Variable Structure Systems Theory Research Articles

Distributed generation contribution to primary frequency control through virtual inertia and damping by reference conditioning

Penetration of converter-based distributed generation units (DGUs) rises quickly in the power systems. These generation units, which do not have any rotating masses, reduce the total system inertia, thus challenging both frequency control and system stability. In this work, to allow DGUs to contribute to primary frequency control, a sliding-mode reference conditioning loop (SMRC) is proposed. In this way, the DGUs aim to constrain both frequency deviation and rate of change of frequency within the boundaries established in the grid codes. The conditioning loop only acts if there is a risk of exceeding any of the established boundaries. Through variable structure system theory is shown that the conditioning loop behaves like a temporary contribution of virtual inertia and damping. Simulation results show that the conditioning loop allows DGUs to contribute to improving primary frequency control performance. Thus, exceeding the established boundaries is avoided with efficient use of energy.

Dynamic Performance Improvement of Doubly Fed Induction Motor Based on Hybrid Computational Technique and Variable Structure Control

The sliding mode control (SMC) methodology based on the theory of variable structure systems has been widely used for robust control of nonlinear systems. Nevertheless, this type of control has an essential inconvenience, which is the chattering phenomenon caused by the discontinuous control part. In order to reduce the effects of the chattering phenomenon, second order sliding mode (SOSM) seems to be a very attractive solution. To eliminate the remains of chattering phenomenon, a new control scheme based on fuzzy second order sliding mode control (FSOSMC) is proposed in this paper. This fuzzy second order sliding mode controller is destined to the speed control of doubly fed induction motor (DFIM) which is based on the decoupling control to enhance robustness under different operating conditions such as load torque and in the presence of parameters variation.
 The simulation results for various scenarios show the performances of the proposed control in terms of, precision, rapidity and stability for the high powers DFIM operating at variable speeds.

Robust Predictive Control of High-Density Cascaded DC Voltage Link Power Converters

Cascaded dc voltage link power converters typically employ a significant amount of energy storage at the intermediate link. The dc bus voltage is assumed to be stiff enough to provide decoupling between the source and load, allowing dynamic regulation functions to be implemented at the load and source terminals independently. In these cases, the size of the dc bus capacitance is dictated by requirements of steady-state ripple voltage, ripple current rating, ride-through considerations, and, more importantly, voltage overshoot during source and load transients. Design tradeoffs in realizing a stable system with acceptable transient performance often place a lower bound in the value of dc bus capacitance. In this paper, a robust predictive controller based on integrated and coupled control at the intermediate dc link, source, and load terminals is presented. The approach permits the use of a small amount of intermediate energy storage compared to conventional decoupled designs. The predictive control aspect of the proposed approach features cost function minimization and accurate duty ratio calculations based on converter model that accounts for small values of dc link capacitance. Although this allows stable operation of the system, it leads to persistent steady state error and transient overshoot voltages. The robust aspect of the proposed approach is based on the theory of variable structure systems. It introduces a capacitor charge restoration function that overcomes the drawbacks of the predictive control by squarely addressing uncertainty of model parameters and operating conditions. The resulting significant reduction in size of the capacitive reactive components opens the prospect of replacing electrolytic capacitors that have a limited life span with film capacitors with much longer life in emerging applications. The proposed approach is presented in a step-by-step manner using a dc-to-dc converter example and further extended to a dc-to-ac inverter case. Extensive computer simulations and experimental results from a laboratory-scale prototype of an example system are used to demonstrate the viability of the proposed controller.

Robust integral controllers for high‐order class‐D power amplifiers

This study presents variable structure system theory based robust integral controllers for class-D power amplifiers. These amplifiers are highly efficient switching type power amplifiers with negligible losses. Sensorless and current feedback based integral controllers with sliding modes are designed to provide robust tracking performance with negligible phase delays and distortions. The methods are capable of providing high-quality outputs by maximising gain and minimising the tracking error and phase shifts. The validity, feasibility and robustness performance of the controllers are investigated through circuit realisations.

