State Variables Of System Research Articles

Stability analysis of integrated power system with pulse load

The stability of an integrated power system (IPS) with pulse load involves both the trend of change in the system state during the whole period and the problem of whether to cause an unacceptable oscillation and an increase or decrease in the system state variable during a pulse period, which will pose a great challenge to the IPS. This paper considers the system stability in two aspects: the stability of system state variables in a periodic steady state under the action of pulse load, which refers to the stability of the periodic orbit, and the problem mentioned above, which cannot be described according to the stability of the equilibrium point and so needs further research. The analysis of the first aspect can lay the foundation for a study of the second aspect. This paper presents a mathematical model of the IPS with pulse load, uses the periodic-orbit method to analyze the system stability and stable margin and drives a state space averaging model of the system. For a relatively small state variable disturbance of the system under small signal disturbance, the state-space averaging method proves to be approximate to the periodic-orbit method. On this basis, the conventional state-space averaging method can be used for the analysis of system stability. The simulation and calculation show that the proposed method is feasible and effective.

Adaptive backstepping‐based control design for uncertain nonlinear active suspension system with input delay

SummaryThis paper addresses the control problem of adaptive backstepping control for a class of nonlinear active suspension systems considering the model uncertainties and actuator input delays and presents a novel adaptive backstepping‐based controller design method. Based on the established nonlinear active suspension model, a projector operator–based adaptive control law is first developed to estimate the uncertain sprung‐mass online, and then the desirable controller design and stability analysis are conducted by combining backstepping technique and Lyapunov stability theory, which can not only deal with the actuator input delay but also achieve better dynamics performances and safety constraints requirements of the closed‐loop control system. Furthermore, the relationship between the input delay and the state variables of this vehicle suspension system is derived to present a simple and effective method of calculating the critical input delay. Finally, a numerical simulation investigation is provided to illustrate the effectiveness of the proposed controller.

The Use of Integral Adaptation Principle to Synthesize Robust Control of Electric Vehicle Wheel Slip

The usage of "motor-wheel" systems requires the electric vehicle control system improvement by using the characteristics of the wheel adhesion to the road surface. One of the aspects of such improvement is the enhancement of the algorithms for the functioning of the antilock braking system (ABS). In developing the ABS control algorithms, various approaches and methods of modern control theory are used, including methods based on the estimation of wheel slip, traction force, wheel friction coefficient using linear and nonlinear estimation methods, linear and nonlinear regulators. This work illustrates the application of the principle of high order integral adaptation (PIA) of Synergetic Control Theory (SCT) for constructing a robust control law for an electric vehicle wheel slip. The main features of the SCT contain: firstly, a fundamental change in the goals of the behavior of the synthesized systems; secondly, direct consideration of the natural properties of nonlinear objects; thirdly, the formation of an analytical mechanism for generating feedbacks, i.e. control laws. PIA consists in introducing nonlinear integrators into the control law that compensate for disturbances without their immediate estimation. The obtained in this work control law has a fairly simple structure, is focused on using physically accessible state variables of the braking system, and its implementation does not require immediate estimation of disturbances or building a complex neural network to calculate disturbances. The results of computer simulations of the synthesized robust control law for ABS indicate its effectiveness in functioning under conditions of external environment uncertainty.

Adaptive Neural-Network-Based Dynamic Surface Control for Stochastic Interconnected Nonlinear Nonstrict-Feedback Systems With Dead Zone

In this paper, an adaptive neural-network-based dynamic surface control (DSC) method is proposed for a class of stochastic interconnected nonlinear nonstrict-feedback systems with unmeasurable states and dead zone input. First, an appropriate state observer is constructed to estimate the unmeasured state variables of the stochastic interconnected system. Then radial basis function neural networks combined with adaptive backstepping technique are applied to model the unknown nonlinear system functions of the stochastic interconnected system; and the DSC method is adopted to ensure the computation burden is greatly reduced. Furthermore, the proposed controllers guarantee that the closed-loop stochastic interconnected system is semi-globally bounded stable in probability. In the end, two simulation examples are provided to show the effectiveness and practicability of the proposed control scheme.

