Pure Time Delay Research Articles

Stability prediction method of time-varying real-time hybrid testing system on vehicle-bridge coupled system

In recent years, real-time hybrid testing (RTHT) has been applied for the dynamic testing of high-speed trains running on bridges. A guarantee of stability for the RTHT system is essential to achieve a safe and reliable result. However, the inherent time-varying characteristics of the vehicle-bridge coupled system pose challenges to RTHT stability prediction. This study aims to develop a stability prediction method specifically tailored for time-varying RTHT system. Firstly, the vehicle-bridge coupled RTHT was modelled using a discrete state–space representation with a comprehensive consideration of the time-varying vehicle-bridge interaction and the dynamics of the shaking table. Subsequently, a time-varying stability criterion was derived from the periodic time-varying state matrix, forming the basis for a relative stability prediction method. The validity of the proposed method was confirmed through simulations and experiments employing a single-axle interaction within the vehicle-bridge coupled RTHT system. The coupled system consisted of a quarter-car model and simply supported beams were used as an example to evaluate the stability and accuracy of the time-varying RTHT. The results showed that the stability increased with increasing vehicle speed. Reducing the pure time delay of the shaking table improved both stability and accuracy. Increasing the effective frequency of the shaking table improved the accuracy but may reduce the stability of the RTHT.

Impedance-Based AC/DC Terminal Modeling and Analysis of the MMC-BTB System

Impedance-based small-signal stability analysis is widely applied in practical engineering with modular multilevel converters (MMCs). However, the deficiencies of existing impedance models (IMs) and the idealized extension for the single MMC influence the analyses in multiterminal systems. In this paper, these gaps are filled by focusing on an MMC-based back-to-back system. To obtain the steady-state harmonics of the system, a numerical method is initially proposed based on Newton–Raphson iteration in the frequency domain. Then, by substituting the shared terminal dynamics with active or passive devices, theoretical AC/DC IMs based on typical control loops with pure time delays are directly established via multiharmonic linearization. Further aided by the derived IMs, two neglected aspects in the current literature are investigated, including the influence of power transformers on low-frequency impedance characteristics and the rationality of using simplified IMs for high-frequency resonance studies. The stability of interlinking systems needs to be comprehensively analyzed at both AC and DC terminals. The analyses help to position the instability source, obtain the stability margin, and guide the supplementary control strategy. All IMs and analyses are verified via frequency scans and simulations in PSCAD.

Closed-form expressions for the pure time delay in terms of the input and output Laguerre spectra

The pure time delay operator is considered in continuous and discrete time under the assumption of the input signal being integrable (summable) with square. Then the input and the output signals are uniquely given by their Laguerre spectra. It is shown that a discrete convolution operator with polynomial Markov parameters constitutes a common description of the delay operator in the continuous and discrete case. Closed-form expressions for the delay value in terms of the output and input Laguerre spectra are derived. The expressions hold for any feasible value of the Laguerre parameter and can be utilized for e.g. building time-delay estimators that allow for non-persistent input. A simulation example is provided to illustrate the principle of Laguerre-domain time-delay modeling and analysis with perfect disturbance rejection.

Decoupled $dq$ Current Control of Grid-Tied Packed E-Cell Inverters in Vehicle-to-Grid Technologies

This article investigates a decoupled vector current control strategy for grid-tied single-phase nine-level Packed E-Cell (PEC) inverters for vehicle-to-grid (V2G) technologies. The control design is based on a loop shaping approach, where performance specifications such as desired closed-loop bandwidth, closed-loop stability, robustness to pure time-delays in control loops/process, and decoupling between direct ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d$</tex-math></inline-formula> ) and quadrature ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> ) axis of control signals are specified in the frequency domain. The control design problem is formulated as a convex optimization problem whose solution results in a multivariable controller in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> framework. The effectiveness of the proposed control strategy in terms of robust stability, current tracking, and improved total harmonic distortion is evaluated by experimental and simulation results under several case studies. The results also show that the designed controller provides the desired transient response as well as decoupling between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> output currents.

