Delayed State Feedback Control Research Articles

Wind and Wave-Induced Vibration Reduction Control for Floating Offshore Wind Turbine Using Delayed Signals

Active vibration control is a critical issue of the wind turbine in the field of marine energy. First, based on a three-degree-of-freedom wind turbine, a state space model subject to wind and wave loads is obtained. Then, a delayed state feedback control scheme is illustrated to reduce the vibration of platform pitch angle and tower top foreaft displacement, where the control channel includes time-delay state signals. The designed controller’s existence conditions are investigated. The simulation results show that the delayed feedback H∞ controller can significantly suppress wind- and wave-induced vibration of the wind turbine. Furthermore, it presents potential advantages over the delay-free feedback H∞ controller and the classic linear quadratic regulator in two aspects: vibration control performance and control cost.

Stability analysis of a class of variable fractional-order uncertain neutral-type systems with time-varying delay

Variable fractional-order (VFO) differential equations are a beneficial tool for describing the nonlinear behavior of complex dynamical phenomena. In comparison with the constant FO derivatives, it describes the memory properties of such systems that can vary in the time domain and spatial location. This article investigates the stability and stabilization of VFO neutral systems in the presence of time-varying structured uncertainties and time-varying delay. FO Lyapunov theorem is adopted to achieve order-dependent and delay-dependent criteria for both nominal and uncertain VFO neutral delay systems. The obtained conditions are given in respect of linear matrix inequality by designing a delayed state feedback controller. Simulations verify the main results.

Finite-Time Synchronization of Neural Networks With Infinite Discrete Time-Varying Delays and Discontinuous Activations.

This article investigates finite-time synchronization of neural networks (NNs) with infinite discrete time-varying delays and discontinuous activations (DDNNs). By virtue of theory of differential inclusions, comparison strategies, and inequality techniques, finite-time synchronization of the underlying DDNNs can be developed via a discontinuous state feedback control law, and the synchronous settling time can be estimated. The delayed state feedback controller and finite-time stability theorem are not employed during the analysis. As a special case, finite-time synchronization of NNs with bounded delays and discontinuous activations is given. Finally, two examples are provided to illustrate the validity of the theories.

Output tracking control for state-dependent switched systems with input delay

This paper investigates the H∞ output tracking control problem for state-dependent switched systems with delays, where the existence of input delay is fully considered. Based on hysteresis switching strategy, a state-dependent switching law is designed through dividing the whole state space. In contrast to general time-dependent switching, the switching instants need not be predetermined and all subsystems can be unstable under state-dependent switching. Meanwhile, we design a delayed state-feedback controller that takes into account the effect of input delay. In the framework of Lyapunov–Krasovskii (L-K) functional method, some sufficient conditions for ensuring the H∞ output tracking performance of the switched system with delays are obtained by employing state-dependent switching and delayed state-feedback control. Moreover, the information of input delay and state delay are both included in linear matrix inequalities (LMIs). In addition, the obtained results are further extended to the system with parameter uncertainties by establishing the corresponding state-dependent switching law and some sufficient conditions. The effectiveness of the proposed results is demonstrated by two examples and their simulations.

Suppress chatter in milling of thin-walled parts via fixture with active support

In this study, we designed an integrated fixture system using eddy current sensors and piezoelectric actuators. With this system, active supporting forces are exerted on thin-walled workpieces to adjust their stiffness in a real-time manner and thus to suppress chatter in milling. When modeling this system, we used a mass–stiffness–damping element to characterize the dynamic behavior of the actuator under high-speed responses, and we considered the electromechanical coupling between the mechanical elements and the drive circuit of the actuator. We then proposed an optimal delayed state feedback controller for the closed-loop system. The delayed state is obtained by introducing the time delay in milling dynamics into the regular state feedback, and the optimal gain is worked out through the differential quadrature and gradient descent, which is a much more computationally efficient method than the classic semi-discretization. Among all similar approaches, our strategy leads to the largest stability region for milling of thin-walled parts and requires the least energy input, which are proved by simulations and experiments.

