Top PDF Robust Stability of Fractional Order Time-Delay Control Systems: A Graphical Approach

Robust Stability of Fractional Order Time-Delay Control Systems: A Graphical Approach

Robust Stability of Fractional Order Time-Delay Control Systems: A Graphical Approach

The paper deals with a graphical approach to investigation of robust stability for a feedback control loop with an uncertain fractional order time-delay plant and integer order or fractional order controller. Robust stability analysis is based on plotting the value sets for a suitable range of frequencies and subsequent verification of the zero exclusion condition fulfillment. The computational examples present the typical shapes of the value sets of a family of closed-loop characteristic quasipolynomials for a fractional order plant with uncertain gain, time constant, or time-delay term, respectively, and also for combined cases. Moreover, the practically oriented example focused on robust stability analysis of main irrigation canal pool controlled by either classical integer order PID or fractional order PI controller is included as well.
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A PID Controller Design Approach for Robust Stability of Arbitrary Order Plants with Time Delays

A PID Controller Design Approach for Robust Stability of Arbitrary Order Plants with Time Delays

The robust controller design method suggested here is capable of ensuring closed loop stability for arbitrary order plants with additive uncertainty, which makes is applicable for wide range of plants. Future research can be done in the area of controller design for multi-area power system generation control, multivariable feed-back control systems, and robust performance for arbitrary order plants with additive uncertainty.

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Stability and time delay tolerance analysis approach for networked control systems

Stability and time delay tolerance analysis approach for networked control systems

simpler procedure, and it should have no difficulties for prac- tical design engineers to accept this approach. Clearly, the MADB with the first-order finite difference approximation is comparable with the LMI method. Furthermore, we found good agreement between the third-order finite difference approximation and the fourth-order Pade approximation. The simulation based results for the MADB show that the estimated MADB through the proposed method sufficiently achieves the system stability. A simple controller design method has been developed by the authors based on the method presented in this paper. In the controller design method a stabilizing controller can be derived for a given network time delay. In all the case studies or examples, only linear system examples are given. The method is lim- ited to linear systems only. The authors are now working on extending the methods to nonlinear systems, such as, multiconverter and inverter system and engine and electrical power generation systems [32, 33].
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Robust Adaptive Control for Fractional-order Financial Chaotic Systems with System Uncertainties and External Disturbances

Robust Adaptive Control for Fractional-order Financial Chaotic Systems with System Uncertainties and External Disturbances

Up to now, controlling and synchronizing chaos in fractional-order financial systems has also been in- vestigated, for example, in [1, 10, 13, 14, 27, 32, 41, 43, 47, 46]. In [14], a sliding mode controller was designed to synchronize fractional-order financial systems in master-slave structure. In [41], a nec- essary condition was given to show the existence of 1-scroll, 2-scroll even multi-scroll chaotic at- tractors in fractional-order financial systems. Ac- tive control method was used in [27, 47]. An active controller with multiple conflicting objectives was constructed in [32]. It should be highlighted that a key assumption in the above literatures is that the model of the financial systems should be known. However, most of real world systems are subjected to system uncertainties and external disturbances, especially in financial systems [7, 8, 27, 33, 34, 36, 44]. On the other hand, in financial systems, sys- tem uncertainties do exist because of limited siz- es of weather variables, political events, and other human factors. The existence of systems uncer- tainties and external disturbances could decrease the control performance, or even lead to instability of the system [35]. It is meaningful to consider the control of financial systems with system uncer- tainties and external disturbances. Thanks to the works of Li et al. [20], the Lyapunov direct method (also called the Lyapunov second method) has been extended to fractional-order nonlinear systems. In this paper, a robust adaptive controller is proposed to solve the control problem of fractional-order fi- nancial chaotic systems with both system uncer- tainties and bounded external disturbances. The fractional-order Lyapunov approach is used to an- alyze the stability of the system. Specifically, the main contributions of this study include:
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Fractional-Order Time Delay Compensation in Deadbeat Control for Power Converters

Fractional-Order Time Delay Compensation in Deadbeat Control for Power Converters