An advanced control strategy for engine thermal management systems with large pure time delay

Stable and precise temperature control can effectively improve the engine’s fuel consumption and emissions. An advanced engine thermal management system (AETMS) composed of electric actuators has great potential in increasing the temperature tracking control accuracy and decreasing the system energy consumption. Time-varying disturbance and pure time delay in the system make it challenging to harmoniously control multiple actuators to ensure efficient temperature tracking performance. In addition, a reasonable power distribution of the actuators is beneficial to reduce the parasitic energy consumption of the system and further improve the system efficiency. In this article, an adaptive optimization control strategy consisting of a state predictor, a disturbance estimator, an energy consumption optimization block and a state tracking controller is proposed for the temperature tracking and energy consumption optimization of AETMS. Experimental verification was performed on a range extender bench of an extended-range electric vehicle, and the results show that the system achieves high-precision temperature control and energy consumption near the theoretical optimal value under changing working conditions. The temperature steady-state error is within 0.3 oC, and the temperature adjustment time is within 100 s after the first overshoot.

Deterministic learning-based neural network control with adaptive phase compensation

Under the persistent excitation (PE) condition, the real dynamics of the nonlinear system can be obtained through the deterministic learning-based radial basis function neural network (RBFNN) control. However, in this scheme, the learning speed and accuracy are limited by the tradeoff between the PE levels and the approximation capabilities of the neural network (NN). Inspired by the frequency domain phase compensation of linear time-invariant (LTI) systems, this paper presents an adaptive phase compensator employing the pure time delay to improve the performance of the deterministic learning-based adaptive feedforward control with the reference input known a priori. When the adaptive phase compensation is applied to the hidden layer of the RBFNN, the nonlinear approximation capability of the RBFNN is effectively improved such that both the learning performance (learning speed and accuracy) and the control performance of the deterministic learning-based control scheme are improved. Theoretical analysis is conducted to prove the stability of the proposed learning control scheme for a class of systems which are affine in the control. Simulation studies demonstrate the effectiveness of the proposed phase compensation method.

String stability of automated vehicles based on experimental analysis of feedback delay and parasitic lag

Recent literature shows that automated vehicle (AV) significantly impacts traffic flow stability. However, as a widely used longitudinal AV technology, the Adaptive Cruise Control (ACC) system still has several unknown features that lack field data for modeling. We ran a series of novel tests with two ACC vehicles to simulate the behavior of the AV platoon in the field experiment. We designed a linear car-following controller in the upper layer system and tested the string stability of the ACC vehicle platoon. Data is collected through the vehicle's GPS sensor and upper controller. These data can help us estimate the feedback delay in the upper layer and parasitic lag in the lower layer. The data analysis results specify the range of different time delays and further optimize the dynamic response model in the lower layer. Then we propose an improved longitudinal model based on a first-order inertia system with a pure time delay in the dynamic response process. The experimental results show that the improved longitudinal model is twenty percent more accurate than the traditional first-order inertia model. Finally, we analyze the string stability of the improved longitudinal model. The results indicate that the improved longitudinal model has more strict stability conditions than the traditional model. Although the current feedback delay can satisfy the string stability criterion, the parasitic lag in the dynamics response process cannot satisfy the stability criterion. In this study, a customized ACC car-following controller is implemented in the field experiments, and thus all hypotheses and analysis results are validated by field data.

Finite-time energy-to-peak control for Markov jump systems with pure time delays

This study investigates finite-time energy-to-peak control for pure-time-delay Markov jump systems. The main objective is to obtain some theorems such that the corresponding pure-time-delay Markov jump systems are finite time energy-to-peak stable or stabilizable. First, based on mathematical transformation, the pure-time-delay Markov jump systems are described in a model description that includes the current system state and several distributed time-delay items. Second, according to linear matrix inequality (LMI) theory, a positive energy functional is constructed, which includes a triple integral item. Then, after some mathematical operations, some sufficient conditions are obtained for Markov jump systems to be finite-time energy-to-peak stable or stabilizable. The obtained results are expressed in LMIs, which can be conveniently solved by computers. Finally, examples are given to show the usefulness of the obtained theorems.

