including multiple distributed generation(DG)units is analyzed by linearizing the nonlinear power flow model around the nominal operating point and applying theorems from linear algebra.It is indicated that the droop controller stabilizes the microgrid system with dominantly inductive tie-line impedances for all values of resistive-inductive loads,while for the case of resistive-capacitive loads the stability is conditioned on an upper bound on the load susceptances.The robust performance of the designed-synthesis controller is studied analytically,compared with the similar analysis in an control(benchmark)framework,and verified by simulations for a four DG benchmark microgrid.Furthermore,the robustness of the droop controllers is analyzed by Monte Carlo simulations in the presence of local voltage fluctuations and phase differences among neighboring DGs.展开更多
基金supported by the National Natural Science Foundation of China (60874117)the 111 Project (B07009)
文摘A new robust fault-tolerant controller scheme integrating a main controller and a compensator for the self-repairing flight control system is discussed.The main controller is designed for high performance of the original faultless system.The compensating controller can be seen as a standalone loop added to the system to compensate the effects of fault guaranteeing the stability of the system.A design method is proposed using nonlinear dynamic inverse control as the main controller and nonlinear extended state observer-based compensator.The stability of the whole closed-loop system is analyzed.Feasibility and validity of the new controller is demonstrated with an aircraft simulation example.
文摘Robust stability for a series of nonlinear systems is presented in this paper. Through different region descriptions, the problem of stability for a complex nonlinear system is transformed into ones of the robust stabilities of several linear time-invariant systems. To get useful robust stability conditions, an expression for interval system is given, and the relationship between the internal stability and low- or supper-bound stability of interval systems is discussed. Thus, the polynomial matrix inequality for the determination of system robust stability is developed. Based on the equivalency transformation of the inequality, the solvable condition of the inequality is obtained. By means of the condition, robust stability theorem for interval systems is presented and a new design method of feedback control for nonlinear system is achieved. Applications to flight controller design show that the new method is efficient for uncertain system design.
基金This paper has been supported by the National Natural Science Foundation of Chaina.
文摘In this paper, a discussion is devoted to the theory and method of a reversed-frame normalization design to robust flight control system. The robust stability theory of the normal transfer function matrix with the same characteristic gain loci is proved. An example of flight control system design shows the application and advantage of this method.
基金This project is supported by Aeronautics Foundation of China (No. 00E51022)
文摘To alleviate the chattering problem, a new type of fuzzy global sliding mode controller (FGSMC) is presented. In this controller, the switching gain is estimated by fuzzy logic system based on the reachable conditions of sliding mode controller(SMC), and genetic algorithm (GA) is used to optimize scaling factor of the switching gain, thus the switch chattering of SMC can be alleviated. Moreover, global sliding mode is realized by designing an exponential dynamic sliding surface. Simulation and real-time application for flight simulator servo system with Lugre friction are given to indicate that the proposed controller can guarantee high robust performance all the time and can alleviate chattering phenomenon effectively.
基金This project was supported by the Aeronautics Foundation of China (00E21022).
文摘Flight simulator is an important device and a typical high-performance position and speed servo system used in the hardware-in-the-loop simulation of flight control system. Friction is the main nonlinear resistance in the flight simulator servo system, especially in a low-speed state. Based on the description of dynamic and static models of a nonlinear Stribeck friction model, this paper puts forward sliding mode controller to overcome the friction, whose stability is
文摘With the rapid development of China’s civil aviation industry,the teaching method of operating knowledge of flight principles has changed greatly,which creates a good implementation environment to improve the safety of civil aviation in our country.At present,the main training content of air route transport pilots in China is basic aviation theory,initial flight training,airline modification,etc.The principles of flight control are an important part of basic aviation theoretical knowledge training,which will involve a large number of flight technology training content,instructors will also be based on the pilot type.Teaching flight control theory and practical knowledge requires relatively high theoretical learning ability of students,and the learning effect of this part of theoretical knowledge will directly affect the quality of subsequent learning,but also directly affect the effectiveness of flight training.This paper focuses on the analysis of the basic concepts of flight control,studies the existing problems in the teaching of flight control principles,summarizes the teaching measures of flight control principles,aiming to provide a reference to teaching personnel.
