Frequency domain stability criteria for fractional-order control systems

This paper concerns about the frequency domain stability criteria for fractional-order control systems. On the base of characteristics of the fractional-order equations solutions, we consider the Nyquist stability criterion in a wider sense and obtain a more common means to analyze the stability of fractional-order systems conveniently. Finally, this paper illustrates the generalized stability criteria with an example to show the effect of the parameters variation on the fractional-order control systems.

An improved approach to H-two control withregional stability constraints

This paper presents an improved method for H-two control with regional stability constraints for the closedloop system. The controller is given by the convex combination of a set of fixed gains. Both continuous and discrete-time systems in a known polytopic domain are investigated. New LMI-based sufficient conditions for the existence of parameterdependent Lyapunov functions are proposed. Numerical examples are given to show the proposed conditions provide useful and less conservative results for the problems of H-two control with regional stability constraints.

Model Predictive Control of Nonlinear Systems: Stability Region and Feasible Initial Control

This paper proposes a new method for model predictive control （MPC） of nonlinear systems to calculate stability region and feasible initial control profile/sequence, which are important to the implementations of MPC. Different from many existing methods, this paper distinguishes stability region from conservative terminal region. With global linearization, linear differential inclusion （LDI） and linear matrix inequality （LMI） techniques, a nonlinear system is transformed into a convex set of linear systems, and then the vertices of the set are used off-line to design the controller, to estimate stability region, and also to determine a feasible initial control profile/sequence. The advantages of the proposed method are demonstrated by simulation study.

Stability analysis of traffic flow with extended CACC control models

To further investigate car-following behaviors in the cooperative adaptive cruise control（CACC） strategy,a comprehensive control system which can handle three traffic conditions to guarantee driving efficiency and safety is designed by using three CACC models.In this control system,some vital comprehensive information,such as multiple preceding cars’ speed differences and headway,variable safety distance（VSD） and time-delay effect on the traffic current and the jamming transition have been investigated via analytical or numerical methods.Local and string stability criterion for the velocity control（VC） model and gap control（GC） model are derived via linear stability theory.Numerical simulations are conducted to study the performance of the simulated traffic flow.The simulation results show that the VC model and GC model can improve driving efficiency and suppress traffic congestion.

Stability analysis of the simplest Takagi-Sugeno fuzzy control system using circle criterion

A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.

State-feedback H_2/H-infinity controller design with D-stability constraints for stochastic systems

This paper addresses the state-feedback H2/H-infinity controller design that satisfies D-stability constraints for stochastic systems. Firstly, the concept of regional stability for stochastic systems is defined in linear matrix inequality（LMI） regions; Secondly, the characterization about stochastic D-stability is presented. This paper introduces a new technique to solve the regional stability problem for stochastic systems, which is different from the pole placement technique ever used in deterministic systems. Based on this, in the state-feedback case, mixed H2/H-infinity synthesis with D-stability constraints is discussed via LMI optimization.

Randomized Algorithm for Determining Stabilizing Parameter Regions for General Delay Control Systems

This paper proposes a method for determining the stabilizing parameter regions for general delay control systems based on randomized sampling. A delay control system is converted into a unified state-space form. The numerical stability condition is developed and checked for sample points in the parameter space. These points are separated into stable and unstable regions by the decision function obtained from some learning method. The proposed method is very general and applied to a much wider range of systems than the existing methods in the literature. The proposed method is illustrated with examples.

Impact of Electric Vehicle Aggregator with Communication Time Delay on Stability Regions and Stability Delay Margins in Load Frequency Control System

This paper investigates the impact of electric vehicle(EV)aggregator with communication time delay on stability regions and stability delay margins of a single-area load frequency control(LFC)system.Primarily,a graphical method characterizing stability boundary locus is implemented.For a given time delay,the method computes all the stabilizing proportional-integral(PI)controller gains,which constitutes a stability region in the parameter space of PI controller.Secondly,in order to complement the stability regions,a frequency-domain exact method is used to calculate stability delay margins for various values of PI controller gains.The qualitative impact of EV aggregator on both stability regions and stability delay margins is thoroughly analyzed and the results are authenticated by time-domain simulations and quasi-polynomial mapping-based root finder(QPmR)algorithm.