Sliding mode control with integral sliding surface for linear uncertain impulsive systems with time delays

This paper devotes to the problem of sliding mode control (SMC) for linear uncertain impulsive systems with time delays and matched disturbances. An SMC scheme based on a novel integral-type sliding function with an impulse regulation term is proposed. The sliding function is designed so that the finite-time reachability of the sliding surface can be guaranteed for any given impulses. A linear delayed state feedback control law with switching gains is introduced to stabilize the resulting sliding mode dynamics, which is able to improve robust performance against parameter uncertainty. The existence conditions of the delayed state feedback control laws are derived by employing a piecewise discontinuous Lyapunov functional. It is shown that the desired switching gains can be obtained by solving a set of LMIs through a convex optimization procedure. Finally, the correctness and validity of the theoretical results are fully verified in a practical application with several different types of impulse inputs.

On Stability Switches and Bifurcation of the Modified Autonomous Van der Pol–Duffing Equations via Delayed State Feedback Control

This paper considers the Modified Autonomous Van der Pol–Duffing equation subjected to dynamic state feedback, which can well characterize the dynamic behaviors of the nonlinear dynamical systems. Both the issues of local stability switches and the Hopf bifurcation versus time delay are investigated. Associating with the τ decomposition strategy and the center manifold theory, the delay stable intervals and the direction and stability of the Hopf bifurcation are all determined. Specifically, the computation of purely imaginary roots (symmetry to the real axis), the positive real root formula for cubic equation and the sophisticated bilinear form of adjoint operators are proposed, which make the calculations mentioned in our discussion unified and simple. Finally, the typical numerical examples are shown to illustrate the correctness and effectiveness of the practical technique.

Improved robustH∞stability analysis and stabilization of uncertain systems with stochastic input time‐varying delays

AbstractThis article focus on the robustH∞stability analysis and controller design for a class of uncertain and disturbed continuous‐time systems with input time‐varying delays characterized by stochastic Bernoulli distributions. First, robustH∞stability conditions for linear continuous systems with interval input time‐varying delays is investigated. A delay‐distribution‐approach is considered to reduce the conservatism of the stability conditions from the convenient selection of a Lyapunov–Krasovskii functional (LKF), which considers both the lower and upper bounds of the stochastic time‐varying delay to derive new delay‐dependentH∞stability conditions in terms of linear matrix inequalities (LMIs). Then, derived from the proposed stability conditions, LMI‐based conditions for the design of stabilizing robustH∞delayed state feedback controller are proposed. Finally, five numerical examples are considered to show the effectiveness of the proposed stability analysis and controller design conditions, in comparison to previous related results.

An observer-based H∞ linear parameter varying controller for time delayed linear parameter varying systems using dilated linear matrix inequalities and Wirtinger inequality

In this study, we give a method for the design of linear parameter varying (LPV) observers in order to perform an LPV time delayed state feedback control for LPV systems with time varying delay. We derive some tractable analysis and synthesis conditions expressed in terms of linear matrix inequalities (LMIs). We show how it is possible to reduce significantly the conservatism of the quadratic approach by using parameter dependent Lyapunov-Krasovskii functional and LMI dilation techniques jointed to the Wirtinger integral inequality. We also present a method that makes it possible to do without the separation principle when determining the observer and the state feedback parameters. The synthesis problem is formulated without this principle. A numerical example is provided to illustrate the effectiveness of our approach that leads to a better H∞ level compared with other results, from literature, for the same example.

Finite-time stability of coupled impulsive neural networks with time-varying delays and saturating actuators

The paper considers the stability of coupled impulsive neural networks with time-varying delays and saturating actuators in finite time. Based on a delayed state feedback controller, the stability of coupled impulsive neural networks with time-varying delays and saturating actuators can be achieved in finite time. Combined with Lyapunov-based finite-time stability theory, some sufficient conditions are obtained to ensure the stability of coupled impulsive neural networks with time-varying delays and saturating actuators in finite time by using polytopic representation approach and sector nonlinearity model approach, respectively. Moreover, the setting time of coupled impulsive neural networks with saturating actuators is given, and it is found to be related to both the initial state and impulse effect. Furthermore, as special cases, some finite-time stability results of coupled impulsive neural networks with saturating actuators are given under a memoryless controller. Finally, two simulation examples are used to test the effectiveness of the obtained results.