Terminal Impact Angle Constraint Guidance With Dual Sliding Surfaces and Model-Free Target Acceleration Estimator

In this paper, a new guidance law based on the variable structure system theory and an associated model-free target acceleration estimator are proposed. The composite guidance-estimation law is designed to intercept constant-velocity and maneuvering targets by missiles at a desired terminal impact angle. Specifically, the scenario of intercepting the targets with speed-disadvantaged missiles, which has not been studied in detail in the literature available, is considered in this paper. A multiple solution problem for the terminal impact angle and a final line-of-sight angle is clarified in this paper. To solve this problem, the generalized variable structure theory is used and an additional sliding mode surface is introduced in the proposed guidance law, by which missiles can reach a wider range of the final impact angle. In addition, the nonsingular terminal sliding mode control method is applied so that the states of the guidance dynamic system are finite time convergent. In order to intercept maneuvering targets, a Kriging-based model-free finite impulse response filter is employed. Based on this filter, this paper puts forward some improvements, including a data preprocessing method and a parameter offline tuning method by the simulated annealing algorithm. In this way, a model-free target acceleration estimator with strong practicality in engineering is proposed. The stability condition of the proposed composite guidance-estimation law is obtained via the Lyapunov theorem. Finally, simulation results in different initial intercepting scenarios are presented to validate the advantage of the proposed guidance law and target acceleration estimator.

Nonlinear robust observer for structures with configuration-dependent natural frequencies: experimental and theoretical results

The theoretical development of advanced controllers and observers has greatly surpassed the experimental work in this field. The current study represents a significant step toward an overall objective of providing experimental validation of these advanced concepts. Therefore, the present work focuses on validating the robust performance of a self-tuning nonlinear observer in accurately estimating the state variables of a structure whose natural frequencies are configuration-dependent. The observer design is based on both the variable structure systems theory and the self-tuning fuzzy logic scheme. Its robustness and self-tuning characteristic allows the use of an imprecise model of the system and eliminates the need for the extensive tuning associated with a fixed rule-based expert fuzzy inference system. The physical system is selected to be a spherical robotic manipulator where only the protruding portion of the third link from the second link is considered to be flexible. The prismatic joint causes the length of the flexible link to vary, which induces significant variations in the natural frequencies of the link. The observer has been implemented to estimate the generalized coordinates of the flexible motion under two different types of excitation. The first one involves disturbances in the initial conditions or the use of initial impulsive forces. While in the second type, the structural deformations are induced by the rigid body motion of the arm during a tracking maneuver. Same numerical values for the observer’s parameters were used in conducting both theoretical and experimental works. The results demonstrate the robustness of the observer in accurately estimating the generalized coordinates of the flexible motion of the third link in spite of significant modeling imprecision and external disturbances.

이륜 도립진자 이동로봇을 위한 강인제어기 설계

The research on two-wheeled inverted pendulum (TWIP) mobile robots has been ongoing in a number of robotic laboratories around the world. In this paper, we consider a robust controller design for the TWIP mobile robot driving on uniform slopes. We use a 2 degree-of-freedom (DOF) model which is obtained by restricting the spinning motion in a 3 DOF motion dynamic equation. In order to design the robust controller guaranteeing stability of the TWIP mobile robot driving on inclined surface, we propose a sliding mode control based on the theory of variable structure systems and design a sliding surface using the theory of the linear quadratic regulation (LQR). For simulation, the dynamic model of the TWIP mobile robot is constructed using Mathworks` Simulink and the sliding mode control is also implemented using Simulink. From simulation results, we show that the proposed controller effectively controls the TWIP mobile robot driving on slopes.

