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In the present paper, a new algorithm for solving the control problem in electrical power systems, is introduced. This new algorithm is based on the sliding mode property existing in variable structure system (VSS). The resulting control law is discontinuous by its nature. However, it does not require accurate informations about the system parameters or its manner of variation. The only requirements are the maximum and minimum limits of variation for each parameter, An adaptive controller is designed for an electrical power system, on the basis of that new algorithm The main function of the controller is the frequency control of the electrical power system, meanwhile, it can be used for stability improvement, Theoretical and computational results, using that controller insure the frequency control property in the electrical power system model. The adaptive property verifies under rapid and wide range of parameters variation and also, under the effect of a unit step external disturbance.

This study considers the fault-tolerant control (FTC) issue for a class of linear interconnected parabolic distributed parameter systems by utilising the backstepping-based sliding mode control technique. The original interconnected system, which suffers from process/actuator faults and matched disturbances, is converted into a stable target system by using an invertible backstepping transformation. Two types of kernel functions, the distinct diffusivity and the same diffusivity, are obtained. A sliding mode FTC scheme is developed to eliminate the destabilising effects caused by process/actuator faults and matched disturbances. An industrial application example is presented to validate the applicability and the relevance of the developed methodology.

Dynamic flux balance models (DFBM) are used in this study to infer metabolite concentrations that are difficult to measure online. The concentrations are estimated based on few available measurements. To account for uncertainty in initial conditions the DFBM is converted into a variable structure system based on a multiparametric linear programming (mpLP) where different regions of the state space are described by correspondingly different state space models. Using this variable structure system, a special set membership-based estimation approach is proposed to estimate unmeasured concentrations from few available measurements. For unobservable concentrations, upper and lower bounds are estimated. The proposed set membership estimation was applied to batch fermentation of E. coli based on DFBM.

In this paper, a simple new design method of the sliding mode control based on the integral compensation of an output error is described. The key to this method is to obtain a control with a switching function. The proposed linear control input is robust against plant parameter deviations and external disturbances. We confirmed the effectiveness of the proposed method through simulation of a second and a third order plant.

The denomination Fractional Order Calculus has been widely used to describe the mathematical analysis of differentiation and integration to an arbitrary non-integer order, including irrational and complex orders. First proposed around three hundred years ago, it has attracted much interest during the past three decades (Oldham & Spanier (1974), Miller & Ross (1993), Podlubni (1999)). The increased interest in fractional systems in the past few decades is due mainly to a large body of physical evidence describing fractional order behavior in diverse areas such as fluid mechanics, mechanical systems, rheology, electromagnetism, quantitative finances, electrochemistry, and biology. Fractional order modeling provides exceptional capabilities for analysing memory-intense and delay systems and it has been associated with the exact description of complex transport phenomena such as fractional history effects in the unsteady viscous motion of small particles in suspension (Coimbra et al. 2004, L’Esperance et al. 2005). Although fractional order dynamical and control systems were studied only marginally until a few decades ago, the recent development of effective mathematical methods of integration of non-integer order differential equations (Charef et al. (1992); Coimbra & Kobayashi (2002), Diethelm et al. (2002); Momany (2006), Diethelm et al. (2005)) has resulted in a number of control schemes and algorithms, many of which have shown better performance and disturbance rejection compared to other traditional integer-order controllers (Podlubni (1999); Hartly & Lorenzo (2002), Ladaci & Charef (2006), among others). Variable order (VO) systems constitute a generalization of fractional order representations to functional order. In VO systems the order of the derivative changes with respect to either the dependent or the independent variables (or both), or parametrically with respect to an external functional behavior (Samko & Ross, 1993). Compared to fractional order applications, VO systems have not received much attention, although the potential to characterize complex behavior by the functional order of differentiation or integration is clear. Variable order formulations have been utilized, among other applications, to describe the mechanics of an oscillating mass subjected to a variable viscoelasticity damper and a linear spring (Coimbra, 2003), to analyze elastoplastic indentation problems (Ingman & Suzdalnitsky (2004)), to interpolate the behavior of systems with multiple fractional terms (Soon et al., 2005), and to develop a statistical mechanics model that yields a macroscopic constitutive relation for a viscoelastic composite material undergoing compression at varying strain rates (Ramirez & Coimbra, 2007). Concerning the dynamics and control of VO

International audience; This study considers the fault-tolerant control (FTC) issue for a class of linear interconnected parabolic distributed parameter systems by utilising the backstepping-based sliding mode control technique. The original interconnected system, which suffers from process/actuator faults and matched disturbances, is converted into a stable target system by using an invertible backstepping transformation. Two types of kernel functions, the distinct diffusivity and the same diffusivity, are obtained. A sliding mode FTC scheme is developed to eliminate the destabilising effects caused by process/actuator faults and matched disturbances. An industrial application example is presented to validate the applicability and the relevance of the developed methodology.

