Time-delayed Control Research Articles

Stability Region of a Time-Delayed Single-Area Load Frequency Control System with Demand Response and Fractional-Order PI Controller

Bu araştırmada, dinamik talep cevabı (DTC) içeren zaman gecikmeli bir bölgeli yük frekans kontrol (YFK) sisteminde kesir dereceli oransal - integral (FOPI) denetleyicinin sistemin kararlılığını garantileyen parametre değerleri hesaplanmıştır. Tüm FOPI kontrolör kazançlarını hesaplamak için etkili ve basit bir grafiksel yöntem uygulanmıştır. Belirli bir zaman gecikmesi için yöntem, FOPI denetleyicinin parametre uzayında bir kararlılık bölgesi oluşturan tüm dengeleyici orantılı-integral (PI) denetleyici kazançlarını (𝐾𝑃, 𝐾𝐼) düzleminde hesaplamaktadır. Bu işlem, sistemin karakteristik denkleminin reel ve sanal kısımları sıfıra eşitlenerek gerçekleştirilmiştir. Son olarak, Matlab/Simulink ortamında yapılan benzetim çalışmaları yardımıyla FOPI denetleyici içeren bir bölgeli YFK-DTC sistemi için elde edilen sonuçlar doğrulanmıştır.

Communication-Efficient Event-Triggered Time-Delay Control and Its Application to Robot Manipulators

This article proposes a communication-efficient event-triggered time-delay control (ET-TDC) scheme, which is more intelligent, consumes fewer network resources, and is more suitable for practical applications, such as network control systems over bandwidth-limited communication channels. The proposed controller ensures a fast convergence rate and high tracking performance because it is based on TDCs that are well known for achieving high tracking performance. To maintain these properties, the proposed control scheme adopts a performance-preserving ET strategy, whereby the communication effort between the controllers and actuators can be significantly reduced. The ET condition of the proposed controller is devised to ensure system stability by using a Lyapunov function. Finally, the performance of the proposed ET-TDC is demonstrated through a numerical simulation and an experiment using a two-link robot manipulator.

Stability, Bifurcation, and Chaos Control of Two-Sided Market Competition

Benefitting from the popular uses of internet technologies, two-sided market has been playing an increasing prominent role in modern times. Users and developers can interact with each other through two-sided platforms. The two-sided market structure has been investigated profoundly. Through building a dynamics two-sided market model with bounded rational, stability conditions of the two-sided market competition system are presented. With the help of bifurcation diagram, Lyapunov exponent, and strange attractor, the stability of the two-sided market competition model is simulated. At last, we use the time-delayed feedback control (TDFC) method to control the chaos. Our main results are as follows: (1) when the adjustment speed of two-sided increases, the system becomes bifurcation, and chaos state happens finally. When the system is stable, the consumer fee is positive while developer fee is negative. (2) When the user externality increases, the stable area of the system increases, and the difference in user externality leads the whole system more stable. When the system is stable, the developer fee decreases. (3) The stable area becomes larger when developer externality increases; when the system is stable, the user fee becomes lower and developer fee becomes higher when developer externality increases. (4) The TDFC method is presented for controlling the chaos; we find that the system becomes more stable under the TDFC method.

A Deployment Approach Toward Time-Energy Efficient Robust Performance for Interceptors

Abstract This paper proposes an automatic time-energy efficient robust control (ATERC) deployment approach for selecting either a near-optimal closed-loop control law or a robust control law based on the requirement of the system. The near-optimal closed-loop control law is designed by applying the population-based sine-cosine algorithm (SCA) to the considered interceptor problem. While the robust control law is formulated by using an artificial time delayed control (TDC) approach. In presence of external disturbances, the ATERC methodology deploys the TDC-based robust guidance law to the interceptor, while in the absence of such uncertainties the SCA-based near-optimal guidance law is applied in order to improve the time-energy minimization. This guidance approach also incorporates input saturation which expands its applicability. Using Lyapunov stability analysis, this work establishes an uniformly ultimately bounded (UUB) stability for the discussed system on application of the proposed control approach. Extensive simulation studies involving nonmaneuvering targets and targets performing bank-to-bank maneuver, affirms the efficiency of the proposed approach.