Fractional-order control for a novel chaotic system without equilibrium

The control problem is discussed for a chaotic system without equilibrium in this paper. On the basis of the linear mathematical model of the two-wheeled self-balancing robot, a novel chaotic system which has no equilibrium is proposed. The basic dynamical properties of this new system are studied via Lyapunov exponents and Poincare map. To further demonstrate the physical realizability of the presented novel chaotic system, a chaotic circuit is designed. By using fractional-order operators, a controller is designed based on the state-feedback method. According to the Gronwall inequality, Laplace transform and Mittag-Leffler function, a new control scheme is explored for the whole closed-loop system. Under the developed control scheme,the state variables of the closed-loop system are controlled to stabilize them to zero. Finally, the numerical simulation results of the chaotic system with equilibrium and without equilibrium illustrate the effectiveness of the proposed control scheme.

Delay Aware Power System Synchrophasor Recovery and Prediction Framework

This paper presents a novel delay aware synchrophasor recovery and prediction framework to address the problem of missing power system state variables due to the existence of communication latency. This capability is particularly essential for dynamic power system scenarios where fast remedial control actions are required due to system events or faults. While a wide area measurement system can sample high-frequency system states with phasor measurement units, the control center cannot obtain them in real-time due to latency and data loss. In this work, a synchrophasor recovery and prediction framework and its practical implementation are proposed to recover the current system state and predict future states utilizing existing incomplete synchrophasor data. The framework establishes an iterative prediction scheme, and the proposed implementation adopts recent machine learning advances in data processing. Simulation results indicate the superior accuracy and speed of the proposed framework, and investigations are made to study its sensitivity to various communication delay patterns for pragmatic applications.

Investigate on a Simplified Multi-Port Interline DC Power Flow Controller and Its Control Strategy

A DC power flow controller (DCPFC) can help to facilitate power flow routing in the multi-terminal high-voltage direct current (HVDC) transmission system. Realizing its multi-port output can effectively improve the device regulate range and capability. Based on analysis of the traditional multi-port interline DC power flow controller (MI-DCPFC), this paper presents a switches reduced topology of MI-DCPFC. In addition, for solving the problem of coupling of the port-output voltage of the traditional MI-DCPFC, a novel control strategy based on carrier phase shifting pulse width modulation (CPS-PWM) is proposed. It implements the decoupling of the port-output voltage of MI-DCPFC, which can ensure completely independent tracking of the power flow regulating commands for different controlled lines. Moreover, key relationships between the system state variables are also analyzed and detailed in this study. Finally, the performance of the proposed controller and control strategy are confirmed with the simulation and experiment studies under different conditions.

DECOMPOSITION OF LINEAR DISCRETE CONTROLLED SYSTEM WITH A SMALL STEP

When solving problems of optimal control of objects from various fields of science and technology, difficulties arise due to the high dimensionality of models and the presence of several temporal factors. In this regard, the problem is the decomposition of models. The paper proposes a method for decomposing a linear discrete controlled system with small steps. The equivalent system obtained with the complete separation of the state variables of a linear discrete controlled system with a small step has all the properties of the original system. It consists of two subsystems of low order, whose solutions are found independently, and they are connected only by the control function. The proposed approach combines the methods of asymptotic and approximate methods of analysis.

Optimal allocation of wind capacity considering the impact of generation uncertainty based on zonotope limited security regions

The increasing wind capacity integration brings new challenges to power system planning and operation, due to the intermittency and uncertainty of its power generations. This paper determines the optimal allocation of wind capacity with considerations of the impact of uncertainty in wind generation using the zonotope-based method, for the sack of reducing the possible violations of operation limits caused by wind power fluctuations. The uncertain variations of wind power are bounded by a zonotope and then propagated through a linearised power flow to get another zonotope, which captures all possible values of the system state variables. The state-bounding zonotope is then added to the optimal model to quantify and assess the impact of generation uncertainty on system static performance. The proposed method is applied to IEEE 33-bus system, the results prove the validity of the method and show that the zonotope based set-theoretic method is more efficient than probabilistic methods when focusing on the operation limits with considerations of the uncertainty of multiple renewable energy sources.

Adaptive Neural Control for Nonaffine Pure-Feedback System Based on Extreme Learning Machine

For nonaffine pure-feedback systems, an adaptive neural control method based on extreme learning machine (ELM) is proposed in this paper. Different from the existing methods, this scheme firstly converts the original system into a nonaffine system containing only one unknown term by equivalent transformation, thus avoiding the cumbersome and complex indirect design process of traditional backstepping methods. Secondly, a high-performance finite-time-convergence-differentiator (FD) is designed, through which the system state variables and their derivatives are accurately estimated to ensure the control effect. Thirdly, based on the implicit function theorem, the ELM neural network is introduced to approximate the uncertain items of the system, which simplifies the repeated adjustment process of the network training parameters. Meanwhile, the minimum learning parameter algorithm (MLP) is adopted to design the adaptive law for the norm of the network weight vector, which significantly reduces calculations. And it is theoretically proved that the closed-loop control system is stable and the tracking error is bounded. Finally, the effectiveness of the designed controller is verified by simulation.