Incremental state model in predictive control: A new fuzzy control proposal for nonlinear systems

In this work, a fuzzy predictive optimal control for multivariable nonlinear systems with pure time delays is presented. Therefore, dynamic local linear state models are used at each point of the state space obtained by fuzzy Takagi-Sugeno (T-S) modelling. The modelling error is considered as white noise, and the state is observed using the Kalman Filter (KF). This method does not take into account possible input constraints. Therefore, it applies to systems where there are no saturation problems. In this work, a new approach in the Model Predictive Control (MPC) method is proposed by calculating the control signal increment as a function of the error between a reference state vector and the prediction at N-steps of the state vector instead of using the traditional MPC approach which is based on calculating the error between a reference and the predicted output. The proposed method has a satisfactory tracking performance. The main feature of the proposed method is that it attains computational savings compared to other methods that have used incremental state models, which making it more appropriate for real-time applications.

Reliable and straightforward PID tuning rules for highly underdamped systems

Proportional-Integral-Derivative (PID) controllers reign absolute when automatic control is applied. There is an expressive number of tuning rules for these controllers in literature. However, for highly oscillatory (or highly underdamped) systems, such as the ones found in oil production and polymerization reactors, the available methods provide poor closed-loop performance and robustness. Besides, most of these tuning rules are developed for systems based on a first-order with pure time delay (FOPTD) transfer function and for parallel form PID controllers. Therefore, the focus of this paper is the development of appropriate tuning rules for highly underdamped systems through non-cancellation of dominant poles and easily adjustable robust performance, making them applicable for both series and parallel PID controllers, since the proposed tuning only places the controller zeros at the real axis. The new tuning rules were developed for these systems and were tested on 15,000 different transfer functions described by a second-order with pure time delay (SOPTD) expression. Additionally, a recommendation interval is also provided in which the controller gain can be varied online or by simulations to achieve the desired trade-off between performance and robustness. The proposed rules are also validated using two case studies: the suppression of slugging in oil production and the temperature control of an industrial gas phase polyethylene reactor.

Joint tracking coefficients and the time delay of a nonstationary linear system, preceded by a static nonlinearity

SummaryThe paper considers a block‐oriented nonlinear Hammerstein system that consists of a linear block with real‐valued time‐varying unknown coefficients and a pure time delay, preceded by the static nonlinearity. The joint tracking of linear block coefficients and the time delay while processing observation samples is under consideration. The difficulty of the tracking process consists in the initial nonconvexity of the objective function to be minimized, in respect of the time delay. To obtain current estimates of the true coefficients and the time delay it is necessary to overcome the multiextremality of the objective function. A global optimization problem could be solved by changing a form of the nonconvex objective function into a convex one. The optimization problem has been subdivided into two problems that are analyzed in this article, as well. The first one consists of removal of the objective function multiextremality in respect of the time delay, while hunting for the global extremum. Therefore, the well‐known approach based on the method of corrective operators, which is used to transform the multiextremal criterion into a unimodal function for the nonstationary Wiener system, is developed here for the Hammerstein one. The other problem consists of the applicability of unified adaptive algorithms, used for Wiener systems in the case of Hammerstein systems. The recursive parametric identification technique, based on the adaptive algorithm procedures, is developed here for the nonstationary block‐oriented Hammerstein systems, too. The applicability of algorithms is supported by various simulation tests solved by computer for distinct inputs and for two static nonlinearities.

