Robust Stabilizing Regions of Fractional-order PI~λ Controllers for Fractional-order Systems with Time-delays

This study focuses on a graphical approach to determine the robust stabilizing regions of fractional-order PIλ（proportional integration） controllers for fractional-order systems with time-delays. By D-decomposition technique, the existence conditions and calculating method of the real root boundary（RRB） curves, complex root boundary（CRB） curves and infinite root boundary（IRB）lines are investigated for a given stability degree. The robust stabilizing regions in terms of the RRB curves, CRB curves and IRB lines are identified by the proposed criteria in this paper. Finally, two illustrative examples are given to verify the effectiveness of this graphical approach for different stability degrees.

The Static Stability Region of an Integrated Electricity-Gas System Considering Voltage and Gas Pressure

In an integrated electricity-gas system(IEGS),load fluctuations affect not only the voltage in the power system but also the gas pressure in the natural gas system.The static voltage stability region(SVSR)method is a tool for analyzing the overall static voltage stability in a power system.However,in an IEGS,the SVSR boundary may be overly optimistic because the gas pressure may collapse before the voltage collapses.Thus,the SVSR method cannot be directly applied to an IEGS.In this paper,the concept of the SVSR is extended to the IEGS-static stability region(SSR)while considering voltage and gas pressure.First,criteria for static gas pressure stability in a natural gas system are proposed,based on the static voltage stability criteria in a power system.Then,the IEGS-SSR is defined as a set of active power injections that satisfies multi-energy flow(MEF)equations and static voltage and gas pressure stability constraints in the active power injection space of natural gas-fired generator units(NGUs).To determine the IEGSSSR,a continuation MEF(CMEF)method is employed to trace the boundary point in one specific NGU scheduling direction.A multidimensional hyperplane sampling method is also proposed to sample the NGU scheduling directions evenly.The obtained boundary points are further used to form the IEGSSSR in three-dimensional(3D)space via a Delaunay triangulation hypersurface fitting method.Finally,the numerical results of typical case studies are presented to demonstrate that the proposed method can effectively form the IEGS-SSR,providing a tool for IEGS online monitoring and dispatching.

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.

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.

Closed-loop control of epileptiform activities in a neural population model using a proportional-derivative controller

Epilepsy is believed to be caused by a lack of balance between excitation and inhibitation in the brain. A promising strategy for the control of the disease is closed-loop brain stimulation. How to determine the stimulation control parameters for effective and safe treatment protocols remains, however, an unsolved question. To constrain the complex dynamics of the biological brain, we use a neural population model（NPM）. We propose that a proportional-derivative（PD） type closed-loop control can successfully suppress epileptiform activities. First, we determine the stability of root loci, which reveals that the dynamical mechanism underlying epilepsy in the NPM is the loss of homeostatic control caused by the lack of balance between excitation and inhibition. Then, we design a PD type closed-loop controller to stabilize the unstable NPM such that the homeostatic equilibriums are maintained; we show that epileptiform activities are successfully suppressed. A graphical approach is employed to determine the stabilizing region of the PD controller in the parameter space, providing a theoretical guideline for the selection of the PD control parameters. Furthermore, we establish the relationship between the control parameters and the model parameters in the form of stabilizing regions to help understand the mechanism of suppressing epileptiform activities in the NPM. Simulations show that the PD-type closed-loop control strategy can effectively suppress epileptiform activities in the NPM.

Main active faults and seismic activity along the Yangtze River Economic Belt:Based on remote sensing geological survey

The Yangtze River Economic Belt(YREB)spans three terrain steps in China and features diverse topography that is characterized by significant differences in geological structure and presentday crustal deformation.Active faults and seismic activity are important geological factors for the planning and development of the YREB.In this paper,the spatial distribution and activity of 165 active faults that exist along the YREB have been compiled from previous findings,using both remote-sensing data and geological survey results.The crustal stability of seven particularly noteworthy typical active fault zones and their potential effects on the crustal stability of the urban agglomerations are analyzed.The main active fault zones in the western YREB,together with the neighboring regional active faults,make up an arc fault block region comprising primarily of Sichuan-Yunnan and a“Sichuan-Yunnan arc rotational-shear active tectonic system”strong deformation region that features rotation,shear and extensional deformation.The active faults in the central-eastern YREB,with seven NE-NNE and seven NW-NWW active faults(the“7-longitudinal,7-horizontal”pattern),macroscopically make up a“chessboard tectonic system”medium-weak deformation region in the geomechanical tectonic system.They are also the main geological constraints for the crustal stability of the YREB.

