State Variables Of System Research Articles

Affine linear parameter‐varying embedding of non‐linear models with improved accuracy and minimal overbounding

In this study, automated generation of linear parameter-varying (LPV) state-space models to embed the dynamical behaviour of non-linear systems is considered, focusing on the trade-off between scheduling complexity and model accuracy and the minimisation of the conservativeness of the resulting embedding. The LPV state-space model is synthesised with affine scheduling dependency, while the scheduling variables themselves are non-linear functions of the state and input variables of the original system. The method allows to generate complete or approximative embedding of the non-linear system model and also it can be used to minimise the complexity of existing LPV embeddings. The capabilities of the method are demonstrated on simulation examples and also in an empirical case study where the first-principle motion model of a three degrees of freedom (3DOF) control moment gyroscope is converted by the proposed method to an LPV model with low scheduling complexity. Using the resulting model, a gain-scheduled controller is designed and applied on the gyroscope, demonstrating the efficiency of the developed approach.

A unified method to the design of an improved high frequency sliding mode current controller for DC/DC boost converter in continuous current condition based on analogue implementation

In this study, an improved high frequency sliding mode current controller is proposed for DC/DC power converters in continuous current condition using analogue-based implementation. The sliding mode control is a variable frequency method. In this strategy, the controller frequency is a function of summation of all time delays of different parts of control circuit. If these delays increase, the switching frequency extremely decreases, steady error of the output voltage increases; and also, the converter frequency may be less than the audible frequency. In practical applications, it is extremely important that the output voltage tracks exactly its reference signal. Moreover, the switching frequency of a power converter must be more than $$ 20\;{\text{kHz}} $$ in practice. A good way for enhancement of the switching frequency and dynamical performance of the sliding mode method is to use all state variables of the controlled system in the sliding manifold. This attempt has been made for the voltage regulation and input current control of a typical Boost converter in this paper. Using sliding mode theory and Filippov’s method, the stability of the suggested controller is established. Simulations and practical implementation of the proposed system show that the developed controller is successful to control the converter at high frequencies by removing the voltage error in steady region, despite using low speed and cheap electrical devices in the control circuit.

Representing scientific knowledge for quantitative analysis of physical systems

Representation of scientific knowledge in ontologies suffers so often from the lack of computational knowledge required for inference. This article aims to perform quantitative analysis on physical systems, that is, to answer questions about values of quantitative state variables of a physical system with known structure. For this objective, we incorporate procedural knowledge on two distinct levels. At the domain-specific level, we propose a representation model for scientific knowledge, i.e. variables, theories, and laws of nature. At the domain-independent level, we provide an algorithm which, given a system S with known structure and a relevant scientific theory T, extracts a constraint network, whose variables are state variables of S defined by T, and whose constraints raise from relevant laws in T. The constraint network is then solved, to build a system of equations whose unknowns are the output variables of S. The proposed representation model and reasoning algorithm are evaluated by applying them to classic analysis examples.

Performance-Oriented Fault Detection for Nonlinear Control Systems via Data-Driven T-S Fuzzy Modeling Technique

This article studies the performance-oriented fault detection (FD) for nonlinear control systems in the data-driven framework. Unlike the traditional residual- or test statistic-based FD methods, the proposed approach focuses on evaluating the system performance changes/degradations caused by the faults. Specifically, the regulation performance described by an infinite-time cost function is first introduced as a control performance index of the feedback system. Using only the process input and output (I/O) data, a Takagi–Sugeno fuzzy dynamic model is constructed with the aid of subspace identification method. Then, the internal system state variables are expressed in terms of the I/O data and a fuzzy cost function is proposed to approximate the performance index. On this basis, the temporal difference error induced by the Bellman equation is adopted as the process evaluation indicator, whose threshold is determined through the randomized algorithm. To demonstrate the effectiveness of the proposed FD approach, case studies are performed in the end on a ship propulsion system and a three-tank system.