Data-Driven Modeling of Wireless Power Transfer Systems With Multiple Transmitters

This article develops a new method of data-driven modeling for a class of multiple-transmitter single-receiver wireless power transfer (WPT) systems. A continuous-time multiple-input single-output (MISO) model with pure time delays is used to characterize the input–output behavior of the system, where the transfer functions associated with each input channel are not constrained to have the same denominator. Moreover, the time delays are allowed to be a fraction of the sampling interval in order to account for the delay effects that stem from circuit components and wireless communication, which are, by nature, often a fraction of the sampling interval. An optimal refined instrumental variable method is proposed to estimate the parameters and time delays of the MISO model based on sampled input–output data. In contrast to the conventional circuit-theory-based modeling methods that rely on circuit parameters and result in models which are often complex, the proposed data-based method yields parsimonious models, whose parameters are directly estimated from input–output data. Due to the easy availability of sampled data in control engineering applications, the proposed method is clearly more user-friendly, having a broad prospect for efficient operation of WPT systems, such as prediction, optimization, and control. Numerical and experimental results are presented to validate the effectiveness and merit of the proposed method.

Data-Driven Modeling of Wireless Power Transfer Systems With Slowly Time-Varying Parameters

This article considers the data-driven modeling of a class of phase-controlled wireless power transfer (WPT) systems, where the load may vary slowly with respect to time. The dominant mode analysis suggests that a model of the Hammerstein type, which consists of a static nonlinearity function, followed by a linear time-varying model with a pure time delay, is the best structure to describe the input–output relationship of the system. On this basis, we derive a small-signal model that is linear in the variables in order to aid control design and allow the associated model parameters to be estimated from sampled input–output data using the standard refined instrumental variable (RIV) method. In the presence of a time-varying load, however, the plant model parameters may not be correctly estimated if the load response is not removed. In order to address this problem, a new recursive RIV method is proposed, in which an effective technique is introduced to track the load response, so allowing the parameters and time delay of the time-varying model to be accurately estimated. The effectiveness of the proposed method is verified by applying it to both a simulation model and a laboratory system.

Decoupling Adaptive Smith Prediction Model of Flatness Closed-Loop Control and Its Application

Flatness control system is characterized by multi-parameters, strong coupling, pure time delay, which complicate the establishment of an accurate mathematical model. Therefore, a control scheme that combines dynamic decoupling, PI (Proportion and Integral) control and adaptive Smith predictive compensation is proposed. To this end, a dynamic matrix is used to decouple the control system. A multivariable coupled pure time-delay system is transformed into several independent generalized single-loop pure time-delay systems. Then, a PI-adaptive Smith predictive controller is constructed for the decoupled generalized single-loop pure time-delay system. Simulations show that the scheme has a simple and feasible structure, and good control performance. When the mathematical model of the control system is inaccurate, the control performance of adaptive Smith control method is evidently better than that of the ordinary Smith control method. The model is successfully applied to the cold rolling production site through LabVIEW, and the control accuracy is within 5I. This study reveals a new solution to the problem of coupled pure time-delay in flatness control system.

Approximate and exact stability analysis of 1-DOF and 2-DOF single-actuator real-time hybrid substructuring

This paper presents approximate and exact stability analysis to determine the critical time delays of one and two degree of freedom (DOF) single-actuator real-time hybrid substructuring (RTHS). The approximate stability analysis is based on applying the Routh-Hurwitz stability criterion using a first-order Taylor expansion of the actuator dynamics represented by a constant gain and pure time delay. The exact stability analysis involves solving the critical frequencies first by canceling the exponential delay term of the closed-loop characteristic equation through multiplication by its complex conjugate. The exact critical time delays are then found using the phase of the closed-loop characteristic equation evaluated at the critical frequencies. These stability analysis techniques are applied to several 1-DOF and 2-DOF mass-spring configurations of single-actuator RTHS. Results show that the critical time delays are highly dependent on the mass, stiffness, and damping partitioning of the physical and numerical substructures as well as the actuator gain. This information provides useful insight into the stability behavior of a particular substructure partitioning configuration to evaluate the feasibility of conducting RTHS tests of these systems.