Edge drop control of cold rolled silicon steel strip based on model predictive control

The closed-loop edge drop control system of cold rolled silicon steel strip is a typical time-delay control system, and the measurement time-delay has a great influence on the stability of the control system. In order to improve the stability and control accuracy of the closed-loop edge drop control system, an edge drop control model based on model predictive control for cold rolled silicon steel strip is proposed in this paper. In order to improve the accuracy of control system model parameters, the priori efficiency coefficients of work roll shifting (WRS) for edge drop control are determined by rolling experiments, and the online optimization of priori efficiency coefficients is realized by process data. On this basis, the time delay analysis of control system is completed by equal flow method, and a closed-loop control strategy for edge drop control is developed by introducing predictive aging value into model predictive control. Finally, trajectory smoothing is used to complete the smooth output of predicted control, and then improve the dynamic characteristics of the closed-loop edge drop control system. Theoretical analysis, simulation experiments and application show that the model prediction-based edge drop control method has higher accuracy and faster response characteristics compared with conventional control method, and can realize high-precision edge drop control process of cold rolled silicon steel strip.

Dynamic Gate Delay Time Control of Si/SiC Hybrid Switch for Loss Minimization in Voltage Source Inverter

The voltage source inverter (VSI) based on the Si/SiC hybrid switch (HyS) offers a better cost/performance tradeoff than the full-SiC VSI design. However, the Si/SiC hybrid VSI bears huge power losses with fixed gate turn-off delay time. In this article, a novel dynamic optimal gate turn-off delay time control method of Si/SiC HyS-based VSI is proposed to achieve the maximum efficiency over a wide load range. The optimal gate turn-off delay time is obtained by a load current-based mathematic power loss model. A 20-kHz 5-kW prototype of the single-phase constant current (CC) VSI using a 1200-V/25-A insulated gate bipolar transistor (IGBT) and a 1200-V/12.5-A SiC MOSFET is built to validate the proposed method. In comparison with the fixed gate turn-off delay time control method, the proposed method achieves 8% total power loss reduction and 0.24% conversion efficiency improvement at 1.5-kW output power.

A nonlinear time delay control influence in simulation aircraft tail contain a vertical cantilever beam

Nonlinear time delay saturation controller (NTDSC) is used to minimize the vibrations of a vertical cantilever beam simulated as an airplane tail within harmonic excitation force. In the case of primary and 1:2 internal resonance as a simultaneous resonance case, an analytic solution is obtained by employing the multiple time scale perturbation technique to solve the nonlinear differential equations and modeling the system with NTDSC. Time histories and Poincare portraits were created to demonstrate the system without and with controller. The time-history response, as well as the impacts of the parameters on the system and controller, were simulated numerically using the MATLAB program. A good match is found when the approximate solutions are compared to the numerical simulations via the Runge–Kutta method fourth-order (RK4). The stability investigation of the steady state solution in the studied simultaneous resonance case is reviewed and analyzed via the Routh-Huriwitz approach. The impact of controller parameters and time delays on system response curves are examined. Also, the operation’s safe zone is established from the outcomes of the effect via various values of time delays on the system after adding the control scheme. The numerical and analytical solutions at time-history were compared using the MATLAB program to confirm their comparability. The outcomes of this study were used to develop a theoretical foundation for the system’s design and construction. A comparison is made with recently released papers to appear the difference between this study and the others.

Observer-based feedback stabilization of a reaction-diffusion equation with variable coefficients and boundary input delay

Abstract In this paper, we consider the stabilization issues of a reaction-diffusion equation with variable coefficients and boundary input delay. At first, we design an observer based on the system output to estimate the state of the system. Due to the present of time delay in control, we design a dynamic feedback controller based on the state information of observer, that is called the integral-type controller. By selecting appropriate kernel functions, we prove that the closed-loop system is exponentially stable. Herein, our approach mainly is based on the idea of ‘feedback equivalence’. By some equivalence transformations, we establish connection between the closed-loop system and a stable system.