Heave compensation systems are widely used to decouple the load motion from wave-induced vessel motion for the equipment handling on the ocean. Researches have been made to achieve successful compensation, yet few of them discusses the inherent constraints of the systems, such as bounded compensator's stroke and max actuator's velocity. This paper presents a solution for active heave compensation systems with such constraints by means of variable structure control. The controller's complexity on design procedures and effectiveness are compared with a trajectory planning control method which turns out that the variable structure controller is more suitable to apply to the active heave compensators. The back-stepping method is used to robustly stabilize this variable structure system and for the aim of a decrease on the high robust gain due to uncertain friction term, a modified decoupled friction observer is used which is also verified by both theoretical and experimental analyses. To compensate for the time delay of the motion reference unit (MRU), a heave prediction algorithm is used. The experimental results show that most heave motion can be compensated when the motion and its velocity are feasible, while no hit occurs otherwise.

The paper deals with some new results on the averaging theory approach for the analysis of feedback controlled pulsewidth modulation power electronic converters. It develops some considerations regarding the averaging approximation of time-variant differential systems proving an analytical relationship between the accuracy with which the solution of the averaged model converges to the solution of the original time-variant model (i.e., the switched model) and the switching frequency of the converters. This relation is valid both for stable and unstable systems. Moreover, this paper confirms, as corollary, that under suitable conditions (verified during the standard operations of the power electronic converters) the averaged model uniformly converges to the switched model.

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.

The aim of this paper is to introduce a matrix approach for approximate solving of non-commensurate fractional variable order linear control systems in state-space form. The approach is based on switching schemes that realize variable order derivatives. The obtained numerical solution is compared with simulation and analog model results.

The paper proposes a new Variable Structure System (VSS) control algorithm and its application in underwater robotics. The main features of the proposed approach consist on the usage of coupled switching surfaces, and on the usage of an adaptive adjustment method for their parameters in order to accelerate the transient processes. The adaptive algorithm of linear and nonlinear switching surfaces coefficients, is based on the stabilization of the sliding mode parameter close to the reference value. In this paper, it is shown how the proposed approach improves the system transient processes and the energy efficiency in comparison with conventional VSS, neutralizing also some drawbacks. The proposed adaptive VSS algorithm is applied to control a Remotely Operated Vehicle (ROV), and simulation results confirm the advantages to apply it.

Variable universe is through a group of nonlinear contraction expansion factors online timely to adjust the input domain, so that the input domain is subdivided as detailed as possible at surrounding the expected control points. It is characteristic of constant rules, quick response, and high stability precision. In this paper, a nonlinear hybrid fuzzy system was established by introducing adjusting parameters to combine Mamdani fuzzy system and Takagi–Sugeno (T–S) fuzzy system. The input–output expression of the nonlinear hybrid fuzzy system based on variable universe was deduced according to the hybrid inference rules and contraction expansion factors. Furthermore, the second-order approximation of the nonlinear hybrid fuzzy system based on variable universe on the second-order continuously differentiable function was proved by multiple Taylor formula and maximum norm, and a sufficient condition for the approximation of the nonlinear hybrid fuzzy system was disclosed when adjusting parameters and approximation accuracy are known. Finally, the simulation example confirmed that the established nonlinear hybrid fuzzy system based on variable universe has better approximation performance than other systems under different adjusting parameter meanings.

Linear time-invariant discrete-time plant, with no restrictions on the form of the state equation and with scalar control, is considered. The exponentially stabilizing state feedback control algorithm is developed by Lyapunov’s second method leading to the variable structure system with chattering free sliding modes. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspace S, in finite time and with prescribed velocity estimate. Inside the sliding subspace S, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, direct current (DC) servo motor, and simulation and experimental results are given. Also, it is compared with another already known algorithm from literature.

An application of binary state latch device with proper real-time control algorithm for energy redistribution application is introduced in this thesis. Unlike traditional tuned vibration absorber, the latch device can be viewed as variable semi-active dampers such as magnetorheological (MR) and piezoelectric friction dampers. The distinct difference between other semi-active dampers and our latch device is that other semi-active dampers can provide continuous resistance according to the amount of input current, however, the binary latch device can only provide two different values of resistance - either the maximum or no resistance at all. This property brings the latch possibly having higher maximum and minimum ratio of resistance than MR dampers. As for the operating structure, the mechanism of latch element is nearly the same as the piezoelectric friction dampers which the resistance force is provided according to the normal force acting on two rough plates. Nonetheless, because of the characteristic of the binary states output of the latch element, this make it very different from the ordinary variable dampers. Since it is either being turned on or turned off, a novel control law is required for shifting energy. Also, because of the simplicity of the binary states output, it is very accessible to implement the controller on Field Programmable Gate Array (FPGA). With this accessibility, it is promising to apply plenty of latch elements in the same time for large scale application, such as multi-agent networks. In this thesis, an energy-based analytic solution is proposed to illustrate the universal latch-off condition. And a latch-on condition under ideal situations is discussed. At the end, a control law under nonideal condition is being suggested for real-time periodically excited system. We found that energy redistribution is achievable by using the proper control law under fairly broad conditions. Master of Science