A Modified Model Predictive Control Scheme

In implementations of MPC (Model Predictive Control) schemes, two issues need to be addressed. One is how to enlarge the stability region as much as possible. The other is how to guarantee stability when a computational time limitation exists. In this paper, a modified MPC scheme for constrained linear systems is described. An offline LMI-based iteration process is introduced to expand the stability region. At the same time, a database of feasible control sequences is generated offline so that stability can still be guaranteed in the case of computational time limitations. Simulation results illustrate the effectiveness of this new approach. Keywords Model predictive control - linear matrix inequality - stability region - terminal region - feasibility Xiao-Bing Hu received the B.S. degree in Aviation Electronic Engineering at Civil Aviation Institute of China, Tianjin, China, in 1998, the M.S. degree in Automatic Control Engineering at Nanjing University of Aeronautics & Astronautics, Nanjing, China, in 2001, and the Ph.D. degree in Aeronautical and Automotive Engineering at Loughborough University, UK, in 2005.He is currently a Research Fellow in Department of Informatics at Sussex University, UK. His major field of research includes predictive control, artificial intelligence, air traffic management, and flight control. Wen-Hua Chen received his MSc and Ph.D. degrees from Department of Automatic Control at Northeast University, China, in 1989 and 1991, respectively.From 1991 to 1996, he was a Lecturer in Department of Automatic Control at Nanjing University of Aeronautics & Astronautics, China. He held a research position and then a Lectureship in Control Engineering in Center for Systems and Control at University of Glasgow, UK, from 1997 to 2000. He holds a Lectureship in Flight Control Systems in Department of Aeronautical and Automotive Engineering at Loughborough University, UK. He has published one book and more than 60 papers on journals and conferences. His research interests are the development of advanced control strategies and their applications in aerospace engineering.

Real-time digital image stabilization based on regional field image gray projection

Digital image stabilization technique plays important roles in video surveillance and object acquisition.Many useful electronic image stabilization algorithms have been studied.A real-time algorithm is proposed based on field image gray projection which enables the regional odd and even field image to be projected into x and y directions and thus to get the regional gray projection curves in x and y directions,respectively.For the odd field image channel,motion parameters can be estimated via iterative minimum absolute difference based on two successive field image regional gray projection curves.Then motion compensations can be obtained after using the Kalman filter method.Finally,the odd field image is adjusted according to the compensations.In the mean time,motion compensation is applied to the even field image channel with the odd field image gray projection curves of the current frame.By minimizing absolute difference between odd and even field image gray projection curves of the current frame,the inter-field motion parameters can be estimated.Therefore,the even field image can be adjusted by combining the inter-field motion parameters and the odd field compensations.Finally,the stabilized image sequence can be obtained by synthesizing the adjusted odd and even field images.Experimental results show that the proposed algorithm can run in real-time and have a good stabilization performance.In addition,image blurring can be improved.

Optimal Robust Control for Unstable Delay System

Proportional-Integral-Derivative control system has been widely used in industrial applications.For uncertain and unstable systems,tuning controller parameters to satisfy the process requirements is very challenging.In general,the whole system’s performance strongly depends on the controller’s efficiency and hence the tuning process plays a key role in the system’s response.This paper presents a robust optimal Proportional-Integral-Derivative controller design methodology for the control of unstable delay system with parametric uncertainty using a combination of Kharitonov theorem and genetic algorithm optimization based approaches.In this study,the Generalized Kharitonov Theorem(GKT)for quasi-polynomials is employed for the purpose of designing a robust controller that can simultaneously stabilize a given unstable second-order interval plant family with time delay.Using a constructive procedure based on the Hermite-Biehler theorem,we obtain all the Proportional-Integral-Derivative gains that stabilize the uncertain and unstable second-order delay system.Genetic Algorithms(GAs)are utilized to optimize the three parameters of the PID controllers and the three parameters of the system which provide the best control that makes the system robust stable under uncertainties.Specifically,the method uses genetic algorithms to determine the optimum parameters by minimizing the integral of time-weighted absolute error ITAE,the Integral-Square-Error ISE,the integral of absolute error IAE and the integral of time-weighted Square-Error ITSE.The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example.

Seismic Activity and Fuzzy Comprehensive Evaluation of Crustal Stability in the Beijing Region

This paper discusses the seismic activity in Beijing M unicipality and its adjacent areas (which are referred to as the Beijing region in the paper). By using fuzzy mathematics, the factors controlling regional crustal stability are transformed into fuzzy information and then a model of fuzzy diagnosis is established. A fuzzy comprehensive evaluation of regional crustal stability in the Beijing region is made according to the seismic and geological conditions of the region.