Non-linear modelling of elastic hysteretic damping in the time domain

Elastic hysteretic damping is defined as the dissipation of energy at a rate that is weakly dependent on frequency of vibration. In this article, we propose that the elastic hysteretic damping can be achieved by a simple modification to the viscous damping model. The proposed modification is based on computing an instantaneous correction factor that recursively depends on the state variables of the system. This correction factor is related to the rate by which the velocity changes with respect to the displacement. The new model compares quite favourably with the other existing solutions in the time-domain and differences between the solutions become evident for higher damping ratios. It is found that the new model predicts consistently the weak variation in the loss factor as a function of frequency. In addition to its simple mathematical formulation, the proposed model is superior to the existing solutions in that it does not require knowledge of the past history of motion neither the knowledge of the excitation frequency and is extensible to any type of loading. Various aspects pertaining to the linearity of the proposed approach are finally discussed.

A novel nonsmooth approach for flexible multibody systems with contact and friction in 3D space

For computational multibody system dynamics, contact and friction problems are very complex and important problems. Therefore, this paper proposes a novel nonsmooth method for flexible multibody systems with contact and friction in 3D space. Considering the nonsmooth effect of contact and friction on the state variable of the multibody systems, the proposed method is divided into two parts: (i) the change of state variables under the action of smooth force and (ii) the change of state variables caused by contact and friction. Furthermore, for the contact part, the Newton’s impact law and the classical Coulomb friction model are employed to deal with normal impact contact impulse and tangential friction contact impulse, respectively. In addition, Fischer–Burmeister function and Karush–Kuhn–Tucker conditions are also used to solve the normal impact contact impulse and tangential friction contact impulse. What’s more, since the symplectic discrete format performs well robustness to numerical results, the discrete format of the proposed method is based on the symplectic discreteness, and it is expected to obtain the robust numerical results. Finally, several numerical examples are tested by the proposed nonsmooth method, and the numerical simulation results verify the effectiveness of the proposed approach.

Smart Grid State Estimation with PMUs Time Synchronization Errors

State Estimation (SE) is one of the essential tasks to monitor and control the smart power grid. This paper presents a method to estimate the state variables combining the measurement of power demand at each bus with the data collected from a limited number of Phasor Measurement Units (PMUs). Although PMU data are usually assumed to be perfectly synchronized with the Coordinated Universal Time (UTC), this work explicitly considers the presence of time-synchronization errors due, for instance, to the actual performance of GPS receivers and the limited stability of the internal oscillator. The proposed algorithm is a recursive Kalman filter which not only estimates the state variables of the power system, but also the frequency deviations causing clock offsets which eventually affect the timestamps of the measures returned by different PMUs. The proposed solution was tested and compared with alternative approaches using both synthetic data applied to the IEEE 123 bus distribution feeder and real-field data collected from a small-size medium-voltage (MV) distribution system located inside the EPFL campus in Lausanne. Results show the validity of the proposed method in terms of state estimation accuracy. In particular, when some synchronization errors are present, the proposed algorithm can estimate and compensate for them.

An Extended Kalman Filter, with pre-adjusted covariance matrices, applied to the sensorless speed control of three-phase induction motors

With the emergence of sensorless control methods, there was a need for the use of estimators and/or state observers to give it the robustness and precision required in the drive of induction motors. This work deals with the application of the Extended Kalman Filter (EKF) in the estimation of rotor speed and position, aiming at the implementation of the indirect vector control technique in a sensorless speed control system for three-phase induction motors. The mathematical development of the system state variables associated with the EKF stochastic process is presented in this study, and point out its application under variable speed and load conditions, which are imposed on these motors in everyday life. The sensorless control strategy was tested through routine lines in the Matlab® software, simulating operating conditions of this type of engine, being proven its performance, as well as the convergence times consistent with the usual requirements of high performance systems. The main contributions of this work are the use of a reduced-order EKF (ROEKF) and the preset of covariance matrices to accelerate convergence in speed and position estimates for future implementations in currently accessible digital signal processors.