A self-tuning robust observer for marine surface vessels

The current work aims at developing a nonlinear, self-tuning, robust observer to estimate state variables pertinent to the control of under-actuated marine surface vessels. The state estimator combines the advantages of the variable structure systems theory with those of the self-tuning fuzzy logic algorithm. It does not require an exact knowledge of the system dynamics or the construction of a rule-based expert fuzzy inference system. However, the upper bounds of both modeling imprecision and external disturbances must be known. The convergence of the estimation process is guaranteed by forcing the tuning parameters to satisfy inequalities stemming from the sliding conditions. The observer has been implemented herein to provide accurate estimate of the state variables that are needed by an integrated guidance and control system for the autonomous operation of an under-actuated marine surface vessel. The observer along with the integrated guidance and control system have been tested on a six degree-of-freedom ship model that considers numerous uncertainties associated with wave excitation, nonlinear restoring forces, retardation forces, sea-current and wind resistive loads. The theoretical results prove that the proposed self-tuning observer can produce accurate estimates of the state variables in the presence of significant modeling imprecision and environmental disturbances. In addition, they illustrate the use of estimated state variables in the guidance and control system with minimal impact on the close-loop performance of the marine vessel.

Impact of discontinuous harvesting on fishery dynamics in a stock-effort fishing model

We consider a stock-effort fishing model with discontinuous harvesting strategies. Under some reasonable assumptions on the discontinuous harvesting function, we are able to confirm the well-posedness of the model, describe the structure of possible equilibria as well as establish the stability/instability of the equilibria. Most interestingly, we find that the solutions of the fishing model can arrive at a sliding mode in finite time. A qualitative analysis shows that the goal of maintaining the system at a sustainable equilibrium and optimizing the harvesting can be achieved by introducing the discontinuous harvesting strategies. From the viewpoint of optimal harvesting, we can obtain that discontinuous harvesting strategies are superior to continuous harvesting strategies, which are usually adopted in previous literature. The main difficulty resides in the discontinuity of the model, and is conquered by exploiting the theory of differential equations with discontinuous righthand sides and variable structure system theory.

Online payload estimation for the control of underactuated mechanical systems

This paper presents a payload estimation scheme for underactuated robotic manipulators with passive joints that are not driven by actuators. In the proposed scheme, only the payload, which can be quite uncertain when a robot performs various tasks, is estimated, because the manipulator’s electrical and other mechanical parameters are generally known in advance. In comparison to other adaptive schemes for underactuated robotic manipulators, the proposed scheme produces satisfactory transient performance and also reduces the computational burden in real-time implementation. The proposed estimation law is also based on the theory of Variable Structure Systems. In contrast to existing adaptation laws that have an integral form, the proposed law estimates uncertain payload using lowpass filtering of a switching signal that is always bounded, which avoids the parameter-drifting problem that is often encountered when using the previous integral laws. Real-time experiments are conducted using an inverted pendulum and the experimental results demonstrate the feasibility and effectiveness of the proposed scheme.

A Coordinated Multi-Switch Attack for Cascading Failures in Smart Grid

This paper explores distributed smart grid attack strategies to destabilize power system components using variable structure system theory. Here, an opponent is able to remotely control multiple circuit breakers within a power system, say through data corruption or communication network attack, to destabilize target synchronous generators through application of state-dependent breaker switching. In contrast to attack via a single breaker, the multi-switch case provides additional degrees of freedom that can lead to stealthier and wide-scale cascading failures. We provide a dynamical systems context for formulating distributed multi-switch strategies and execute such attacks on the New England 10-generator 39-bus test system.

A Framework for Modeling Cyber-Physical Switching Attacks in Smart Grid

Security issues in cyber-physical systems are of paramount importance due to the often safety-critical nature of its associated applications. A first step in understanding how to protect such systems requires an understanding of emergent weaknesses, in part, due to the cyber-physical coupling. In this paper, we present a framework that models a class of cyber-physical switching vulnerabilities in smart grid systems. Variable structure system theory is employed to effectively characterize the cyber-physical interaction of the smart grid and demonstrate how existence of the switching vulnerability is dependent on the local structure of the power grid. We identify and demonstrate how through successful cyber intrusion and local knowledge of the grid an opponent can compute and apply a coordinated switching sequence to a circuit breaker to disrupt operation within a short interval of time. We illustrate the utility of the attack approach empirically on the Western Electricity Coordinating Council three-machine, nine-bus system under both model error and partial state information.