Fixed-time synchronization of stochastic memristor-based neural networks with adaptive control

In this study, we consider the fixed-time synchronization problem for stochastic memristor-based neural networks (MNNs) via two different controllers. First, a new stochastic differential equation is established using differential inclusions and set-valued maps. Next, two kinds of control protocols are designed, including a nonlinear delayed state feedback control scheme and a novel adaptive control strategy, by which fixed-time synchronization of MNNs can be achieved. Then based on stochastic analysis techniques and a Lyapunov function, some sufficient criteria are obtained to ensure that stochastic MNNs achieve stochastic fixed-time synchronization in probability. In addition, the upper bound of the settling time is estimated. Finally, simulation results are provided to demonstrate the validity of the proposed schemes.

Structural vibration control using delayed state feedback via LMI approach: with application to chatter stability problems

This paper considers the problem of active vibration control in machining processes to prevent dynamic instability and chatter. A method for robust delayed-state feedback control is presented based on Lyapunov–Krasovskii functionals (LKFs). For fast computation and realizability, a partial state feedback approach based on a reduced order model of structural vibration is considered that matches available sensors and captures the main vibratory modes that impact on stability limits. Robustness to neglected dynamics and other model errors are accounted for by a frequency domain description of model uncertainty, augmented with the basic LKF stability condition. The controller synthesis problem is formulated as a set of linear matrix inequality equations that can be solved numerically using convex optimization methods. Evaluations on a hardware-in-the-loop flexible structure test-bed show that feedback controllers optimized via the LKF stability condition provide significant improvements in stability regions compared with optimized PD control and quadratic regulation. The results confirm the methodology as a useful approach for robust chatter control based on combined flexible structure and cutting process models.

Global Stabilization of Fractional-Order Memristor-Based Neural Networks With Time Delay.

This paper addresses the global stabilization of fractional-order memristor-based neural networks (FMNNs) with time delay. The voltage threshold type memristor model is considered, and the FMNNs are represented by fractional-order differential equations with discontinuous right-hand sides. Then, the problem is addressed based on fractional-order differential inclusions and set-valued maps, together with the aid of Lyapunov functions and the comparison principle. Two types of control laws (delayed state feedback control and coupling state feedback control) are designed. Accordingly, two types of stabilization criteria [algebraic form and linear matrix inequality (LMI) form] are established. There are two groups of adjustable parameters included in the delayed state feedback control, which can be selected flexibly to achieve the desired global asymptotic stabilization or global Mittag-Leffler stabilization. Since the existing LMI-based stability analysis techniques for fractional-order systems are not applicable to delayed fractional-order nonlinear systems, a fractional-order differential inequality is established to overcome this difficulty. Based on the coupling state feedback control, some LMI stabilization criteria are developed for the first time with the help of the newly established fractional-order differential inequality. The obtained LMI results provide new insights into the research of delayed fractional-order nonlinear systems. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.

Finite-Time Stabilization for Discontinuous Interconnected Delayed Systems via Interval Type-2 T–S Fuzzy Model Approach

This paper investigates the finite-time stabilization for a class of interconnected systems with nonlinear discontinuous interconnections in which the time-varying delay are considered. By utilizing the universal approximation ability of the fuzzy model, a unified interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy-model-based interconnected delayed system is provided. Then, in order to solve the existence of solution for the concerned system with discontinuous right-hand side, the Filippov solutions are defined based on differential inclusion theory and set-valued analysis. Furthermore, by the IT2 T–S fuzzy model approach, a delayed state feedback controller equipped with discontinuous term and time-varying delays term is proposed. According to the classical finite time stability theory and generalized Lyapunov approach, finite-time stabilization for the discontinuous interconnected delayed system is achieved, and the estimate of settling time is given. Moreover, when the detailed information of time-varying delays is unknown, the finite-time stabilization is also realized via another improved controller, which only depends upon the upper bound of time-varying delays. Finally, the proposed methodologies are illustrated by a numerical example.