Adaptive Fuzzy Fixed-Time Decentralized Control for Stochastic Nonlinear Systems

This article studies the problem of adaptive fuzzy fixed-time decentralized control for nonlinear interconnected systems with stochastic disturbances and unknown nonlinearities. In control design, fuzzy logic systems are utilized to identify the unknown nonlinear functions. Combining stochastic fixed-time Lyapunov stability theory with adaptive backstepping control technique, a fuzzy adaptive fixed-time decentralized control design algorithm is developed by adopting smooth projection operator. It is proved that all the state variables of the closed-loop system are globally fixed-time stable in probability. Finally, both numerical and practical examples are provided to elucidate the feasibility of the proposed control algorithm.

Effect of optimal uncoupling in enhancing synchronization stability in drive-response systems

In this paper, we report the implementation of the method of optimal uncoupling and its effect in enhancing the stability of synchronization in certain coupled third-order chaotic systems. The clipping of phase space of the response system to a finite width having certain orientation about the coordinate axes representing the state variables of the response system insists that those state variables are coupled with their counterpart of the drive system. The stability of synchronization is studied through the master stability function (MSF). The optimal directions of implementing the clipping width to achieve stable synchronization is observed by studying the effectiveness of the clipping fraction and the sufficient range of orientation to identify the optimal directions is reported. The functional work steps for identifying the optimal directions are presented and the synchronization of the response system with the drive within the clipped region of phase space for different orientations of clipping width are studied. The stability of synchronization for different orientations of the clipping widths and the two-parameter bifurcation diagram indicating the negative valued MSF regions obtained for the optimal direction of clipping width are presented. The application of the method of optimal uncoupling in identifying the direction of the implication of the clipping width is discussed and the range of orientation over which the clipping width has to be varied is generalized.

Application of the Kalman filtering technique for nonlinear state estimation in propulsion system

The estimation of the propulsion system states and especially of the main engine is essential for control, diagnosis and performance evaluation. If all the required sensors were available, providing required measurements, the state and performance monitoring is of no particular difficulty. However, not all the required parameters can be measured directly, or the addition of multiple measurement channels is out of appropriateness. Furthermore, the propulsion plant state dynamics is justified by propeller load torque fluctuation that in turn is caused by fluctuating effective inflow velocity into the propeller, and which cannot be measured directly. Thus, the problem of estimating unmeasured state and disturbance variables of the propulsion system is considered and formulated as the design of an unknown input observer under model uncertainty and nonlinearity. To solve the design problem, this paper introduces a nonlinear engine dynamic model to catch the internal engine states and an unscented Kalman filter for concurrently performing disturbance and state estimation. The effectiveness is verified through the experiments.

Maximum power extraction framework using robust fractional-order feedback linearization control and GM-CPSO for PMSG-based WECS

The most important issue in the use of wind energy conversion systems is to ensure maximum power extraction in terms of efficiency. Therefore, maximum power point tracking algorithms are as important as the maximum power point tracking controller. In this study, maximum power extraction frameworks operating the state-of-the-art optimization methods are presented for permanent magnet synchronous generator–based wind energy conversion system. These frameworks consist of a Gauss map–based chaotic particle swarm optimization and a hybrid maximum power point tracking approach that combines feedback linearization technique with fractional-order calculus. The feedback linearization control strategy can fully decouple and linearize the original state variables of the nonlinear system and thus provide an optimal controller crossing wide-range operating conditions. The objective is to maintain the tip speed ratio at its optimal value, which implies the use of a rotational speed loop. The method is based on the feedback linearization technique and the fractional control theory. Gauss map–based chaotic particle swarm optimization, which is a remarkable and recent optimization technique, is utilized to achieve optimum coefficients to efficiently ensure the maximum power point tracking operation in here. A simulation study is carried out on a 3-kW wind energy conversion system to show the effectiveness of the proposed control scheme.