Terminal Impact Angle Constrained Guidance Laws Using Variable Structure Systems Theory

In this brief, variable structure systems theory based guidance laws, to intercept maneuvering targets at a desired impact angle, are presented. Choosing the missile's lateral acceleration (latax) to enforce sliding mode, which is the principal operating mode of variable structure systems, on a switching surface defined by the line-of-sight angle leads to a guidance law that allows the achievement of the desired terminal impact angle. As will be shown, this law does not ensure interception for all states of the missile and the target during the engagement. Hence, additional switching surfaces are designed and a switching logic is developed that allows the latax to switch between enforcing sliding mode on one of these surfaces so that the target can be intercepted at the desired impact angle. The guidance laws are designed using nonlinear engagement dynamics for the general case of a maneuvering target.

부족구동 기계시스템을 위한 적분 슬라이딩 모드 제어기 설계

부족구동시스템은 제어되어야 하는 자유도보다 더 적은 수의 구동부를 가진 시스템으로 특정질 수 있으며, 이런 시스템을 제어하기 위한 알고리즘을 찾는 문제에 대한 관심이 지속적으로 증대되고 있다. 가변구조시스템 이론을 기반으로 하는 슬라이딩 모드 제어기는 비선형 시스템을 제어하는데 있어 강건한 도구를 제공하고 있다. 본 논문에서는 부족구동시스템을 효과적으로 제어하기 위한 적분슬라이딩 함수를 이용한 슬라이딩 모드 제어기를 제안하고, Lyapunov 안정도 이론을 이용하여 점근적 안정성을 입증하였다. 제안된 제어기의 효용성을 검증하기 위해 대표적인 부족구동시스템인 아크로봇 (Acrobot)을 대상으로 시뮬레이션을 수행하였다. 아크로봇의 동적 모델은 Mathworks사의 Simscape을 이용하여 구현하였으며, 제어기 구성은 Simulink를 이용하여 구성하였다. 시뮬레이션 결과는 제안된 제어기의 유용성과 효과성을 입증하였다. The problem of finding control laws for underactuated systems has attracted growing attention since these systems are characterized by the fact that they have fewer actuators than the degrees of freedom to be controlled. A sliding mode control based on the theory of variable structure systems is a robust methodology to control nonlinear systems. In this paper, a sliding mode control with integral sliding function is proposed and asymptotical stability is proved in the Lyapunov's sense for underactuated systems. In order to verify the effectiveness of the proposed control, computer simulations for an acrobot, which is a representative underactuated system, are performed. Using Mathworks' Simulink/Simscape, the acrobot dynamics is implemented and the proposed control is composed. Simulations demonstrate the effectiveness and usefulness of the proposed control.

A practical design sliding mode controller for DC–DC converter based on control parameters optimization using assigned poles associate to genetic algorithm

This paper presents a simple and systematic approach to design sliding mode controller for buck converters. DC/DC switching converters have been used in many applications in recent years. The Sliding Mode Control (SMC) based on Variable Structure System (VSS) theory has been examined for buck switch mode converter type. To obtain a sliding regime, the appropriate sliding surface is selected by assigning poles combined with genetic algorithm. The associated practical problems and the proposed solutions are detailed; like fixed frequency by using pulse width modulation (PWM) as solution and overshoot limitation of the inductor current by using current limiter. A simple and easy to follow design procedure is also described. Simulation results are presented to illustrate the design procedure. The simulation results of the proposed SMC strategy are compared with the adaptive terminal sliding mode control (ATSMC) and PID-SMVC strategies. It is shown that the proposed SMC exhibits a considerable improvement in terms of a faster output voltage response during load changes.