Ritz approximate method for solving delay fractional optimal control problems

In this paper, a numerical method based on the Müntz–Legendre polynomials for solving a class of time-delay fractional optimal control problems (TDFOCPs) is presented. The concept of fractional derivatives is considered in the Caputo sense. The key point of the applied method is that the initial and boundary conditions are imposed upon the approximations of state and control functions. First, the unknown state or control and their delayed functions are approximated by the Müntz–Legendre polynomials basis using the Ritz method then the next one is calculated through the given fractional differential equation. By substituting the estimated values in the cost function, the TDFOCP is converted to an unconstrained linear or nonlinear optimization problem. The convergence of the suggested method is extensively argued and several illustrative examples are presented to show the applicability and effectiveness of the method. It is shown that only a few terms of Müntz–Legendre polynomials are needed for obtaining the high accuracy and satisfactory results. The obtained results are compared with the available results in the literature to demonstrate the superiority of the applied approach. Furthermore, the approximated solutions agree with exact solutions and as α approaches an integer value, the method provides solution for the integer-order optimal control problem.

Optimal transmission of messages in computer networks – an optimal control problem involving control-dependent time-delayed arguments

In this paper, we find the optimal transmission of messages in computer networks. This problem has been formulated as a nondelayed optimal control problem in several recent papers on TCP (transmission control protocol). Since the actual transmission of messages from origins to destinations should consist of both forward transmission delays of the buffers and latency of the links, we remodel the problem as a time-delayed optimal control problem consisting of both control-dependent time-delayed arguments and discrete time-delayed arguments. We then develop a modified control parameterization method for solving this time-delayed optimal control problem. The gradients of the new objective function and constraint functions generated by this modified control parametrization method are derived. A numerical example is solved by using the time-delayed version of the problem that we formulate, as well as the nondelayed version of the problem in the literature. Numerical results clearly illustrate the efficiency of the modified control parameterization method for solving both versions of this optimal transmission problem. Comparison of results of the two versions concerning the optimal transmission rates at the origins, the optimal output flow rates at the destination, and the queue sizes at the buffers are obtained. These comparison results clearly reflect how the optimal transmission of messages in computer networks in real life can be affected by both the forward transmission delays of the buffers and the latency of the links.

Review on control systems and control strategies for excavators

The product performance of excavators continuously improves with industrial development. However, unsighted improvements in the performance of excavators cannot meet the emission standards. Therefore, considerable research on energy conservation, high efficiency, and accurate control strategy should be conducted. At present, power matching research is performed because of the inconvenience of energy transmission. The technical advantages of hybrid power provide a better research direction for the energy-saving research of excavators. Intelligent control algorithms, such as sliding mode control and time-delay control, are added to the control system to improve the trajectory accuracy in excavator trajectory control. The intelligent operation of excavators reduces the requirements of the operating environment and improves operation economy in remote, complex, and dangerous operation spaces. The research statuses of excavators in power matching, hybrid control, trajectory control, and intelligent autonomous operation are reviewed. Finally, six conclusions about the current research status are drawn.

Time-Delayed Active Control of Stall Flutter for an Airfoil via Camber Morphing

This paper investigates a time-delayed active control for suppressing the stall flutter via camber morphing. A time-domain fluid–structure–control coupled solver is presented. This solver composes a computational fluid dynamics (CFD)-based flow solver with dynamic mesh techniques, a one- degree-of-freedom structural solver for a pitching airfoil, and a time-delayed proportional–differential controller that actuates the nonlinear camber morphing of the airfoil. The modules of the structural solver and the controller are both implanted into the CFD-based flow solver OpenFOAM. The proposed solver is first validated with the aerodynamic stall and stall-flutter experimental results, and then it is used for investigating the stall-flutter suppression performance in the time domain with nonlinear camber morphing. The numerical results with various time delays in the active control suggest that the time delay significantly impacts the response suppression effect of the stall flutter. The closed-loop controls with time delays ranging from 0.01 to 0.15 s can suppress stall flutter. The suppression effect reaches the best when as it reduces the amplitude of the limit-cycle response by 60%. The active control mechanism of the time-delayed camber morphing is analyzed in terms of the flow pattern and energy transfer in depth.