Fuzzy logic approach for smooth transition between grid-connected and stand-alone modes of three-phase DG-inverter

In distributed generation systems, the worst case of operation is a sudden transition between Grid-Connected mode (GC) and Stand-Alone mode (SA). In this situation, system state variables, such as abrupt changes in currents, risk to contribute to the destruction of the whole power system. In this work, the use of the Fuzzy Logic (FL)-based approach for smooth transition between GC and SA is investigated. In contrast with the classical approach where the transition is a direct and abrupt change from the GC control mode to the SA mode, the Fuzzy Logic Algorithm (FLA) allows generating a feasible reference trajectory that ensures smooth transition between GC and SA modes through a unified control. Furthermore, the FL is employed to tune the voltage loop control in order to increase the disturbance rejection ability of the voltage loop. Also, the control design and the trajectory planning principle are detailed. The effectiveness of the proposed control is validated by simulation tests and its performance is compared to a conventional control scheme.

Analytical design of dynamic system regulators taking into account the effect of disturbing factors

This article deals with the problem of synthesis of optimal by the minimal value of integral-quadratic criterion dynamic systems, which are described by a model of equations in state variables. Based on finding the Lyapunov matrix and optimization equations, we propose a method for synthesizing a set of feedback loop coefficients with respect to state variables that provide the minimal value of integral quadratic criteria when exposed to external coordinate disturbances. Finding the feedback loop coefficients with respect to state variables of the dynamic system using the proposed method extends the optimization methods of such systems by integral-quadratic criteria in a vector-matrix description taking into account the action of external influences. The synthesis of the coefficients carried out on the example of a second-order dynamic system is also given. This method makes it possible to find the dependences of these coefficients on the initial coordinates of the dynamic system, as well as to synthesize a functional converter whose influence in the feedback loops optimizes the given system

Novel stochastic methods to predict short-term solar radiation and photovoltaic power

Solar forecasting has evolved towards becoming a key component of economical realization of high penetration levels of photovoltaic (PV) systems. This paper presents two novel stochastic forecasting models for solar PV by utilizing historical measurement data to outline a short-term high-resolution probabilistic behavior of solar. First, an uncertain basis functions method is used to forecast both solar radiation and PV power. Three possible distributions are considered for the uncertain basis functions - Gaussian, Laplace, and Uniform distributions. Second, stochastic state-space models are applied to characterize the behaviors of solar radiation and PV power output. A filter-based expectation-maximization and Kalman filtering mechanism is employed to recursively estimate the system parameters and state variables. This enables the system to accurately forecast small as well as large fluctuations of the solar signals. The introduced forecasting models are suitable for real-time tertiary dispatch controllers and optimal power controllers. The PV forecasting models are tested using solar radiation and PV power measurement data collected from a 13.5 kW PV panel installed on the rooftop of our laboratory. The results are compared with standard time series forecasting mechanisms and show a substantial improvement in the forecasting accuracy of the total energy produced.

Double-Loop Control with Hierarchical Sliding Mode and Proportional Integral Loop for 2D Ridable Ballbot

In this study, we propose a nonlinear double-loop control system for a ridable ballbot. An improved nonlinear double-loop control technique based on double-loop control scheme and sliding mode technology is used, and the inner-loop consists of proportional–integral feedback plus feedforward control. A sliding mode control enables the ridable ballbot to balance and transfer on the floor. Feedforward compensation has been added for the stability of the ballbot. As a result, the control system can stabilize all state variables of the ballbot system despite the uncertainties of the system parameters such as model, friction, and external disturbances, and relatively large body inertia. Experiments demonstrate the effectiveness of the proposed control system and the performance validation of the nonlinear double-loop control.

Design and implementation of hybrid Kalman filter for state estimation of power system under unbalanced loads

State estimation technique plays a vital role in predicting the stability of the power system and is done by estimating the primary variables (states) of the system. Voltage magnitudes (V) and angles (δ) at network buses define the state of a power system. Supervisory control and data acquisition is used to monitor and control the power system state variables where in accurate state variable estimation is quite complex due to the presence of noise in the measured data. State estimation (SE) using conventional techniques such as weighted least square, regularised least square, Kalman filter predict the state vectors with still random error due to its parametric limitations. This study proposes hybrid Kalman filter based SE where the limitation in efficient handling of more number of variables using Kalman filter is addressed by regularising the state variables with constrains and the results are validated for 62-bus Indian utility system. The simulation results explain the operational efficiency of the hybrid Kalman filtering method under various load variation conditions and the results are compared with SE using conventional Kalman filtering method.