Fuzzy Sliding Mode Predictive Control of Air Flow Rate for a High-Speed High-Temperature Heat-Airflow Test System

To solve the problem of accurate control of air flow rate of a high-speed high-temperature heat-airflow test system, this paper introduces the working principle, establishes the mathematical model and analyzes the characteristics of the air supply subsystem. According to the characteristics of the air supply subsystem, such as time-varying parameters, time delay and disturbance, which are difficult to control accurately, a new fuzzy sliding mode predictive control algorithm is proposed based on fuzzy sliding mode control and Smith predictor. On this basis, the proposed control algorithm is simulated and studied. The results show that the proposed fuzzy sliding mode predictive control algorithm has good control performance. It can not only achieve high-performance tracking of step, slope, square wave and sinusoidal signals, but also can overcome the influence on the system caused by pure time delay, time-varying parameter and external disturbance.

Basic examination of two substructuring schemes for shake table tests

This study examines two basic substructuring schemes for shake table tests where the dynamics of the table is significantly affected by a specimen. The hybrid simulation (HS) scheme, commonly adopted in substructuring experiments, directly uses the output of a numerical substructure as an input signal to a physical substructure. The dynamical substructuring system (DSS) scheme, developed long after HS, uses feedforward and feedback controllers to minimise the control error produced by the outputs of numerical and physical substructures. Before examining these two schemes, this study introduces a systematic formulation for dividing a multi-degree-of-freedom emulate system into a numerical substructure and a physical substructure with a shake table. Then, controller designs for HS and DSS are discussed for the substructures. The two schemes with basic control approaches were numerically examined through substructuring tests for a linear 3DOF emulate system. DSS with stability was powerful even under a control condition with a pure time delay and inaccurate estimation of the table dynamics, whereas these factors degraded the HS performance. In additional simulations in which nonlinear characteristics were considered, the performance of DSS (HS) was degraded mainly by the nonlinear (inaccurate estimation of the table dynamics). It was found that the stability of substructures with nonlinear characteristics could be roughly assessed by the Nyquist stability criterion. These simulations with/without nonlinear characteristics clarified the performances of the HS and DSS schemes through basic control approaches and stability analysis under practical conditions.

Dynamics of a Predator–Prey-Competition System with Pure Delays

This paper deals with the non-autonomous Lotka–Volterra type one prey-two competitive predator systems with pure time delays. Based on the the comparison method and construction of the multiple Lyapunov functional, some new sufficient conditions on the boundedness, permanence, extinction and global attractivity of the system are established. In addition, two examples with numerical simulations are presented to illustrate the obtained theoretical results.

Tracking coefficients of a nonstationary system, followed by static nonlinearity jointly with the time delay

SummaryThis paper considers a block‐oriented nonlinear Wiener system that consists of a linear block with real time‐varying unknown coefficients and pure time delay followed by a static invertible nonlinearity. Consideration is concentrated on the joint linear block coefficients and time delay tracking by processing observation samples. Two problems are analyzed. The first one is the avoidance of mean‐squares prediction error function multiextremality for time delay while seeking the global minimum. The other problem consists of the applicability of unified adaptive algorithms, based on the schema with corrective operators for the Wiener system. An approach used to transform the multiextremal criterion into a unimodal function for a nonstationary linear system, in respect of the time delay, is developed and analyzed for a block‐oriented nonlinear Wiener system with time‐varying coefficients and a time delay. The recursive parametric identification approach, based on the method of corrective operators, is developed for the nonstationary dynamic Wiener system. Applicability of algorithms is supported by various simulation tests solved by a computer.

Parameters Optimization of the Heating Furnace Control Systems Based on BP Neural Network Improved by Genetic Algorithm

The heating technological requirement of the conventional PID control is difficult to guarantee which based on the precise mathematical model, because the heating furnace for heating treatment with the big inertia, the pure time delay and nonlinear time-varying. Proposed one kind optimized variable method of PID controller based on the genetic algorithm with improved BP network that better realized the completely automatic intelligent control of the entire thermal process than the classics critical purporting (Z-N) method. A heating furnace for the object was simulated with MATLAB, simulation results show that the control system has the quicker response characteristic, the better dynamic characteristic and the quite stronger robustness, which has some promotional value for the control of industrial furnace.