Safe formation control of multiple unmanned aerial vehicles:control design and safety-stability analysis

Both safety and stability are primary performance criteria for multi-unmanned aerial vehicle(multi-UAV)systems in many coordination tasks.Existing approaches often consider safety and stability separately.It is necessary and urgent to develop a safety-stability control strategy to merge these two performance criteria.In this paper,a unified approach is developed to consider safety and stability for multi-UAV formation control.The stability criterion is represented by a Lyapunov function and safety criterion is represented by a barrier function and then a relaxed converse control Lyapunov-barrier theorem is obtained.With the help of a relaxed converse control Lyapunov-barrier function(RCCLBF),a distributed safety-stability formation control strategy is proposed for the multi-UAV system.By transforming the solution of RCCLBF to a Lyapunovlike stabilization problem,we show that the proposed formation control strategy can drive the UAVs staying within a specified safe set.Simulation results are provided to validate the proposed safety-stability formation control strategy.

Adaptive Fuzzy Backstepping Output Feedback Control of Nonlinear Time-delay Systems with Unknown High-frequency Gain Sign

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and singleoutput （SISO） strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.

Frequency Control System with Digital Signal Processing Techniques

The frequency of digitally controlled iodine stabilized He-Ne laser locked to a hyperfine component in ^127I2 was measured using the National Metrology Institute of Japan＇s reference iodine stabilized He-Ne laser. This laser is operated under the conditions of the practical implementation and its frequency with respect to the International Committee for Weights and Measure recommended value is known from international comparisons. Adopting a sampling rate of 120 kHz for the control system of an iodine stabilized He-Ne laser enables frequency deviation of the test laser from the reference laser by ＋ 5 kHz （relative accuracy of 1 ×10^11） thus limited only by the reproducibility of the iodine stabilized He-Ne laser itself.

On Stabilizing Sets of PI Controllers for Multiple Time Delayed Process

This paper considers the problem of stabilizing multiple time delayed processes using proportional integral(PI) controller.The presented approach is based on finding all possible values of control parameters which will result in pure imaginary roots of closed loop characteristic equation under all process parameters fixed.The ergodic search of three PI control parameters are converted from the range of infinity to finite range by introducing trigonometric tangent function.After all possible stability boundaries are obtained,the Nyquist stability method is used to determine the actual stability region of the controller parameters.This method also permits design for simultaneous minimum gain and phase margin requirement.An illustrative example case is also presented.

Finite-time economic model predictive control for optimal load dispatch and frequency regulation in interconnected power systems

This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power system to ensure frequency stability,real-time economic optimization,control of the system and optimal load dispatch from it.A generalized terminal penalty term was used,and the finite-time convergence of the system was guaranteed.The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system,which had two areas connected by an AC tie line.The simulation results demonstrated the effectiveness of the algorithm.

Research on the Impacts of the Inertia and Droop Control Gains from a Variable-Speed Wind Turbine Generator on the Frequency Response

System frequency must be kept very close to its nominal range to ensure the stability of an electric power grid.Excessive system frequency variations are able to result in load shedding,frequency instability,and even generator damage.With increasing wind power penetration,there is rising concern about the reduction in inertia response and primary frequency control in the electric power grid.Converter-based wind generation is capable of providing inertia response and primary frequency response;nevertheless,the primary frequency and inertia responses of wind generation are different from those of conventional synchronous fleets;it is not completely understood how the primary frequency and inertia responses affect the given system under various disturbances and available kinetic energy levels.Simulations are used to investigate the influences of inertia and droop control strategies on the dynamic frequency responses,particularly the index of the second frequency drop under various disturbance and wind conditions.A quantitative analysis provides insight into setting of inertia and droop control coefficients for various wind and disturbance conditions to facilitate adequate dynamic frequency responses during frequency events.

Improving frequency stability of laser by means of temperature-controlled Fabry-Perot cavity

The frequency stability of an all-solid-state Nd:YVO4 laser is significantly improved by means of a specially designed Fabry-Perot (F-P) interferometer used for the frequency standard in the frequency-stabilizing system. The ten.peraturo of the F-P cavity is accurately controlled by a set of thermoelectric cooler (TEC) modules attached on th dy of the cavity and the electronic feedback circuit. We find that the long-term unidirectional frequency shift of the output laser, resulting from the slow increase of the cavity length under the effect of the temperature integration on the cavity body, is essentially eliminated. The frequency stability of the output laser with the power of 530 mW is better than ±200 kHz in 1 minute and ±2.3 MHz iu 40 minutes, respectively. The fluctuation of output power is smaller than ±0.5% over one hour.

