Periodic Time-varying Systems Research Articles

Finite-time resilient control for uncertain periodic piecewise polynomial time-varying systems

This study explores the problem of finite-time resilient control for periodic piecewise polynomial time-varying systems in the face of parameter uncertainties, time-varying state delays and external disturbances. Particularly, the considered system is characterized by dividing the fundamental period of periodic systems into numerous subintervals, each of which can be expressed by using matrix polynomial functions. The foremost intention of this work is to lay out a resilient controller such that the resulting closed-loop system is finite-time bounded and satisfies a mixed [Formula: see text] and passivity performance index. Furthermore, by constructing a periodic piecewise time-varying Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is established in line with Wiritinger’s inequality and matrix polynomial lemma to guarantee the needed outcomes of the system under study. Following this, the gain matrix of the devised controller can be calculated by solving the established constraints. As a final step, we conclude with a numerical example that validates the potential and importance of the theoretical discoveries and the developed control scheme.

Controllability and control for discrete periodic systems based on fully-actuated system approach

The problem of controllability and control of linear discrete-periodic systems is investigated in this paper. The high-order fully-actuated models for linear discrete periodic time-varying systems are constructed, and a controllability criterion based on fully-actuated system models is proposed. On this basis, stabilization as the fundamental issue is studied and periodic state-feedback control laws are designed via fully-actuated systems approach and parametric design, which converted the original problem into the pole assignment problem for linear constant systems. Finally, a numerical example is given to verify the validity and feasibility of the proposed method.

Stabilization of Periodic Piecewise Time-Varying Systems With Time-Varying Delay Under Multiple Cyber Attacks: An Augmented Lyapunov Functional Approach.

This article investigates the asymptotic stabilization of periodic piecewise time-varying systems with time-varying delay under various cyber attacks, particularly deception and DoS attacks. The addressed system is reformed into a number of time-varying subsystems based on the time interval for each period. Following that, a state-feedback controller with periodic time-varying gain parameters is developed to solve the stabilization problem. The control design depicts the possibility of the aforementioned cyber attacks with two mutually exclusive stochastic Bernoulli distributed parameters. Then, an augmented Lyapunov-Krasovskii functional with periodically varying matrices is used to determine the conditions for designing the proposed controller that ensures the mean-square asymptotic stability of the addressed system. The results of numerical examples support the conclusion that the proposed method is effective and superior, regardless of the cyber attacks involved.

Coordinate Transformation-Based Nonlinear Power Decoupling Control for Differential Buck Grid-Tied Inverter

Nonlinear time-varying systems complicate the analysis and controller design compared to nonlinear time-invariant systems. Single-phase differential grid-tied inverter is a classic nonlinear time-varying system. In this article, an input-output linearization (IOL) based coordinate transformation and a nonlinear power decoupling control scheme are proposed for the single-phase differential grid-tied inverter. Because of the transformation, the nonlinear periodic time-varying system is transformed into a nonlinear time-invariant one. Based on the nonlinear time-invariant model, a nonlinear power decoupling control scheme based on the idea similar to back-stepping control is designed, which realizes good grid current control and power decoupling. Furthermore, the small-signal stability of the inverter is proved by eigenvalue analysis method in the linear time-invariant (LTI) framework. Experiment results validate the effectiveness of the proposed control strategy and stability analysis.

Improved Branch Energy Balance Control for Three-Phase to Single-Phase Modular Multilevel Converter for Railway Traction Power Supply

Maintaining the branch energy balance poses a huge challenge to controller design of many modular multilevel converter (MMC) topologies. Aiming at railway traction power supply system application of a three-phase to single-phase MMC with equal input and output frequency, this article proposes a branch energy balance control with an improved common-mode voltage selection. As a result, the capacitor voltage oscillations as well as circulating currents are reduced greatly. As the MMC is a complicated periodic time-varying system, an average theory is used to simplify the analysis and controller design. The controllability analysis of the system is carried out and the results show that the proposed branch energy balance control is controllable under most load conditions. In addition, the stability of the branch energy balance system is validated through frequency response. Finally, experimental results verify the effectiveness of the control scheme by an 18-cell model based on the RT-LAB platform.