Sliding mode control of reaction flywheel-based brushless DC motor with buck converter

Reaction flywheel is a significant actuator for satellites’ attitude control. To improve output torque and rotational speed accuracy for reaction flywheel, this paper reviews the modeling and control approaches of DC–DC converters and presents an application of the variable structure system theory with associated sliding regimes. Firstly, the topology of reaction flywheel is constructed. The small signal linearization process for a buck converter is illustrated. Then, based on the state averaging models and reaching qualification expressed by the Lee derivative, the general results of the sliding mode control (SMC) are analyzed. The analytical equivalent control laws for reaction flywheel are deduced detailedly by selecting various sliding surfaces at electromotion, energy consumption braking, reverse connection braking stages. Finally, numerical and experimental examples are presented for illustrative purposes. The results demonstrate that favorable agreement is established between the simulations and experiments. The proposed control strategy achieves preferable rotational speed regulation, strong rejection of modest disturbances, and high-precision output torque and rotational speed tracking abilities.

A self-tuning guidance and control system for marine surface vessels

An integrated guidance and control system has been developed to enable underactuated marine surface vessels to operate autonomously and yield robust tracking performance in spite of significant external disturbances and modeling imprecision. A nonlinear ship model, accounting for all six degrees-of-freedom of the ship, has been used as a test bed to assess the performance of the proposed scheme. The controller combines the advantages of the variable structure systems (VSS) theory with the self-tuning fuzzy logic scheme. It does not require an accurate dynamic model of the ship or the construction of a rule-based expert system. Its asymptotic stability is ensured by knowing the upper bounds on modeling imprecision and external disturbances and by forcing the tuning parameters to satisfy the sliding conditions. The guidance system is based on the concepts of the variable radius line-of-sight (LOS) and the acceptance circle around the waypoints. The current system varies the LOS radius exponentially with the cross track error in order to achieve a fast convergence rate of the ship to its desired trajectory. The simulation results demonstrate the robust tracking characteristic of the integrated guidance and control system in spite of significant modeling uncertainties and environmental disturbances.

Flexible power control of fuel cells using sliding mode techniques

The energy conversion system considered in this work consists of a fuel cell connected to a DC-bus through a switching converter. Particularly, the paper deals with the control of the electrical variables of this system. The control problem is addressed using tools of variable structure systems theory. The dynamic behavior of the system is first analyzed. Then, sliding mode algorithms to control electrical variables according to different power management objectives are developed. Thus, different control strategies such as fuel cell voltage/current regulation, maximum power point tracking and/or load current regulation can be followed. After studying their stability properties, these algorithms are combined to achieve a globally stable control over the whole electrical operating locus of the fuel cell. Experimental results on a test circuit are presented.

Neuro-fuzzy control of antilock braking system using sliding mode incremental learning algorithm

A neuro-fuzzy adaptive control approach for nonlinear dynamical systems, coupled with unknown dynamics, modeling errors, and various sorts of disturbances, is proposed and used to design a wheel slip regulating controller. The implemented control structure consists of a conventional controller and a neuro-fuzzy network-based feedback controller. The former is provided both to guarantee global asymptotic stability in compact space and as an inverse reference model of the response of the controlled system. Its output is used as an error signal by an incremental learning algorithm to update the parameters of the neuro-fuzzy controller. In this way the latter is able to gradually replace the conventional controller from the control of the system. The proposed new learning algorithm makes direct use of the variable structure systems theory and establishes a sliding motion in terms of the neuro-fuzzy controller parameters, leading the learning error toward zero. In the simulations and in the experimental studies, it has been tested on the control of antilock breaking system model and the analytical claims have been justified under the existence of uncertainty and large nonzero initial errors.

Black‐box position and attitude tracking for underwater vehicles by second‐order sliding‐mode technique

AbstractIn this work we address the tracking control problems for autonomous underwater vehicles (AUVs). The proposed solution is based on the variable structure systems (VSS) theory and, in particular, on the second‐order sliding‐mode (2‐SM) methodology. The tuning of the controller is carried out via black‐box approach, dispensing with the knowledge of the actual AUV parameters, by simply progressively increasing a single gain parameter. The presented stability analysis includes explicitly the unmodelled actuator dynamics and the presence of external uncertain disturbances. The good performance of the proposed scheme is verified by means of simulations on a 6‐DOF AUV. Copyright © 2009 John Wiley & Sons, Ltd.