MTN-based recursive d-step-ahead predictive control of MIMO nonlinear systems with unknown input time-delay in industrial process

PurposeThis paper aims to provide a precise tracking control scheme for multi-input multi-output “MIMO” nonlinear systems with unknown input time-delay in industrial process.Design/methodology/approachThe predictive control scheme based on multi-dimensional Taylor network (MTN) model is proposed. First, for the unknown input time-delay, the cross-correlation function is used to identify the input time-delay through just the input and output data. And then, the scheme of predictive control is designed based on the MTN model. It goes as follows: a recursive d-step-ahead MTN predictive model is developed to compensate the influence of time-delay, and the extended Kalman filter (EKF) algorithm is applied for its learning; the multistep predictive objective function is designed, and the optimal controlled output is determined by iterative refinement; and the convergence of MTN predictive model and the stability of closed-loop system are proved.FindingsSimulation results show that the proposed scheme is of desirable generality and capable of performing the tracking control for MIMO nonlinear systems with unknown input time-delay in industrial process effectively, such as the continuous stirred tank reactor (CSTR) process, which provides a considerably improved performance and effectiveness. The proposed scheme promises strong robustness, low complexity and easy implementation.Research limitations/implicationsFor the limitations of proposed scheme, the time-invariant time-delay is only considered in time-delay identification and control schemes. And the CSTR process is only introduced to prove that the proposed scheme can adapt to practical industrial scenario.Originality/valueThe originality of the paper is that the proposed MTN control scheme has good tracking performance, which solves the influence of time-delay, coupling and nonlinearity and the real-time performance for MIMO nonlinear systems with unknown input time-delay.

Parameter estimation in uncertain delay differential equations via the method of moments

Uncertain delay differential equations model time-delayed automatic control systems in which noises are described by Liu process. Parameter estimation plays a pivotal part in the applications of uncertain delay differential equations. In this paper, we first obtain a difference equation of uncertain delay differential equations by the forward Euler’s method. A function of the parameter is given by the difference equation, which is verified to obey the standard normal uncertainty distribution. By using the method of moments, we employ the observed data to obtain the empirical moments that equal the moments given by the standard normal uncertainty distribution, the estimated value of parameters are derived. Moreover, some examples are investigated to demonstrate that the method of moments is effective. Finally, we provide an uncertain delay logistic model to describe the population dynamics of American by using the method of parameter estimation proposed in this paper.

Delay-Dependent Stability Analysis and Design of Input-delayed Systems by Smooth Sliding Mode Control: Lagrange Theorem Approach

A new smooth sliding mode control design methodology based on Lagrange mean value theorem is proposed for stabilization of single input delayed systems. The Lagrange mean value theorem as a basic theorem of calculus is used for the design of linear sliding mode time-delay controller for the first time. This controller satisfies the sliding condition using a Zhou and Fisher type continuous control law eliminating the chattering effect. The constructive delay-dependent asymptotically stable sliding conditions are obtained by using the augmented Lyapunov-Krasovskii functionals and formulated in terms of simple (4x4)-matrix inequality with scalar elements. Developed design approach can be extended to robust stabilization of sliding system with unknown but bounded input delay. The maximum upper bounds of delay size can be found by using simple optimization algorithms. Helicopter hover control is considered as a design example for illustrating the usefulness of smooth sliding mode approach. Unstable helicopter dynamics are successfully stabilized by using linear sliding mode time-delay controller. For example, settling time is about 20 sec. Therefore, simulation results confirmed the effectiveness of proposed design methodology. Apparently, the proposed method has a great potential in design of time-delayed controllers.

Global [formula omitted]-stabilization of quaternion-valued inertial BAM neural networks with time-varying delays via time-delayed impulsive control

This article deals with global μ-stabilization of quaternion-valued inertial bidirectional associative memory neural networks (QVIBAMNNs) with time-varying delays via time-delayed impulsive control. Firstly, the existence and uniqueness of the equilibrium point are proved by the homeomorphism mapping method. Then, based on an improved differential inequality, sufficient conditions for global μ-stabilization of QVIBAMNNs via time-delayed impulsive control are obtained. Significantly, the activation function in this paper is an extension of Lipschitz condition, which is superior to general quaternion-valued activation function. And quaternion is not required to be decomposed into real or complex values in this paper. Ultimately, some numerical simulations have proved the feasibility of the theorems.