Observer-based fault tolerant control design for periodic piecewise time-varying systems: a fault estimation approach

ABSTRACT This study tackles the fault estimation issue for a continuous-time periodic piecewise time-varying systems (PPTVSs) with delays, fault signal and external disturbances. In particular, the PPTVSs are conjured up by segmenting the fundamental period of the periodic system into a finite number of subintervals. Moreover, fault estimator is designed in line with periodic piecewise observer systems to estimate the immeasurable states of the PPTVSs and the fault signal, simultaneously. Subsequently, in accordance with the estimated values of the fault signal and state dynamics, a fault-tolerant controller is devised. Moreover, by utilising Lyapunov stability theory and matrix polynomial lemma, sufficient criteria are procured in context of linear matrix inequalities to affirm the uniform boundedness of the undertaken system and error system. Further, relying on the acquired constraints, the precise configuration of the fault-tolerant control and observer gain matrices are proffered. Eventually, by offering two illustrative examples including mass-spring-damper system, the utility and potential of presented theoretical insights are validated.

Disturbance Observer-Based Robust Control Design for Uncertain Periodic Piecewise Time-Varying Systems With Disturbances

With the aid of disturbance observer strategy, this article aims to investigate the disturbance rejection and stabilization problems for periodic piecewise time-varying systems that are subject to time-varying delays, parameter uncertainties, nonlinear perturbations and exogenous disturbances. To be more specific, the periodic piecewise time-varying systems are built by segmenting the fundamental period of periodic systems into a limited number of subintervals. Further, the disturbances engendered from an exogenous system are estimated by deploying the disturbance observer and subsequently, on the premise of disturbance that is esimated, a robust controller protocol is constructed for the considered system. Moreover, by bridging the time-varying periodic piecewise Lyapunov-Krasovskii functional with a matrix polynomial lemma, a set of adequate criteria is framed, which confirms the asymptotic stability of the system that is being addressed. Subsequently, on the premise of established criteria, the design of periodic piecewise gain matrices of devised controller and configured observer are presented. Eventually, the importance and potential of the presented theoretical concepts are evidenced through offering a numerical illustration with the simulation results.

An LMI-based Stability Analysis Method of Periodic Linear Time-varying Systems

A necessary and sufficient condition for linear time-varying (LTV) systems to be exponentially stable has been given based on differential Lyapunov inequalities (DLIs). The exponential stability of an LTV system is guaranteed if the DLI for the system has a solution, however, few systematic methods have been reported for finding a solution of DLIs. We focus on a class of periodic LTV systems and propose a sufficient condition to find solutions of DLIs for the class by using linear matrix inequalities (LMIs). Some examples show the effectiveness of the proposed analysis method.

Random response analysis of hydraulic pipeline systems under fluid fluctuation and base motion

Aero hydraulic pipeline systems are subjected to internal fluid fluctuations and random base motions during operation, resulting in time-varying system parameters and nonstationary random responses. To analyse this situation, a nonstationary random response analysis method and a fatigue damage assessment formula for periodic time-varying systems under stationary random excitations are proposed. The nonstationary random response is described by a time-varying power spectral density function, which is strictly characterised by a set of pseudo responses of a periodic time-varying system under a series of harmonic excitations. A frequency-domain iterative solution format for the pseudo responses is constructed and combined with the fast Fourier transform to obtain the time-varying power spectral density function. A fatigue damage assessment formula is derived by discretising the time-varying power spectral density function of the pipeline stress in both the time and frequency domains. The proposed method only requires a few iterations at specific frequency points to calculate each pseudo response in a wide-band random airframe motion environment, showing high computational efficiency. A practical application concerning a section of the wingtip hydraulic pipeline is presented to demonstrate the correctness and efficiency of this method. The variations of pipeline responses and fatigue damage rates under fluid fluctuations and random base motions are also discussed.

Parameter Identification Method for a Periodic Time-Varying System Using a Block-Pulse Function

For periodic time-varying systems, a method of parameter identification based on the block-pulse function is presented. Firstly, the state-space equation of the system was expanded using the block-pulse function, then the recursion formula of the parameter identification of a time-varying system was obtained, according to the irrespective and orthogonal characteristics of the block-pulse function. This study provides a wide range of applications by saving time in calculation with a highly accurate method. The parameter identification was carried out by including the numerical simulation model of a three-degree freedom system and the vibration experiment results of an asymmetrical rotor system. The state space wavelet method and EMD method were compared cross-sectionally with the proposed method; this shows that the proposed method is accurate and effective, which makes it valuable in numerous applications. It also has a certain application value for several related projects.