Disturbance-Compensation-Based Continuous Sliding Mode Control for Overhead Cranes With Disturbances

For practical mechanical systems, uncertainties/disturbances, such as unmodeled dynamics and frictions, are nonignorable factors. For existing control methods, these factors are usually neglected or addressed by a robust way. As a consequence, the nominal control performance of these methods is sacrificed. Moreover, there exists the chattering problem for some existing robust methods, such as sliding mode control laws. To deal with these drawbacks, a continuous global sliding mode controller along with a nonlinear disturbance observer is designed for the regulation and disturbance estimation control of the overhead crane system. Specifically, the original crane dynamic model is transformed into a quasi-integrator-chain form through some transformations. Then, a nonlinear disturbance observer is designed and a continuous global sliding mode control method is introduced on the basis of the constructed disturbance observer. The stability and convergence characteristics are proven through rigorous theoretical analysis. Finally, to demonstrate the performance of the designed controller, a series of experimental tests are performed, and a comparison study between the devised method here and an existing method is given. Note to Practitioners —This article is motivated by the desire to deal with the regulation and disturbance rejection of the overhead crane system. In practical applications, uncertainties/disturbances are unavoidable problems for overhead cranes. For most existing methods, these issues are usually addressed in a robust way. To handle these existing problems, a nonlinear disturbance observer and a continuous global sliding mode controller are proposed for the regulation and disturbance estimation control of the overhead crane system. The disturbance observer is introduced to estimate and compensate for uncertain disturbances, and the sliding mode controller is designed to guarantee the convergence of the state variables of the closed-loop system. In the future, we will try to apply this method to practical overhead cranes.

Risk- and variance-aware electricity pricing

The roll-out of stochastic renewable energy sources (RES) undermines the efficiency of power system and market operations. This paper proposes an approach to derive electricity prices that internalize RES stochasticity. We leverage a chance-constrained AC Optimal Power Flow (CC AC-OPF) model, which is robust against RES uncertainty and is also aware of the resulting variability (variance) of the system state variables. Using conic duality theory, we derive and analyze energy and balancing reserve prices that internalize the risk of system limit violations and the variance of system state variables. We compare the risk- and variance-aware prices on the IEEE 118-node testbed.

Association Analysis-Based Cybersecurity Risk Assessment for Industrial Control Systems

With the adoption of various information and communication technologies and commercial off-the-shelf components, industrial control systems (ICSs) become highly vulnerable to cyberattacks. Dynamic cybersecurity risk assessment (CSRA) plays a vital role in the security protection of ICSs. To reduce the complexity of the modeling process in the dynamic CSRA, an association analysis-based CSRA approach is proposed in this article. It designs a three-layer association network (AN) to infer the probabilities of security incidents. The parameters of the AN are derived through mining the data of historical attack records. From a distance correlation analysis of the process data of the target system, an association matrix is obtained between the system state variables and the key security variables to quantify the cybersecurity risk of the system. A case study is conducted on a coupling tanks control system to demonstrate the effectiveness and timeliness of the proposed approach.

A Functional Unknown Input Observer for Linear Singular Fornasini–Marchesini First Model Systems: With Application to Fault Diagnosis

Estimation of the state variables of dynamical systems in the presence of noise, disturbance, and fault is an important problem in the control and monitoring field. In this article, the mentioned issue is addressed for singular 2-D systems in Fornasini-Marchesini first model (FM-I). In this regard, a functional unknown input observer is proposed to eliminate the effects of unknown inputs and estimate a given linear combination of the system states. Moreover, the proposed observer can be used to estimate the faults and necessary and sufficient conditions for the simultaneous estimation of states and faults are derived. Finally, the performance of the proposed estimation methods is validated through a numerical example and a second-order parabolic heat equation.