The problem of time delay compensation in deadbeat control for power converters are considered but not solved systematically, by far. A linear phase-lead compensation solution is successfully employed in repetitive control systems to compensate the time delay [14]-[16]. However, it is impractical to be adopted in the conventional deadbeat control frame due to its incausal lead-time item. A state estimator is adopted for compensation of computational delay [3]. Also focused on this problem, another simple design method of two steps forward prediction approach is proposed in the frame of model predictive control [10], [17], [18]. In these solutions, computational delay effects are effectively removed and control accuracy is prominently improved. However, as mentioned above, apart from computational delay, many other factors lead to the delay problem in practical systems. In these cases, the above mentioned approaches are not suitable and fail to achieve satisfying control performance. Therefore, a universal delay compensation approach for the deadbeat control schemes should be investigated in practical applications.
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Topological Control and Stability of Dynamic Fractional Order Systems with Generalized Memory

Topological Control and Stability of Dynamic Fractional Order Systems with Generalized Memory

. (10) Remark. Important in the theory of nonlinear physical fractional-order systems is the use the dynamics caused by their observed. Continuous flow in phase space determines the behavior of the system can be studied using a discrete display the induced flow at the section of Poincare. It is a relativistic terms in the rights continuous flow and its discrete in time delay.

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A numerical approach for variable-order fractional unified chaotic systems with time-delay

A numerical approach for variable-order fractional unified chaotic systems with time-delay

The growth of practical applications in the use of fractional calculus has attracted the attention of many engineers and researchers. The advantages of using fractional operators have been shown in the literature [5, 7, 25, 27, 28, 33]. For instance, it has been shown that the behavior of viscoelastic materials can be correctly described by a fractional model with a small number of model parameters compared to using con- ventionals integer-order models with a large number of model parameters [9, 11, 16]. In addition, it has been shown that the fractional-order controllers are more sophisti- cated than regular integer-order controllers due to employing more control parameters [12].
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Disturbance-observer-based robust control for time delay uncertain systems

Disturbance-observer-based robust control for time delay uncertain systems

The guaranteed cost control was investigated for parameter uncertain systems with time delay in [1]. Kim [2] studied the robust stability of time-delayed linear systems with uncertainties. The problem of delay-dependent robust stability was investigated for systems with time-varying structured un- certainties and time-varying delays [3]. A robust controller was proposed in [4] for delay-dependent neutral systems with mixed delays and time-varying structured uncertainties. Sliding mode control scheme was presented for the robust stabilization of uncertain linear input-delay systems with non- linear parametric perturbations in [5]. In [6], the stability of systems in the presence of bounded uncertain time-varying delays in the feedback loop was analysed. Han [7] studied the absolute sta- bility for a class of nonlinear neutral systems using a discretized Lyapunov functional approach. In [8], an adaptive neural control scheme was proposed for a class of uncertain multi-input multi-output (MIMO) nonlinear state time-varying delay systems in a triangular control structure with unknown nonlinear dead-zones and gain signs.
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Analysis of Fractional Order Control System with Performance and Stability

Analysis of Fractional Order Control System with Performance and Stability

In this paper, a new approach to stability for fractional order control system is proposed. Here a dynamic system whose behavior can be modeled by means of differential equations involving fractional derivatives. Applying Laplace transforms to such equations, and assuming zero initial conditions, causes transfer functions with no integer powers of the Laplace transform variable s to appear. In recent time, the application of fractional derivatives has become quite apparent in modeling mechanical and electrical properties of real materials. Fractional integrals and derivatives have originated wide application in the control systems. The measured system and the controller are termed by a set of fractional order differential equations.
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Prediction-based Adaptive Robust Control for a Class of Uncertain Time-delay Systems