Hybrid mathematical models are often represented as continuous functions with discontinuous inputs, or they are visualised as state machines or petri-nets comprising continuous models linked by discontinuous mappings. The analysis and simulation of hybrid (or nonsmooth dynamical) models is plagued with difficulty, necessitating careful consideration of energy losses and state reinitialisation on commutation. The author proposes an alternative model, where states are discontinuous. The engineer familiar with techniques such as signal flow graphs or bond graphs can clearly visualise discontinuities as breaks (or joins) in power flow between parts of the model. A mixed-Boolean state equation can be derived which reflects the physics of switching behaviour. This has two advantages: first, by considering the physics incrementally about the discontinuity it can be simulated without the need for state reinitialisation algorithms, and second, it can be analysed for structural control properties to show how they change with commutation.

The article focuses on the issues of Load Frequency Control (LFC) under non-linear strategies in multi source multi area hydro thermal system. On practical perspective dead band, boiler dynamics, reheat steam turbine along with hydro turbine operating under two different area capacities are considered in the system. When subjected to random load variations in both the areas, the system exhibits higher oscillations. The speed governor matches the generation with the demand. The offset in the area frequencies and tie-line power is removed by using secondary Proportional Integral (PI) controller. The PI controller is tuned using Ziegler Nichols' (ZN) and Fuzzy Gain Scheduling (FGS) method. The influence of high Proportional (P) controller gain during steady state and high Integral (I) controller gain during transient affects the system performance. Variable Structure System (VSS) helps to switch from P to PI controller during transient to steady state based on control error. The concept of VSS is applied to Fuzzy Gain Scheduling (FGS) PI controller. The performance of the optimal Variable Structure Fuzzy Gain Scheduled (VSFGS) controller under non-linear environment is judged and validated using performance indices.

24 p.; Input-to-State Stability (ISS) and the ISS-Lyapunov function have proved to be useful tools for the analysis and design of nonlinear systems in a variety of contexts. Motivated by the fact that many feedback control laws, such as model predictive control or event-based control, lead to discontinuous discrete-time dynamics, we investigate ISS-Lyapunov functions for such systems. ISS-Lyapunov functions were originally introduced in a so-called implication form and, in many cases, this has been shown to be equivalent to an ISS-Lyapunov function of dissipative form. However, for discontinuous dynamics, we demonstrate via an example that this equivalence no longer holds. We therefore propose a stronger implication form ISS-Lyapunov function and provide a complete characterization of ISSLyapunov functions for discrete-time systems with discontinuous dynamics.

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.

In this paper, we derive guaranteed gain, sector, and disk margins for nonlinear optimal and inverse optimal discontinuous feedback regulators that minimize a nonlinear-nonquadratic performance functional for Filippov dynamical systems. Specifically, we consider dynamical systems with Lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving Filippov set-valued maps. In addition, we extend classical dissipativity theory to address the problem of dissipative discontinuous dynamical systems. These results are then used to derive extended Kalman-Yakubovich-Popov conditions for characterizing necessary and sufficient conditions for dissipativity of discontinuous systems using Clarke gradients and locally Lipschitz continuous storage functions. Furthermore, using the newly developed dissipativity notions we develop a return difference inequality to provide connections between dissipativity and optimality of nonlinear discontinuous controllers for Filippov dynamical systems. Specifically, using the extended Kalman-Yakubovich-Popov conditions we show that our discontinuous feedback control law satisfies a return difference inequality if and only if the controller is dissipative with respect to a quadratic supply rate.

The research and verification of a variable structure high voltage power supply unit and its control strategy are introduced. According to the mathematical modeling method, the variable structure system is linearized equivalent analysis and closed-loop system design. The actual parameter verification and theoretical verification of the system are carried out by means of experimental identification, and the research of subsequent control strategies is guided. According to the analysis results and the dynamic parameters of the power supply, a control strategy based on Predictive PI is proposed and simulated. In addition, in order to realize the actual verification of the power supply control algorithm, a power controller based on the ARM and FPGA architecture is designed to be applied to the system. Experiments show that the control strategy can solve the complex variation of the nonlinear and variable structure of the power supply under dynamic conditions, and ensure that the system completes the established parameter indicators.