Optimal Periodic-Gain Fractional Delayed State Feedback Control for Linear Fractional Periodic Time-Delayed Systems

This paper develops the fundamentals of optimal-tuning periodic-gain fractional delayed state feedback control for a class of linear fractional-order periodic time-delayed systems. Although there exist techniques for the state feedback control of linear periodic time-delayed systems by discretization of the monodromy operator, there is no systematic method to design state feedback control for linear fractional periodic time-delayed (FPTD) systems. This paper is devoted to defining and approximating the monodromy operator for a steady-state solution of FPTD systems. It is shown that the monodromy operator cannot be achieved in a closed form for FPTD systems, and hence, the short-memory principle along with the fractional Chebyshev collocation method is used to approximate the monodromy operator. The proposed method guarantees a near-optimal solution for FPTD systems with fractional orders close to unity. The proposed technique is illustrated in examples, specifically in finding optimal linear periodic-gain fractional delayed state feedback control laws for the fractional damped Mathieu equation and a double inverted pendulum subjected to a periodic retarded follower force with fractional dampers, in which it is demonstrated that the use of time-periodic control gains in the fractional feedback control generally leads to a faster response.

Finite-Time Stabilization and Adaptive Control of Memristor-Based Delayed Neural Networks.

Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.Finite-time stability problem has been a hot topic in control and system engineering. This paper deals with the finite-time stabilization issue of memristor-based delayed neural networks (MDNNs) via two control approaches. First, in order to realize the stabilization of MDNNs in finite time, a delayed state feedback controller is proposed. Then, a novel adaptive strategy is applied to the delayed controller, and finite-time stabilization of MDNNs can also be achieved by using the adaptive control law. Some easily verified algebraic criteria are derived to ensure the stabilization of MDNNs in finite time, and the estimation of the settling time functional is given. Moreover, several finite-time stability results as our special cases for both memristor-based neural networks (MNNs) without delays and neural networks are given. Finally, three examples are provided for the illustration of the theoretical results.

Quasi‐synchronisation of fractional‐order memristor‐based neural networks with parameter mismatches

This study addresses the problem of quasi-synchronisation of fractional-order memristor-based neural networks (FMNNs) with time delay in the presence of parameter mismatches. Under the framework of fractional-order differential inclusions and set-valued maps, quasi-synchronisation of delayed FMNNs is discussed and quasi-synchronisation criteria are established by means of constructing suitable Lyapunov function, together with introducing some fractional-order differential inequalities. A new lemma on the estimate of Mittag–Leffler function is derived first, which extends the application of Mittag–Leffler function and plays a key role in the estimate of synchronisation error bound. Then, linear state feedback combined with delayed state feedback control law is designed, which guarantees that for a predetermined synchronisation error bound, quasi-synchronisation of two FMNNs with mismatched parameters will be achieved provided that the feedback gains satisfy the newly-proposed criteria. The obtained results extend and improve some previous published works on synchronisation of FMNNs. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.

Delayed state feedback \(H_\infty\) control for periodic-review inventory systems

We investigate delayed state feedback control of a periodic-review inventory management system with perishable goods. The stock under consideration is replenished from multiple supply sources. By using delayed states as well as current states of the inventory system, a delayed feedback \(H_\infty\) control strategy is developed to mitigate bullwhip effects of the system. Some conditions on the existence of the delayed feedback \(H_\infty\) controller are derived. It is found through simulation results that the proposed delayed \(H_\infty\) control scheme is capable of improving the performance of the inventory management significantly. In addition, the delayed controller is better than the traditional delay-free \(H_\infty\) controller. doi:10.1017/S1446181117000153

DELAYED STATE FEEDBACK CONTROL FOR PERIODIC-REVIEW INVENTORY SYSTEMS

We investigate delayed state feedback control of a periodic-review inventory management system with perishable goods. The stock under consideration is replenished from multiple supply sources. By using delayed states as well as current states of the inventory system, a delayed feedback $H_{\infty }$ control strategy is developed to mitigate bullwhip effects of the system. Some conditions on the existence of the delayed feedback $H_{\infty }$ controller are derived. It is found through simulation results that the proposed delayed $H_{\infty }$ control scheme is capable of improving the performance of the inventory management significantly. In addition, the delayed controller is better than the traditional delay-free $H_{\infty }$ controller.

Delayed State Feedback Control for Milling Process

Dynamics of milling process is governed by a set of delay differential equations with periodic coefficients. The secondary Hopf bifurcation and period doubling bifurcation are two of main mechanisms which result into instability of the milling processes. This paper proposes a delayed state feedback controller through the discrete optimal control method to suppress the vibration of milling process. Numerical results reveal that the designed controller can suppress the vibrations of milling process efficiently as well as improve the stability of the cutting processes with the introduced time delay. The influence of designed time delay on control performance and robustness are also discussed.