Stochastic life-cycle analysis: renewal-theory life-cycle analysis with state-dependent deterioration stochastic models

For the life-cycle analysis (LCA) of deteriorating engineering systems, it is critical to model and incorporate the various deterioration processes and associated uncertainties. This paper proposes a renewal-theory life-cycle analysis (RTLCA) with state-dependent stochastic models (SDSMs) that describe the deterioration processes. The SDSMs capture the multiple deterioration processes and their interactions through modelling the changes in the system state variables due to different deterioration processes. Then proper capacity and demand models that take the time-variant state variables as input are adopted to fully capture the impact of deterioration processes on the capacity, demand, and other time-variant performance indicators of the engineering system. The SDSMs are then integrated into RTLCA to efficiently evaluate various life-cycle performance quantities such as availability, operation cost and benefits of the engineering system. To implement the proposed formulation, a sampling-based approach is adopted to simulate samples from the relevant probability density functions (PDFs) to estimate the life-cycle performance quantities, while stochastic simulation-based approach is adopted to estimate the time-variant performance indicators needed to inform intervention activities. As an illustration, the proposed formulation is used to analyse the life-cycle performances of an example reinforced concrete bridge subject to deterioration due to corrosion and seismic loading.

Feedback error learning-based type-2 fuzzy neural network predictive controller for a class of nonlinear input delay systems

In this paper, a type-2 fuzzy neural network predictive (T2FNNP) controller has been designed in the feedback error learning (FEL) framework for a class of input delay nonlinear systems considering of unknown disturbance and uncertainties. In this method, the predictor has been utilized to estimate the future state variables of the controlled system to compensate for the time-varying input delay. To establish the control objectives, the predicted states are fed to the controller which is in FEL framework and includes T2FNN parallel with classical feedback controller. Using the proposed T2FNNP controller, it is shown that the system output tracks the reference signal in presence of the measurement noise, time-varying delay, and bounded disturbance. An appropriate Lyapunov function has been exploited to study stability of the closed-loop system and to derive the adaptation laws for both the predictor and controller. A flexible joint robot system has been used to validate performance of the proposed T2FNNP controller and has been compared with a type-1 fuzzy sliding predictive controller through some simulations. The results indicate the efficiency of the proposed T2FNNP controller in dealing with time-varying delay as well as high level of measurement noise which exists in the sensor.

Ecological network analysis metrics: The need for an entire ecosystem approach in management and policy

In this paper, we identified seven ecological network analysis (ENA) metrics that, in our opinion, have high potential to provide useful and practical information for environmental decision-makers and stakeholders. Measurement and quantification of the network indicators requires that an ecosystem level assessment is implemented. The ENA metrics convey the status of the ecological system state variables, and mostly, the flows and relations between the various nodes of the network. The seven metrics are: 1) Average Path Length (APL), 2) Finn Cycling Index (FCI), 3) Mean Trophic level (MTL), 4) Detritivory to Herbivory ratio (D:H), 5) Keystoneness, 6) Structural Information (SI), and 7) Flow-based Information indices. The procedure for calculating each metric is detailed along with a short evaluation of their potential assessment of environmental status.

Data-driven robust fault tolerant linear quadratic preview control of discrete-time linear systems with completely unknown dynamics

In this paper, we propose a data-driven robust fault tolerant preview control scheme for discrete-time LTI systems with completely unknown dynamics. In general, this work consists of three key design parts. Firstly, the Markov parameters sequence is identified to extract system feature from data. Then, robust linear quadratic preview control policy composed of finite data feedback, integral operation and preview action is designed through establishing data-space characterisation and solving the related convex optimisation problem. Thirdly, an active fault tolerant method composed of fault detection, isolation, estimation and corresponding compensation is further constructed to accommodate fault influence. Note that all these involved designs are performed at Markov parameters sequence level. Thus above integrated preview control scheme can avoid the priori knowledge requirements including system matrices, order, and state variables. The effectiveness of the obtained results is finally verified via a case study of the injection moulding machine.

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

SummaryThis paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.