Computation of Delay-Dependent Stability Regions for Electric Power Systems with Time Delay

Bu çalışma, bir özdeğer izleme yöntemi kullanarak güç sistem dengeleyici (GSD) ve otomatik gerilim regülatörü (OGR) içeren zaman gecikmeli jeneratör uyarma kontrol sisteminin zaman gecikmeleri düzleminde kararlılık bölgesini elde etmeyi ve zaman gecikmesine bağlı kararlılık analizini incelemektedir. Elektrik güç sistemlerinde gerilim ve frekans kararlılığının sürdürülmesi bakımından haberleşme alt yapısına ve ölçme sistemlerine ihtiyaç duyulmaktadır. Ancak, haberleşme alt yapısı ve ölçme sistemlerinden dolayı sistemin dinamik davranışını ve kararlılığını olumsuz etkileyen zaman gecikmeleri meydana gelmektedir. Bu çalışmada, jeneratör uyarma kontrol sisteminin durum denklem modellerini kullanarak özdeğerlerini ve bu özdeğerlere karşılık gelen zaman gecikmesi değerlerini belirleyen bir yöntem kullanılmıştır. Ayrıca, bu gecikme değerleri kullanılarak gecikmeye bağlı bir kararlılık bölgesi elde edilmiştir. Kararlılık analizleri için, GSD ve OGR içeren tek makineli sonsuz baralı (TMSB) bir güç sistemi seçilmiştir. Gecikmeye bağlı kararlılık bölgelerinin doğruluğu, zaman düzleminde gerçekleştirilen benzetim çalışmaları ve zaman gecikmeli sistemlerin köklerini kompleks düzlemde hesaplayan QPmR (the quasi-polynomial mapping-based root finder) algoritması ile gösterilmiştir.

Delay-based stabilisation and strong stabilisation of LTI systems by nonsmooth constrained optimisation

Stabilisation and strong stabilisation (i.e. the problem of stabilising by a stable controller) of linear time-invariant (LTI) multi-input multi-output systems are considered. The considered systems may be finite-dimensional or time-delay systems, which may have multiple discrete time delays. The controllers to be designed may also be either finite-dimensional or time-delay LTI controllers. In the controller design phase, a constrained nonsmooth optimisation-based design method is employed. The effectiveness of the proposed method is illustrated through various benchmark examples which are solved by using the recently developed Matlab-based software called DrStabilization . The examples also show that, in many cases, time-delay controllers may have certain advantages over conventional finite-dimensional controllers.

Bifurcation Analysis of Periodic Oscillation in a Hematopoietic Stem Cells Model with Time Delay Control

Underlying the state feedback control, the complex dynamical disease of the hematopoietic stem cells model based on Mackey’s mathematical description is analyzed. The bifurcating periodical oscillation solutions of the system are continued by applying numerical simulation method. The limit point cycle bifurcation and period doubling bifurcation are observed frequently in the continuation process. The attraction basins of the positive equilibrium solution shrink as the differentiate rate is ascending and the observed Mobiüs strain is simulated with boundary as the period-2 solution. The period doubling bifurcation leads to period-2, period-4, and period-8 solutions which are simulated. Starting from period doubling bifurcation point, the continuation of the bifurcating solution routes to homoclinic solution is finished. The simulation results improve the comprehension related to the spontaneous dynamical character manifested in the hematopoietic stem cells model.

Bifurcation control of a delayed fractional-order prey-predator model with cannibalism and disease

In this paper, the bifurcation control for a fractional-order delayed prey-predator system with disease and cannibalism is investigated. Firstly, the existence, uniqueness and non-negativity of the solutions are studies, and the stability of equilibrium points are discussed. Next, taking time delay as the bifurcation parameter, the conditions of creation for Hopf bifurcation are confirmed. Then, two feedback controllers are introduced, which successfully control the Hopf bifurcation, and bifurcation control of the two controllers are simply compared theoretically. Finally, numerical simulations show that cannibalism has an significant influence in controlling the stability of the model, and when the parameters are appropriate, the disease can be removed. Meanwhile, the feedback controllers can control the bifurcation well. In general, the control effect of time-delay feedback controller should be better than that of traditional feedback controller. However, we found that the control effect of the traditional feedback controller is better than the time-delay feedback controller, the control effect completely depends on the selection of parameters.