文摘The attitude tracking control problem for a satellite with parameter uncertainties and external disturbances is considered in this paper. For this class of multi-input multi-output uncertain nonlinear systems, a design method of robust output tracking controllers is proposed based on the upper-bounds of the uncertainties. Using the input/output feedback linearization approach and Lyapunov method, a control law is designed, which guarantees that the system output exponentially tracks the given desired output. The proposed controller is easy to compute and complement. Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties in the system.
文摘A dynamic model of a remotely operated vehicle(ROV)is developed.The hydrodynamic damping coefficients are estimated using a semi-predictive approach and computational fluid dynamic software ANSYS-CFX?and WAMIT?.A sliding-mode controller(SMC)is then designed for the ROV model.The controller is subsequently robustified against modeling uncertainties,disturbances,and measurement errors.It is shown that when the system is subjected to bounded uncertainties,the SMC will preserve stability and tracking response.The paper ends with simulation results for a variety of conditions such as disturbances and parametric uncertainties.
基金supported by the National Natural Science Foundation of China(61174102)the Jiangsu Natural Science Foundation of China(SBK20130033)+1 种基金the NUAA Fundamental Research Funds(NS2013028)the Specialized Research Fund for the Doctoral Program of Higher Education(20133218110013)
文摘The robust bounded flight control scheme is developed for the uncertain longitudinal flight dynamics of the fighter with control input saturation invoking the backstepping technique. To enhance the disturbance rejection ability of the robust flight control for fighters, the sliding mode disturbance observer is designed to estimate the compounded disturbance including the unknown external disturbance and the effect of the control input saturation. Based on the backstepping technique and the compounded disturbance estimated output, the robust bounded flight control scheme is proposed for the fighter with the unknown external disturbance and the control input saturation. The closed-loop system stability under the developed robust bounded flight control scheme is rigorously proved using the Lyapunov method and the uniformly asymptotical convergences of all closed-loop signals are guaranteed. Finally, simulation results are presented to show the effectiveness of the proposed robust bounded flight control scheme for the uncertain longitudinal flight dynamics of the fighter.
文摘The problem of robust stabilization for nonlinear systems with partially known uncertainties is considered in this paper. The required information about uncertainties in the system is merely that the uncertainties are bounded, but the upper bounds are incompletely known. This paper can be viewed as an extension of the work in reference [1]. To compensate the uncertainties, an adaptive robust controller based on Lyapunov method is proposed and the design algorithm is also suggested. Compared with some previous controllers which can only ensure ultimate uniform boundedness of the systems, the controller given in the paper can make sure that the obtained closed-loop system is asymptotically stable in the large. Simulations show that the method presented is available and effective.
基金The project was supported by Aeronautics Foundation of China (00E51022).
文摘Using the future desired input value, zero phase error controller enables the overall system's frequency response exhibit zero phase shift for all frequencies and a small gain error at low frequency range, and based on this, a new algorithm is presented to design the feedforward controller. However, zero phase error controller is only suitable for certain linear system. To reduce the tracking error and improve robustness, the design of the proposed feedforward controller uses a neural compensation based on diagonal recurrent neural network. Simulation and real-time control results for flight simulator servo system show the effectiveness of the proposed approach.
文摘This paper aims to provide a parametric design for robust flight controller of the model-scale helicopter. The main contributions lie in two aspects. Firstly,under near-hovering condition,a procedure is presented for simplification of the highly nonlinear and under-actuated model of the model-scale helicopter. This nonlinear system is linearized around the trim values of the chosen flight mode,followed by decomposing this high-order linear model into three lower-order subsystems according to the coupling properties among channels.After decomposition,the three subsystems are obtained which include the coupling subsystem between the roll( pitch) motion and the lateral( longitudinal) motion,the subsystem of the yaw motion and the subsystem of the vertical motion. Secondly,by using eigenstructure assignment,the problem of flight controller design can be converted into solving two optimization problems and the linear robust controllers of these subsystems are designed through solving these optimization problems. Besides, this paper contrasts and analyzed the performances of the LQR controller and the parametric controller. The results demonstrate the effectiveness and the robustness against the parametric perturbations of the parametric controller.
