Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control

This paper focuses on the stochastic analysis of a viscoelastic bistable energy harvesting system under colored noise and harmonic excitation, and adopts the time-delayed feedback control to improve its harvesting efficiency. Firstly, to obtain the dimensionless governing equation of the system, the original bistable system is approximated as a system without viscoelastic term by using the stochastic averaging method of energy envelope, and then is further decoupled to derive an equivalent system. The credibility of the proposed method is validated by contrasting the consistency between the numerical and the analytical results of the equivalent system under different noise conditions. The influence of system parameters on average output power is analyzed, and the control effect of the time-delayed feedback control on system performance is compared. The output performance of the system is improved with the occurrence of stochastic resonance(SR). Therefore, the signal-to-noise ratio expression for measuring SR is derived, and the dependence of its SR behavior on different parameters is explored.

Design and analysis of active disturbance rejection control for time-delay systems using frequency-sweeping

For the typical first-order systems with time-delay,this paper explors the control capability of linear active disturbance rejection control(LADRC).Firstly,the critical time-delay of LADRC is analyzed using the frequency-sweeping method and the Routh criterion,and the stable time-delay interval starting from zero is accurately obtained,which reveals the limitations of general LADRC on large time-delay.Then in view of the large time-delay,an LADRC controller is developed and verified to be effective,along with the robustness analysis.Finally,numerical simulations show the accuracy of critical time-delay,and demonstrate the effectiveness and robustness of the proposed controller compared with other modified LADRCs.

Effects of time-delayed vibration absorber on bandwidth of beam for low broadband vibration suppression

The effects of time-delayed vibration absorber(TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given,and the results show that the introduction of time-delayed feedback control(TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad bands for vibration suppression, multiple TDVAs are uniformly distributed on a continuous beam,and the relationship between the dynamic responses and the TDFC parameters is investigated. The obtained relationship shows that the TDVA has a significant regulatory effect on the vibration behavior of the continuous beam. The effects of the number of TDVAs and the nonlinearity on the bandgap variation are discussed. As the multiple TDVAs are applied, according to the different requirements on the location and bandwidth of the effective vibration suppression band, the optimization criteria for the TDFC parameters are given, which provides guidance for the applications of TDVAs in practical projects such as bridge and aerospace.

Group Hybrid Coordination Control of Multi-Agent Systems With Time-Delays and Additive Noises

A new kind of group coordination control problemgroup hybrid coordination control is investigated in this paper.The group hybrid coordination control means that in a whole multi-agent system(MAS)that consists of two subgroups with communications between them,agents in the two subgroups achieve consensus and containment,respectively.For MASs with both time-delays and additive noises,two group control protocols are proposed to solve this problem for the containment-oriented case and consensus-oriented case,respectively.By developing a new analysis idea,some sufficient conditions and necessary conditions related to the communication intensity betw een the two subgroups are obtained for the following two types of group hybrid coordination behavior:1)Agents in one subgroup and in another subgroup achieve weak consensus and containment,respectively;2)Agents in one subgroup and in another subgroup achieve strong consensus and containment,respectively.It is revealed that the decay of the communication impact betw een the two subgroups is necessary for the consensus-oriented case.Finally,the validity of the group control results is verified by several simulation examples.

Effects of Physical Parameters and Time-Delay Coefficients on the Amplitude and Frequency Bandwidth of Saturation Controller for a Beam Vibration

In this paper, the influence of physical parameters on the width of saturated control frequency band and the influence of time delay parameters on the stability of saturated control system are studied. The analytical solution of the motion equation of the system when the main resonance and the 1:2 internal resonance occur simultaneously is obtained by multiple scale method, experimentally measured natural frequencies of nonlinear beams. The effects of excitation amplitude, delay feedback coefficients and nonlinear coefficients on saturation control are investigated. The results of the study show that the bandwidth of the saturation control can be increased by increasing the value of the external excitation, the nonlinear coefficients enhance the nonlinear phenomena of the system.

PD-type iterative learning control for nonlinear time-delay system with external disturbance

The PD-type iterative learning control design of a class of affine nonlinear time-delay systems with external disturbances is considered. Sufficient conditions guaranteeing the convergence of the n-norm of the tracking error are derived. It is shown that the system outputs can be guaranteed to converge to desired trajectories in the absence of external disturbances and output measurement noises. And in the presence of state disturbances and measurement noises, the tracking error will be bounded uniformly. A numerical simulation example is presented to validate the effectiveness of the proposed scheme.

Parameter design for a vibration absorber with time-delayed feedback control

Traditional passive vibration absorbers are effective only when their natural frequencies are close to those of the excitations. To solve this problem, a vibration absorber with time-delayed feedback control is proposed to suppress vibration of the primary system under excitation with changing frequency. Firstly, the mechanical model of the delay coupled system is established. Then, the displacement transfer ratio of the system is obtained. The stability of the system is analyzed since delay may result in destabilization. Next, in order to design the control parameters, the vibration absorption performances of the proposed time-delayed vibration absorber are studied. The vibration absorption region is shown. The results show that time-delayed feedback control is able to change the response of the system. The effective vibration absorption frequency band is adjustable by tuning the control gain and time delay. The effective frequency band can be widened when choosing appropriate control parameters. The vibration absorption performances can be greatly improved by the time-delayed absorber. In addition, the optimum control parameters are obtained. Finally, the experimental prototype is constructed. Several tests with different control parameters are taken. The experimental and analytical results match quite well.

Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay

One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay.The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval.The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer.The second contribution of this paper is to introduce a novel LyapunovKrasovskii functional,which includes a cubic polynomial on a time-varying delay,in stability analysis of time-delay systems.Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities,two stability criteria are derived for two cases of the time-varying delay.A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.

Decentralized robust guaranteed cost control for a class of interconnected singular large-scale systems with time-delay and parameter uncertainty

The decentralized robust guaranteed cost control problem is studied for a class of interconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality （LMI） via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.

An Improved Approach to Delay-dependent Robust Stabilization for Uncertain Singular Time-delay Systems

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality （LMI）. Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.

Adaptive Fuzzy Observer Backstepping Control for a Class of Uncertain Nonlinear Systems with Unknown Time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Robust reliable guaranteed cost control for uncertain singular systems with time-delay

The robust reliable guaranteed cost control for uncertain singular delay systems with actuator failures and a given quadratic cost function is studied. The system under consideration involves constant time-delay and norm-bounded parameter uncertainties. The purpose is to design state feedback controllers which can tolerate actuator failure, such that the closed-loop system is stable, and the specified cost function has an upper bound for all admissible uncertainties. The sufficient conditions for the solvability of this problem are obtained by a linear matrix inequality （LMI） method. Furthermore, a numerical example is given to demonstrate the applicability of the proposed approach.

Stability analysis and design of time-delay uncertain systems using robust reliability method

A robust reliability method for stability analysis and reliability-based stabilization of time-delay dynamic systems with uncertain but bounded parameters is presented by treating the uncertain parameters as interval variables.The performance function used for robust reliability analysis is defined by a delayindependent stability criterion.The design of robust controllers is carried out by solving a reliability-based optimization problem in which the control cost satisfying design requirements is minimized.This kind of treatment makes it possible to achieve a balance between the reliability and control cost in the design of controller when uncertainties must be taken into account.By the method,a robust reliability measure of the degree of stability of a time-delay uncertain system can be provided,and the maximum robustness bounds of uncertain parameters such that the time-delay system to be stable can be obtained.All the procedures are based on the linear matrix inequality approach and therefore can be carried out conveniently.The effectiveness and feasibility of the proposed method are demonstrated with two practical examples.It is shown by numerical simulations and comparison that it is meaningful to take the robust reliability into account in the control design of uncertain systems.

Non-fragile observer-based passive control for descriptor systems with time-delay

This paper investigates the problem of non-fragile observer-based passive control for descriptor systems with time-delay. The perturbations in both the control gain and observer gain of the observer-based controller are considered. For the cases of the additive perturbations and multiplicative perturbations, sufficient conditions are given such that the closed-loop systems are admissible and passive with dissipation η. The observer-based controller gains could be obtained from the solutions of linear matrix inequalities （LMIs）. Moreover, the maximum dissipation of the system is provided. Simulation examples are given to show the effectiveness of the deign methods.

Adaptive neural network tracking control for a class of unknown nonlinear time-delay systems

For a class of unknown nonlinear time-delay systems, an adaptive neural network （NN） control design approach is proposed. Backstepping, domination and adaptive bounding design technique are combined to construct a robust memoryless adaptive NN tracking controller. Unknown time-delay functions are approximated by NNs, such that the requirement on the nonlinear time-delay functions is relaxed. Based on Lyapunov-Krasoviskii functional, the sem-global uniformly ultimately boundedness （UUB） of all the signals in the closed-loop system is proved. The arbitrary output tracking accuracy is achieved by tuning the design parameters. The feasibility is investigated by an illustrative simulation example.

Analysis of Absolute Stability for Time-delay Teleoperation Systems

In this paper, a new bilateral control algorithm based on absolute stability theory is put forward, which aims at the time-delay teleoperation system with force feedback from the slave directly. In the new control algorithm, the delay-dependent stability, instead of delay-independent stability, is taken as the aim of control design. It improves the transparency of the system at the price of unnecessary stability. With this algorithm, the time-delay teleoperation systems have good transparency and stability. A simulation system is established to verify the effect of this algorithm.

New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities

This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems(MJTDSs),whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance,auxiliary function-based double integral inequality is combined with extended Wirtinger's inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function(ALKF) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally,numerical examples are given to show the effectiveness and the merits of the proposed method.

Robust adaptive control for interval time-delay systems

This paper focuses on the robust adaptive control problems for a class of interval time-delay systems and a class of large-scale interconnected systems. The nonlinear uncertainties of the systems under study are bounded by high- order polynomial functions with unknown gains. Firstly, the adaptive feedback controller which can guarantee the stability of the closed-loop system in the sense of uniform ultimate boundedness is proposed. Then the proposed adaptive idea is extended to robust stabilizing designing method for a class of large-scale interconnected systems. Here, another problem we address is to design a decentralized feedback adaptive controller such that the closed-loop system is stable in the sense of uniform ultimate boundedness for all admissible uncertainties and time-delay. Finally, an illustrative example is given to show the validity of the proposed approach.

Observer-based robust predictive control of singular systems with time-delay and parameter uncertainties

The problem of observer-based robust predictive control is studied for the singular systems with norm-bounded uncertainties and time-delay, and the design method of robust predictive observer-based controller is proposed. By constructing the Lyapunov function with the error terms, the infinite time domain ＂min-max＂ optimization problems are converted into convex optimization problems solving by the linear matrix inequality （LMI）, and the sufficient conditions for the existence of this control are derived. It is proved that the robust stability of the closed-loop singular systems can be guaranteed by the initial feasible solutions of the optimization problems, and the regular and the impulse-free of the singular systems are also guaranteed. A simulation example illustrates the efficiency of this method.