Improved method for analysing the dynamic response of gear transmission systems

PurposeThe purpose of this paper is to propose an improved method which can shorten the calculation time and improve the calculation efficiency under the premise of ensuring the calculation accuracy for calculating the response of dynamic systems with periodic time-varying characteristics.Design/methodology/approachAn improved method is proposed based on Runge–Kutta method according to the composition characteristics of the state space matrix and the external load vector formed by the reduction of the dynamic equation of the periodic time-varying system. The recursive scheme of the holistic matrix of the system using the Runge–Kutta method is improved to be the sub-block matrix that is divided into the upper and lower parts to reduce the calculation steps and the occupied computer memory.FindingsThe calculation time consumption is reduced to a certain extent about 10–35% by changing the synthesis method of the time-varying matrix of the dynamics system, and the method proposed of paper consumes 43–75% less calculation time in total than the original Runge–Kutta method without affecting the calculation accuracy. When the ode45 command that implements the Runge–Kutta method in the MATLAB software used to solve the system dynamics equation include the time variable which cannot provide its specific analytic function form, so the time variable value corresponding to the solution time needs to be determined by the interpolation method, which causes the calculation efficiency of the ode45 command to be substantially reduced.Originality/valueThe proposed method can be applied to solve dynamic systems with periodic time-varying characteristics, and can consume less calculation time than the original Runge–Kutta method without affecting the calculation accuracy, especially the superiority of the improved method of this paper can be better demonstrated when the degree of freedom of the periodic time-varying dynamics system is greater.

Relaxed design conditions using Takagi-Sugeno fuzzy models and Lyapunov-Floquet transformation for controlling time-varying periodic systems

This manuscript approaches the Takagi-Sugeno fuzzy control technique, the Lyapunov-Floquet transformation, and their applications for controlling linear time-varying systems. Each of the techniques is applied in the control of a linear time-varying periodic system in order to compare their effectiveness. A hybrid control method involving the Takagi-Sugeno fuzzy control and the Lyapunov-Floquet transformation is proposed. In this method, the stability of the closed-loop system is mathematically guaranteed. In addition, this new procedure can reduce the conservatism of time-varying periodic systems with uncertainties in the input matrix. Finally, an application of the hybrid method is presented in a time-varying periodic system considering a constraint on input and uncertainties on the input matrix.

Research and Application of Data-Driven Modeling Method for Gear System Based on Time-Varying Characteristics

The time-varying characteristics of the gear system have an essential influence on its vibration and stability characteristics. Aiming at this characteristic and taking the generalized force caused by load torque as input and dynamic transmission error as output, a data-driven modeling method for gear time-varying system is studied using the periodic time-varying system identification theory. The effectiveness of the proposed method is verified by the lumped mass model of the gear system. This method has high modeling accuracy and can accurately characterize the time-varying characteristics of the gear system. Then, the virtual experimental platform of gear system dynamics is established based on the finite element theory. The method successfully extends to the virtual experimental platform, laying a foundation for analyzing the gear system’s dynamic characteristics.

Observer-based tracking control design for periodic piecewise time-varying systems

In this study, the problem of robust tracking problem for continuous-time periodic piecewise time-varying delay systems with disturbances and uncertainties has been examined by using observer-based H∞ tracking control protocol. Precisely, the state space representation of the system is formulated to reconstruct the unmeasurable states via the available informations of input/output dynamics. Based on the suitable Lyapunov-Krasovskii functional with periodic piecewise time-varying Lyapunov matrix, a set of sufficient conditions in the form of linear matrix inequalities is derived which affirms the robust asymptotic tracking performance and satisfactory disturbance attenuation for the addressed model. Particularly, the matrix polynomial approach is utilized which makes the analysis to be more flexible and amenable to convex optimization tool. Accordingly, the period time-varying controller and observer gains are computed through the feasible solution of derived matrix inequalities. Conclusively, the simulation results are presented to confirm the efficiency and applicability of the theoretical outcomes.