基金Sponsored by the Ministerial Level Advanced Research Foundation(A26020060253)
文摘An investigation into the aircraft flight simulation and control system is presented in this paper. The study was firstly focused on the establishment of an integrated hardware-in-the-loop(HITL) platform for aircraft flight simulation based on MATLAB/Simulink + dSPACE. The platform combines the abundant software and hardware resources of dSPACE simulation platform to simulate the flight attitude of an aircraft in six-DOF ( degree of freedom) motion. Based on the platform, the study was then focused on the flight numerical simulation by taking a loitering aerial vehicle as an example. An aircraft mathematical model was created for a modular design and off-line numerical simulation based on MATLAB/Simulink. Finally, the study was focused on the control system design of the loitering aerial vehicle and conduct of an HITL simulation experiment for the vehicle pitch control. The experiment verifies the system design and control effectiveness. Research results show that the dSPACE simulation system provides a real time good experimental platform to improve the efficiency of study and development of a flight control system.
文摘In this paper, sensitivity approaches are taken to analyze and design an integrated flight propulsion control system where the interaction between subsystems direitly affects the stability property and handling performances of the aircraft. The eigenvalue sen sitivity approach is employed to study the effect of coupling parameters on system stability and gain sensitivity approach is used to direct the reduced states feedback suboptimal control system design. Simulation results show that the integrated flight propulsion control system designed by sensitivity approaches is of good performance.
文摘There is proposed an adaptive sliding controller in task space on the base of the linear Newton-Euler dynamic equation of motion platform in a six-DOF flight simulator. The uncertain parameters are divided into two groups: the constant and the time-varying. The controller identifies constant uncertain parameters using nonlinear adaptive controller associated with elimination of the influences of time-varying uncertain parameters and compensation of the external disturbance using sliding control. The results of numerical simulation attest to the capability of this control scheme not only to, with deadly accuracy, identify parameters of motion platform such as load, inertia moments and mass center, but also effectively improve the robustness of the system.
文摘Based on nominal model, a novel global sliding mode controller (GSMC) with a new control scheme is proposed for a practical uncertain servo system. This control scheme consists of two combined controllers, One is the global sliding mode controller for practical plant, the other is the integral backstepping controller for nominal model. Modeling error between practical plant and nominal model is used to design GSMC. The steady-state control accuracy can be guaranteed by the integral backstepping control law, and the global robustness can be obtained by GSMC. The stability of the proposed controller is proved according to the Lyapunov approach. The simulation results both of sine signal and step signal tracking for 3-axis flight table are investigated to show good position tracking performance and high robustness with respect to large and parameter changes over all the response time.
文摘The super-maneuver flight performance has a very high tactical value, and the development of this tactical value has great significance. A discussion is devoted to the study of intelligent control methods and technologies of real-time distributed 3-dimensional animation simulation for the super-maneuverable attack of new generational fighter in this paper. A flight control system of super-maneuver is reconstructed by adopting three layers BP neural networks of number 3, and the fire/flight coupler is designed by introducing a fuzzy control rule whose universe of discourse and gain are regulated adaptively on the line. Furthermore, a new method of real-time distributed 3-dimensional animation simulation is put forward, and a real-time distributed 3-dimensional animation simulation tool platform is constructed in this paper. The simulation result is lifelike, perceivable directly and useful.
文摘This work investigates the problem of controller design for the inverters in an islanded microgrid.Robust-synthesis controllers and local droop controllers are designed to regulate the output voltages of inverters and share power among them,respectively.The designed controllers alleviate the need for additional sensors to measure the states of the system by relying only on output feedback.It is shown that the designed-synthesis controller properly damps resonant oscillations,and its performance is robust to the control-loop time delay and parameter uncertainties.The stability of a droop-controlled islanded microgrid including multiple distributed generation(DG)units is analyzed by linearizing the nonlinear power flow model around the nominal operating point and applying theorems from linear algebra.It is indicated that the droop controller stabilizes the microgrid system with dominantly inductive tie-line impedances for all values of resistive-inductive loads,while for the case of resistive-capacitive loads the stability is conditioned on an upper bound on the load susceptances.The robust performance of the designed-synthesis controller is studied analytically,compared with the similar analysis in an control(benchmark)framework,and verified by simulations for a four DG benchmark microgrid.Furthermore,the robustness of the droop controllers is analyzed by Monte Carlo simulations in the presence of local voltage fluctuations and phase differences among neighboring DGs.