Weak and strong stabilization of linear systems

We study the problem of stabilizing a distributed linear system on a subregion of its geometrical domain. We are concerned with two methods： the first approach enables us to characterize a stabilizing control via the steady state Riccati equation, and the second one is based on decomposing the state space into two suitable subspaces and studying the projections of the initial system onto such subspaces. The obtained results are performed through various examples.

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.

Quantitative Assessment and Zonation of Regional Crustal Stability in China

On the basis of the synthetic analysis of present regional tectonic stress field in China, this paper follows three steps to do crustal stability assessment: (1) zonation of preevaluation area for regional crustal stability assessment and zonation; (2) choice, taking value and weight distribution of quantitative evaluation indices and determination of evaluation standards; (3) assessment and zonation of regional crustal stability using fuzzy mathematics in China.

Engineering Geological Study of Regional Tectonic Stability in the Area of the Longyang Gorge Power Station on the Huanghe (Yellow) River

In the stability study of the regional structures in the area of the Longyang Gorge Hydroelectrical Power Station, a model of the current stress-deformation field of the area was constructed based on analyses of available data of regional surveys and historical earthquakes and field investigations of active faults and ancient earthquakes. This model was examined and verified by physical and mathematical simulation experiments, and quantitative relations and data were obtained.

Fractional-order Virtual Inertia Control and Parameter Tuning for Energy-storage System in Low-inertia Power Grid

As conventional synchronous generators are replaced by large-scale converter-interfaced renewa-ble-energy sources(RESs),the electric power grid en-counters the challenge of low rotational inertia.Conse-quently,system frequency deviation is exacerbated and system instability may occur when the frequency deviates beyond the acceptable range.To mitigate this effect,this study proposes a virtual inertia control(VIC)strategy based on a fractional-order derivative and controller parameter-tuning method.The tuning method uses the stability boundary locus and provides a stability criterion for identifying the stability region in the parameter space.The controller parameters are then optimized within the identified stability region to suppress frequency deviation and enhance system robustness.The proposed controller and tuning method is applied to a battery energy-storage system(BESS)in a low-inertia power system with the integration of RESs.Time-domain simulations are carried out to verify the stability region and compare the per-formance of the optimized proposed controller to that of the traditional integral-order controller.The simulation results show that the stability-analysis method is effective and that the fractional-order VIC,tuned with the pro-posed method,outperforms the traditional method in both frequency-regulation performance and parametric robustness.Index Terms—Virtual inertia control,frequency regu-lation,fractional-order controller,stability region,pa-rameter tuning.

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.

Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System

In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integralderivative(PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasi-polynomials, is used to seek the set of complete stabilizing proportional-integral/proportional-integral-derivative(PI/PID) parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be a triangle.

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.

ON THE EXPLICIT TWO-STAGE FOURTH-ORDER ACCURATE TIME DISCRETIZATIONS

This paper continues to study the explicit two-stage fourth-order accurate time discretizations[5-7].By introducing variable weights,we propose a class of more general explicit one-step two-stage time discretizations,which are different from the existing methods,e.g.the Euler methods,Runge-Kutta methods,and multistage multiderivative methods etc.We study the absolute stability,the stability interval,and the intersection between the imaginary axis and the absolute stability region.Our results show that our two-stage time discretizations can be fourth-order accurate conditionally,the absolute stability region of the proposed methods with some special choices of the variable weights can be larger than that of the classical explicit fourth-or fifth-order Runge-Kutta method,and the interval of absolute stability can be almost twice as much as the latter.Several numerical experiments are carried out to demonstrate the performance and accuracy as well as the stability of our proposed methods.

On expansion of estimated stability region:Theory,methodology,and application to power systems

The expansion of the estimated stability region plays an important role in the stability analysis of nonlinear systems.However,current literatures have not provided a complete mathematical description for this problem.This paper reveals that essentially the enlargement or the compression of the estimated stability region results directly from the diffeomorphism map,which is induced by the flow contained in the stability region.By proving that any integration algorithm with an order higher than one can approximately trace the flow of the system,a generalized methodology is proposed to construct various algorithms to realize the enlargement or the compression of the estimated stability region.With this methodology,two new algorithms based on symbolic calculation are suggested to reduce the computational burden.Furthermore,this methodology is applied to construct a scalable numerical algorithm to calculate the critical clearing time(CCT) of the power system for given faults.Tests on the IEEE 10-machine 39-bus system show that the computational results coincide well with the step-by-step simulation with high accuracy.