Adaptive neural control of nonlinear periodic time-varying parameterized mixed-order multi-agent systems with unknown control coefficients

Adaptive neural control of nonlinear periodic time-varying parameterized mixed-order multi-agent systems with unknown control coefficients

A polynomial blossoming approach to stabilization of periodic time-varying systems

This paper proposes a novel polynomial blossoming approach to designing stabilizing controller for a class of periodic time-varying systems. Utilizing multi-convexity of a non-homogeneous symmetric matrix polynomial, the approach can provide a series of convex optimization conditions to guarantee the negativity/positivity of matrix polynomial. Special cases of the proposed approach are also discussed, giving the conclusion that our approach generalizes two existing matrix polynomial approaches. For periodic systems formulated with [0,1]-bounded time-varying coefficients, the designed stabilizing controller not only involves user-selectable varying gains over time intervals that are possibly non-identical to the system fundamental period, but can also guarantee the exponential stability of the closed-loop system. The effectiveness of our approach is validated and illustrated through two application-oriented simulation examples.

General Multi-Frequency Small-Signal Model for Resonant Converters

AbstractResonant converters are periodic time-varying system, one of whose distinctive features is the sideband effect. To be specific, when a small-signal perturbation is injected into the converter, a series of sideband frequency components will occur. The two sideband frequency components around the switching frequency determine the small-signal response of the resonant tank if it has sufficient band-pass filtering. Using complex Fourier series, the relationship between different frequency components can be described with a series of gains. This paper derives all the necessary transfer functions between different frequencies for resonant converters. Combining them together forms a general small-signal model of resonant converters. There are multiple frequency components, i.e., the perturbation frequency and two sideband frequencies in this model, hence the name multi-frequency model. Two kinds of inverters, i.e., the full-bridge and half-bridge structure, and three modulation methods, i.e., the switching frequency control, the duty-cycle control, and the input voltage control are considered in this paper. The experimental results verify the validity of the proposed model.

Robust control design for delayed periodic piecewise time-varying systems with actuator faults

This paper is mainly focused on the stabilization problem of uncertain delayed periodic piecewise time-varying systems inclusive of disturbances and faults in actuators. More specifically, the considered system is encompassed of periodic dynamics, which exhibits the nature of switched systems with fixed switching sequence and dwell time. The control protocol is configured in the form of both the present and past state information of the addressed system with passive performance. Moreover, the proposed control approach discloses the stabilization issue mainly by resolving the effect of faults in actuator components. Precisely, the desired periodic gain matrices of the developed controller are calculated by way of solving some matrix inequalities which are derived by making use of Lyapunov stability theory and matrix polynomial approach. As a result, the asymptotic stability of the considered system is ensured in conjunction with satisfied disturbance attenuation index. Conclusively, the simulation results of two numerical examples including mass-spring damping system are presented for validating the theoretical result.

Adaptive neural tracking control for stochastic nonlinear multi-agent periodic time-varying systems

This paper investigates the design of adaptive tracking neural controllers for first- and second-order nonlinear multi-agent periodic time-varying systems described based on random differential equations, respectively. First, the Fourier series expansion and neural networks are used as the main tools to describe the nonlinear periodic disturbance dynamics of the follower, which transforms the completely nonlinear problem into a partially linearizable problem. Then, the fully distributed adaptive neural controllers are developed based on adaptive estimation, in which new estimation methods are designed to address periodic time-varying perturbations. Furthermore, based on the stochastic Lyapunov stability theory, it is proved that the tracking errors converge asymptotically to a small neighborhood of zero in the sense of mean square. Finally, the efficicency of the proposed controllers is verified using simulations.

Observer-based output reachable set synthesis for periodic piecewise time-varying systems

In this paper, the output reachable set synthesis problem for periodic piecewise time-varying systems has been addressed for the first time. Generalized periodic time-varying conditions of the closed-loop system to guarantee the system output bounded by a collection of finite ellipsoids are developed. The decoupling of time-varying observer and controller gains is achieved by a technical lemma . Moreover, by using time-varying matrix functions in multiple linear-interpolative forms and the relaxed quadratic matrix polynomial definiteness results, sufficient condition is developed to determine the periodic time-varying observer and controller with reduced conservatism. A tractable iterative algorithm is proposed to obtain the periodic time-varying observer and controller gains. A numerical example is presented to illustrate the validity of proposed methods.