Prediction-based Adaptive Robust Control for a Class of Uncertain Time-delay Systems

et al. [2015], disturbance observer method was proposed to ensure that the teleoperation of motion control systems was robust to model uncertainties and time-delay. This involved the design of ad hoc flters, namely, a high-pass flter to handle high-frequency noises and a low-pass flter to compensate for the e“ect of delay and disturbances assumed to have low-frequency variations. In Bresch-Pietri et al. [2012], an adaptive control scheme was proposed to completely reject a constant disturbance in the presence of unknown but bounded constant input delay and uncertain parameters. In Han et al. [2012], a sliding mode control (SMC) was proposed in the presence of time-varying in- put delay and bounded matched disturbances to achieve ultimate boundedness of the closed loop system using a singular perturbation approach. The idea of adaptive robust control (ARC) with rigorous stability analysis and its application to motion control problems was presented in Yao and Jiang [2010] and references therein. However, their control law does not address delays in the input. Re- cently, in L´echapp´e et al. [2015b], a new prediction scheme with full state feedback has been proposed that is robust to external disturbances in the presence of input delay, then extended to output feedback in L´echapp´e et al. [2015a], and then to an unknown delay case in L´echapp´e et al. [2016]. But they do not address the e“ect of parametric uncertainties explicitly.
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Robust Stabilization of Fractional Order Systems with Interval Uncertainties via Fractional Order Controllers

Robust Stabilization of Fractional Order Systems with Interval Uncertainties via Fractional Order Controllers

We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.
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A survey of recent advances in fractional order control for time delay systems

A survey of recent advances in fractional order control for time delay systems

Tang et al. [4] propose a novel fractional sliding mode strat- egy with a dynamic essence in order to control several delay based chaotic systems in a master slave configuration. The control strategy is simulated on a multivariable delay chaotic robot by taking into consideration the chattering problem of the sliding mode control. Another innovative sliding mode strategy is detailed in [74] with applications upon a nonlin- ear robotic exoskeleton. Parameter uncertainties and external disturbances lead to a time delay estimation based model-free fractional order nonsingular fast terminal sliding mode con- trol (MFF-TSM), The fractional order controller is designed to for tracking performance, fast speed of convergence, and chatter-free control inputs lacking singularities. Asymptotical stability is also investigated through the Lyapunov theorem. Cascade control structures for delayed systems are exempli- fied in [76]. Both master and slave controllers are of frac- tional order. For the slave controller, a fractional order PD is chosen for the time delayed process, while for the master control, the fractional order SMC law is employed. Numeri- cal simulations validated the proposed approach in terms of time domain performance and stability of the closed loop system. Bode’s ideal transfer function and internal model control principles are used in [57] to analytically develop a fractional order controller combined with a modified Smith predictor targeting robustness to process’ uncertainties. The simulations prove the veracity of the method for systems with long time delays. Another control combination is done in [77] where a hierarchical structure has an event-based supervisor and a lower level fractional order PI controller applied to a wind turbine. The purpose of the supervisor is to analyze and determine the states of the process, while the fractional order controller’s main purpose is to ensure maximum power generation with peak performance and reliability.
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Stability of a Class of Neutral Time Delay Systems with a Robust Control

Stability of a Class of Neutral Time Delay Systems with a Robust Control

Lyapunov stability is a general theory available for any differential equation. Over the past researches on time-delay systems, many useful approaches are applied to guarantee the stability or stabilization of systems. The application of Lyapunov-Krasovskii functional theory has first started for system without neither uncertainties nor control [2] [5], some robust stability conditions based on LMI approach are given. Then, the guaranteed cost control problem for neutral time delay system with feed-back control is investigated. Some papers are interested on stability and stabilization of this type of system where a linear–quadratic cost function is considered
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Asymptotic stability analysis of fractional order neutral systems with time delay

Asymptotic stability analysis of fractional order neutral systems with time delay

Recently, a finite-time stability analysis of fractional time-delay systems has first been presented and reported in []. But until now, only a few papers studied the stability of fractional neutral systems. Though the Lyapunov approach of nonlinear fractional neutral system was extended in [], it is difficult to use the Lyapunov method to study the stabil- ity of fractional neutral systems due to the complicated fractional derivatives. However, based on the algebraic approach, Zhang et al. [] obtained some sufficient conditions for fractional neutral dynamical systems.
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Conformable Fractional Order Sliding Mode Control for a Class of Fractional Order Chaotic Systems

Conformable Fractional Order Sliding Mode Control for a Class of Fractional Order Chaotic Systems