Sensorsless Electrostatic Suspension System Based on Observer Controller

This paper introduces a new type of active electrostatic suspension system without using position sensors. The concept is to design a feedback controller without using position signals of the object instead using the voltage signals. In the working process of the electrostatic suspension system, the capacitance formed between the electrode and the suspended object is treated as a capacitor of two parallel plates, and if the gap length between them is changed the capacitance is then changed. This causes to change the voltage across the capacitance formed between the electrode and suspended object. This voltage is measured, and it then is used to estimate all variables of the system that are the displacement, velocity of the suspended object, and voltage across the capacitance formed. These estimated values are employed in the feedback schema instead of actual states values. The design of the controller follows the classical observer state-space approach. First, a state feedback controller is constructed with the assumption that all the state variables of the suspension system that are displacement, velocity of the suspended object, and voltage across the capacitance formed by the electrodes and the suspended object, are available for feedback. Second, a full observer is designed for estimating all the states from the measured voltage across the capacitance. Finally, the estimated signals produced by the full observer are used in the feedback controller instead of the actual states, and the self-sensing electrostatic suspension without using position sensors is achieved. The experimental and simulation results show that the suspended object successfully levitated at reference gap without using position sensors.

A weighted distributed predictor-feedback control synthesis for interconnected time delay systems

The paper investigates the control design of interconnected time delay systems by means of distributed predictor-feedback delay compensation approaches and event-triggered mechanism. The idea behind delay compensation is to counteract the negative effects of delays in the control-loop by feeding back future predictions of the system state. Nevertheless, an exact prediction of the overall system state vector cannot be obtained providing that each system has only knowledge of their local data regarding the system model and state variables. Consequently, predictor-feedback delay compensation may lose effectiveness if the coupling between subsystems is sufficiently strong. To circumvent this drawback, the proposed distributed predictor-feedback control incorporates extra degree of freedom for control synthesis by introducing new weighting factors for each local prediction term. The design of the weighting factors is addressed, together with the event-triggered parameters, by an algorithm based on Linear Matrix Inequalities (LMI) and the Cone Complementarity Linearization (CCL). Simulation results are provided to show the achieved improvements and validate the effectiveness of the proposed method, even in the case that other control strategies fail to stabilize the closed-loop system.

State Estimation for Situational Awareness of Active Distribution System With Photovoltaic Power Plants

The real-time monitoring of the grid-connected renewable energy generations is of great significance to the operation and control of active distribution systems (ADS). Considering the detailed photovoltaic (PV) system model and ambient influencing factors, this paper develops a state estimation framework for the ADS with integrated PV power plants. Firstly, suitable models of PV arrays and power converters for steady-state state estimation are developed. Based on these models, the state variables of a PV generation system are selected, and the measurement equations are derived. Finally, combined with the state estimation model of distribution networks, a framework for state estimation and bad data processing of an ADS with PV power plants is presented. A parameter estimation approach for PV power plants based on multiple measurement scans is also developed in order to address the practical situation of unknown model parameters. Simulation results show that the proposed framework can effectively capture the operating state of the distribution network and PV power plants. In addition, it enhances the estimation accuracy and bad data processing capability compared to conventional state estimation frameworks.

Observer-based finite-time output feedback control of heat equation with Neumann boundary condition

This paper is concerned with the problem of boundary observer-based finite-time output feedback control for a heat system with Neumann boundary condition and Dirichlet boundary actuator. In this system, it is endowed a single sensor at the left boundary and actuator at the right boundary. First, a backstepping finite-time observer is designed. Based on linear switching observer gains with state-dependent switching, the proposed observer estimates the system state variables in a finite-time only using one displacement boundary measurement. Then, an observer-based linear switching output feedback control with state-dependent switching is presented, which steers any solution of the output feedback closed-loop system to zero in a finite-time. Finally, the simulation results are provided to support the theoretical results.