Controllability and stability of primary frequency control from thermostatic loads with delays

There is an increasing interest in exploiting theflexibility of loads to provide ancillary services to the grid.In this paper we study how response delays and lockout constraints affect the controllability of an aggregation of refrigerators offering primary frequency control(PFC).First we examine the effect of delays in PFC provision from an aggregation of refrigerators, using a two-area power system. We propose a framework to systematically address frequency measurement and response delays and we determine safe values for the total delays via simulations. We introduce a controllability index to evaluate PFC provision under lockout constraints of refrigerators compressors. We conduct extensive simulations to study the effects of measurement delay, ramping times, lockout durations and rotational inertia on the controllability of the aggregation and system stability. Finally, we discuss solutions for offering reliable PFC provision from thermostatically controlled loads under lockout constraints and we propose a supervisory control to enhance the robustness of their controllers.

Frequency Stability of Power System with Large Share of Wind Power Under Storm Conditions

The operation of transmission systems with large share of wind power is specially challenging under storm conditions.Under the stormy wind speed conditions,wind turbine protection system is designed to shut down the turbine to avoid excessive mechanical load.The sudden loss of wind power from large offshore plants is difficult to forecast accurately,which results in a large amount of power imbalance.The severity of such a wind power imbalance towards frequency stability needs to be studied for the future power systems.In addition,the overhead transmission lines can also be affected during storms,thereby increasing their probability of failure in the operation of power system under the islanded conditions.This paper investigates how the stormy weather can threaten the frequency stability of future Danish power system with large share of wind power and how to avoid the frequency instability through proper control and defence strategies such as high-voltage direct current(HVDC)control and load shedding.Sensitivity studies are performed for ramp rates of HVDC control,load shedding strategies,inertia of the system with different volumes of disturbances to understand their impact on frequency stability.

Analysis of the Most Likely Regions of Stability of an NCS and Design of the Corresponding Event-driven Controller

In this paper, some issues related to design and analysis of real networked control systems （NCS） under the focus of the most likely region of stability are addressed. Such a system is cumbersome due to its inherent variable time delays, ranging from microseconds to hours. To show the influence of such huge variations in the control performance, a laboratory-scale luminosity system has been setup using the Internet as part of the control loop with dominant time constant in the order of milliseconds. Proportional and integral （PI） control strategies with and without explicit compensation for the time-delay variations were implemented using an event-driven controller. Using the well-known Monte Carlo method and subsequent analyses of time responses, it has been possible to identify the most likely region of stability. Some experimental results show the influence of the statistical parameters of the delays on the determination of the most likely regions of stability of the NCS and how these can be used in assessment and redesign of the control system. The experiments show that much larger delays than one sample period can be supported by real NCSs without becoming unstable.

Delay-dependent Robust Stability Analysis of Power Systems with PID Controller

This study examines the robust stability of a power system,which is based on proportional-integral-derivative load frequency control and involves uncertain parameters and time delays.The model of the system is firstly established,following which the system is transformed into a closed-loop system with feedback control.On this basis,a new augmented Lyapunov-Krasovskii(LK)functional is established for using the new Bessel-Legendre inequality to estimate the derivative of the functional,which can provide a maximum lower bound.A stability criterion is then derived by employing the LK functional and Bessel-Legendre inequality.Finally,numerical examples are used to demonstrate the validity and superiority of the proposed method.

Nyquist Stability Analysis and Capacitance Selection for DC Current Flow Controllers in Meshed Multi-terminal HVDC Grids

Controllability of DC current/power flow is essentialin multi-terminal HVDC (MTDC) grids, particularly for theMTDC grids in a meshed topology. In this paper, consideringmeshed MTDC (M2TDC) grids with the installation of twoline/multi-lineDC current flow controllers (CFCs), a small-signalmodel of the DC CFCs integrated M2TDC grids is derived,studying the impact of the power losses of the DC CFC andtheir influence on the analysis of energy exchanges. The systemstability analysis is analysed using the Nyquist diagram, which ismore suitable for analyzing complex nonlinear systems with morecompact and reliable indicators of stability in comparison withgain/phase margins shown in the Bode diagram. In addition, aselection method of the interconnected capacitor of the DC CFCis proposed under different operating conditions. The impact ofthe switching frequencies of the DC CFC on the control ranges ofthe DC current flows is analyzed. The effectiveness of the Nyquistanalysis and the capacitance selection method is verified bysimulation studies using PSCAD/EMTDC. The obtained control ranges of the DC CFC with different switching frequenciesand capacitances would be useful for practical engineeringapplications.