Tracking control of manipulators with joint flexibility is considered to achieve a higher control technique performance. An integral variable structure control (IVSC) approach for robot manipulators is presented for accurate servo-tracking in the presence of load variation, parameter uncertainty and nonlinear dynamic interactions. A procedure is proposed for choosing the control function so that it guarantees the existence of the sliding mode and for determining the coefficients of the switching plane and integral control gain. Furthermore, a modified proper continuous function is introduced to overcome the chattering problem. The proposed (IVSC) approach has been simulated for a two-degree of freedom flexible joint robot, each joint modeled by two-equations of second order. Stability is insured by the use of Liapunov's direct method. The simulation results demonstrate the potential of the proposed scheme. Keywords: Flexible joint robot, Integral variable structure system, Sliding mode, Switching plane, Servo- tracking, Stability criterion, Dynamic uncertainty, Chatter.

This paper analyzes a discrete variable structure system for control n-th order plants with nonminimum phase zeros in the input-output transfer function. The problem is solved by using the technique of stable system center. The first is a discrete mathematical model of the system in the normal canonical form for a given system. Then the synthesis of state generator and discrete 'time controller using the center of a stable system. The theoretical results are demonstrated in a numerical example.

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.

This study presents the design of a current control loop and the selection of switching logic for pulse-width modulation (PWM) of three-phase switching converters. This approach is based on a deliberate introduction of the predictive sliding mode motion within a control system. It shows that the selection of the PWM pattern is a direct result of sliding mode existence within the current control closed-loop system. The design specifications are robustness to load electrical parameters, fast dynamic response, reduced switching frequency and simple hardware implementation. To meet previous specifications, a sliding mode controller has been developed, designed as a finite state machine, and implemented within a field programmable gate array device. The switching strategy implemented within the state transition diagram provides for a minimum number of switch state changes by the three-phase converter that is confirmed through simulation and experimental results.

An adaptive robust attitude tracking control law based on switched nonlinear systems is presented for a variable structure near space vehicle (VSNSV) in the presence of uncertainties and disturbances. The adaptive fuzzy systems are employed for approximating unknown functions in the flight dynamic model and their parameters are updated online. To improve the flight robust performance, robust controllers with adaptive gains are designed to compensate for the approximation errors and thus they have less design conservation. Moreover, a systematic procedure is developed for the synthesis of adaptive fuzzy dynamic surface control (DSC) approach. According to the common Lyapunov function theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded by the continuous controller. The simulation results demonstrate the effectiveness and robustness of the proposed control scheme.

An elastic beam system formulated by partial differential equations with initial and boundary conditions is investigated in this paper. An evolution equation corresponding with the beam system is established in an appropriate Hilbert space. The spectral analysis and semigroup generation of the system operator of the beam system are discussed. Finally, a variable structural control is proposed and a significant result that the solution of the system is exponentially stable under a variable structural control with some appropriate conditions is obtained.

A unilaterally constrained perturbed double integrator system is studied in this paper. The aim is to establish uniform finite time stability of the non-linear dynamics in the presence of impacts due to the constraints on the position variable. A non-smooth transformation is utilized to first transform the system into a variable structure system that can be studied within the framework of a conventional discontinuous paradigm. Then, a finite time stable continuous controller is used and stability of the closed-loop dynamics is proven by identifying a new set of Lyapunov functions. The results enable continuous and discontinuous cases to be unified using one parameter that defines the set of Lyapunov functions for each case.

In this paper, a variable structure observer design approach is proposed for a class of nonlinear, large-scale interconnected systems in the presence of unstructured uncertainty. The modern geometric approach is exploited to explore the system structure and a transformation is developed to facilitate observer design. Using the Lyapunov direct method, a robust asymptotic observer is presented which exploits the internal dynamic structure of the system as well as the structure of the uncertainties. The bounds on the uncertainties are nonlinear and are employed in the observer design to reject the effect of the uncertainties. A numerical example is presented to illustrate the approach and the simulation results show that the proposed approach is effective.

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Attitude control of satellites using fluid rings is studied in this paper. A complete dynamics model of a rigid satellite containing fluid rings is developed. It is noticed that when the fluid rings are used as passive controllers they can damp out all attitude disturbances if the satellite is in a circular orbit and only roll―yaw disturbances if the satellite is in an elliptic orbit. However, this passive damping effect is fairly slow. Hence, an active controller is developed to reduce the settling time. To add redundancy to the attitude control system (ACS) of the satellite, four fluid rings in a pyramidal configuration are used. Also, the effect of the failure of one fluid ring on the performance of the ACS of the satellite is tested. Finally, a hybrid controller that is composed of a sliding mode controller and a proportional integral derivative is designed in order to cope with the model uncertainties and eliminate chattering in the response of the system.