In this paper, a novel conformable fractional order (FO) sliding mode control technique is studied for a class of FO chaotic systems in the presence of uncertainties and disturbances. First, a novel FO nonlinear surface based on conformable FO calculus is proposed to design the FO sliding mode controller. Then, asymptotic stability of the controller is derived by means of the Lyapunov direct method via conformable FO operators. The stability analysis is performed in the sliding and reaching phase. In addition, the realization of reaching phase is guaranteed in finite time and the reaching time is calculated analytically. The proposed control approach has some superiorities. Reduction of the chattering phenomenon, high robustness against the uncertainty and external disturbance, and fast convergence speed are the main advantages of the proposed control scheme. Moreover, it has simple calculations because of using conformable FO operators in the control design. The numerical simulations verify the efficiency of the proposed controller.
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Delay-partitioning approach to stability criteria for T-S fuzzy systems with time-varying delay

Delay-partitioning approach to stability criteria for T-S fuzzy systems with time-varying delay

fuzzy systems with interval time-varying delay. Most recently, a novel LKF is es- tablished via the delay-decomposition method, then by means of employing the reciprocally convex approach, [7] has achieved less conservative results than those in [5, 10, 14, 15, 16, 17, 18] for the uncertain T-S fuzzy systems with time-varying delay. However, when revisiting this problem, we find that the aforementioned works still leave plenty of room for improvement.

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Robust stabilization of hybrid uncertain stochastic systems with time varying delay by discrete time feedback control

Robust stabilization of hybrid uncertain stochastic systems with time varying delay by discrete time feedback control

As an important class of hybrid systems, hybrid stochastic differential equations (SDEs) (also known as SDEs with Markovian switching) have been widely employed to model many practical systems that have variable structures subject to random abrupt changes, which may result from abrupt phenomena such as random failures and repairs of compo- nents, sudden environment changes, etc. One of the important issues in the study of hybrid SDEs is the automatic control, with subsequent emphasis being placed on the analysis of stability. A great number of significant results on this subject have been reported in the literature; see, for instance, [–] and the references therein. In particular, we refer the reader to the book [].
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Robust stability and stabilization of LTI fractional order systems with poly topic and two norm bounded uncertainties

Robust stability and stabilization of LTI fractional order systems with poly topic and two norm bounded uncertainties

The fractional calculus dates from the 17th century [1], and it can be defined as a classical mathematical notion and a generalization of the ordinary differentiation and integration not necessarily integer. The significance of fractional-order representation is that it is more adequate to describe real world systems than those of integer-order models [2]. Fractional- order calculus is focused on the whole time and space, but the integer-order calculus only concerned with local attribute at particular time and a certain position [3]. Due to these advantages, fractional calculus is developing fast [4, 5], and its various applications are extensively used in many fields of science and engineering: in material engineering [6], chaos systems [7–9], economic systems [10], robotics [11], and in many more [12–16].
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Absolute Stability of Discrete Time Systems with Delay

Absolute Stability of Discrete Time Systems with Delay

We investigate the stability of nonlinear nonautonomous discrete-time systems with delaying ar- guments, whose linear part has slowly varying coefficients, and the nonlinear part has linear majo- rants. Based on the “freezing” technique to discrete-time systems, we derive explicit conditions for the absolute stability of the zero solution of such systems.

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Structured robust stability and boundedness of nonlinear hybrid delay systems

Structured robust stability and boundedness of nonlinear hybrid delay systems

It is very easy to verify this local Lipschitz assumption. For example, the assumption is satisfied if f and g are continuously differentiable in x and y or they are differentiable in x and y with locally bounded derivatives. It is known that this classical assumption covers many hybrid SDDEs in the real world (see, e.g., books [23, 24] and the references therein). Of course, this assumption is not enough to guarantee the global solution (i.e., no explosion at a finite time). A standard additional condition for the existence and uniqueness of the global solution of the SDDE (4.1) would be the linear growth condition (see, e.g., [18, 23]). However, our aim here is to study the structured robust stability and boundedness of highly nonlinear SDDEs that do not satisfy the linear growth condition. We hence need to propose alternative assumptions.
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