687 research outputs found

    Output tracking via sliding modes in causal systems with time delay modeled by higher order pade approximations

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    Output tracking in a SISO causal uncertain nonlinear system with an output subject to a time delay is considered using sliding mode control. A higher order Pade approximation to a delay function with a known time delay is used to construct a model of a transformed system without a time delayed output and is employed in a feedback sliding mode control. This model functions as a predictor of the plant states and the plant output, but is of nonminimum phase due to the application of the Pade approximation. The method of the stable system center is used to stabilize the internal dynamics of this plant model, and a control is developed using a sliding surface to allow the plant to track an arbitrary reference profile given by an exogenous system with a known characteristic equation. Simulations of the system are performed for the plant model using a first, second and third order Pade approximations and a controller in plant feedback mode. Numerical examples for Pade approximations of increasing order are considered and compare

    Second-order SM approach to SISO time-delay system output tracking

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    A fully linearizable single-input-single-output relative-degree n system with an output time delay is considered in this paper. Using the approach of Pade approximation, system center approach, and second-order sliding-mode (SM) control, we have obtained good output tracking results. The Smith predictor is used to compensate the difference between the actual delayed output and its approximation. A second-order supertwisting SM observer observes the disturbance in the plant. A nonlinear example is studied to show the effect of this methodology

    Stability Analysis of parameter-excited linear Vibration Systems with Time Delay, using the Example of a Sheetfed Offset Printing Press

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    This article describes stability studies on parameter-excited linear vibration systems with time delay. A method for stability analysis is presented. Therefore, the transcendental transmission element of the time delay e-st is approximated as an all-pass element with the rational transfer function by means of the so-called Padé approximation. The system can be represented in the state space and the methods of the Floquet theory can also be applied to the system with approximated time delay. The process can be implemented without great effort in a standardized simulation environment such as MATLAB/SIMULINK, whereby existing models and methods can be reused. The suitability of the method is shown in the well-known example of the Mathieu differential equation with time delay. Variations between different solvers and approximation orders are described. An extended view and the transfer to an industrial application take place with the example of the drive of a sheetfed offset printing machine. The relevant vibration system is represented by an oscillator with several degrees of freedom. The belt, which couples the degrees of freedom of the drive motor and the machine, leads to a periodic (harmonic) parameter excitation of the system due to its inhomogeneous nature. The speed and position control of the drive motor (PI controller) is associated with a time delay, resulting in a system of the type described above

    Characteristic study, its identification and self-tuned approach to control hydro-power plants

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    The water time constant and mechanical time constant greatly influences the power and speed oscillations of hydro-turbine-generator unit. This paper discusses the turbine power transients in response to different nature and changes in the gate position. The work presented here analyses the characteristics of hydraulic system with an emphasis on changes in the above time constants. The simulation study is based on mathematical first-, second-, third- and fourth-order transfer function models. The study is further extended to identify discrete time-domain models and their characteristic representation without noise and with noise content of 10 & 20 dB signal-to-noise ratio (SNR). The use of self-tuned control approach in minimising the speed deviation under plant parameter changes and disturbances is also discussed

    Model order reduction for neutral systems by moment matching

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    Observer Based Cylinder Charge Estimation for Spark-ignition Engines

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    Internal combustion engines require accurate cylinder charge estimation for determining engine torque, controlling air-to-fuel ratio (AFR), and ensuring high after-treatment efficiency. This is challenging due to the highly transient operating conditions that are common in automobile engines. The problem is further complicated by spark ignition (SI) engine technologies such as variable valve timing (VVT) and exhaust gas recirculation (EGR) which are applied to improve fuel economy and reduce pollutant emissions. With manifold filling/emptying/mixing phenomenon and different actuator response times, these technologies significantly increase the complexity of cylinder charge estimation. Current cylinder charge estimation methodologies require a combination of sensors and empirical models to deal with the high degrees of control freedom existent on the engine. But these methods have the drawbacks of great dependency on accurate calibration and poor transient performance. Most importantly, the current methods isolate feed-forward cylinder charge estimation and feedback AFR control. When there is discrepancy between target lambda value and sensed lambda value at exhaust side, the current control/estimation method will trim the fuel injection amount no matter where the error source is. As a matter of fact, the error might come from the throttle flow estimation, the fuel injection flow estimation, EGR flow estimation, or any combination of these error sources. Increased air-path complexity and drawbacks of traditional methods drive the need for cost effective solutions that produce high air/EGR/fuel charge estimation accuracy with the ability to identify the error source while minimizing sensor cost, computational effort, and calibration time. This research first evaluates the existing work on air charge estimation for SI engines with massive experimental tests covering various operating conditions, which are designed for the algorithm verification of this research. Then several estimation methods which utilize both Manifold Absolute Pressure (MAP) and Mass Air Flow (MAF) sensors are studied and analyzed. Reduction of calibration effort and improvement of accuracy are observed from the proposed cylinder air charge estimation methods. Following that, a model is built to study the engine gas path dynamics and characteristics and then simplified to provide system dynamic basis for the following estimation algorithm development. Using the developed model, a disturbance observer based cylinder charge estimation technique is developed based on a combination of sensors including MAF, MAP, and exhaust lambda sensors. This developed algorithm significantly improves engine states estimation accuracy compared to conventional Single-Input-Single-Output (SISO) methods. Also, the augmentation of disturbance observation is able to pin point the source of the estimation error. Through experimental validation, using the developed estimation method with proper parameters, the error source of estimation can be identified and rectified when disturbance is introduced to throttle flow model, EGR flow model, fuel injection flow model or any combination of these models. The structure of the proposed algorithm should adapt to most SI engine configurations. It can help the engine controller to mitigate modeling errors thus improve the performance of physics model based engine control especially AFR control

    Quasilinear Control of Systems with Time-Delays and Nonlinear Actuators and Sensors

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    This thesis investigates Quasilinear Control (QLC) of time-delay systems with nonlinear actuators and sensors and analyzes the accuracy of stochastic linearization for these systems. QLC leverages the method of stochastic linearization to replace each nonlinearity with an equivalent gain, which is obtained by solving a transcendental equation. The idea of QLC is to stochastically linearize the system in order to analyze and design controllers using classical linear control theory. In this thesis, the existence of the equivalent gain for a closed-loop time-delay system is discussed. To compute the equivalent gain, two methods are explored. The first method uses an explicit but complex algorithm based on delay Lyapunov equation to study the time-delay, while the second method uses Pade approximant. It is shown that, under a suitable criterion, Pade approximant can be effectively applied for QLC of time-delay systems. Furthermore, the method of Saturated-Root Locus (S-RL) is extended to nonlinear time-delay systems. It turns out that, in a time-delay system, S-RL always terminates prematurely as opposed to a delay-free system, which may or may not terminate prematurely. Statistical experiments are performed to investigate the accuracy of stochastic linearization compared to a system without time-delay. The impact of increasing the time-delay in the approach of stochastic linearization is also investigated. Results show that stochastic linearization effectively linearizes a nonlinear time-delay system, even though delays generally degrade accuracy. Overall, the accuracy remains relatively high over the selected parameters. Finally, this approach is applied to pitch control in a wind turbine system as a practical example of a nonlinear time-delay system, and its performance is analyzed to demonstrate the efficacy of the approach

    Introducing LQR-fuzzy for a dynamic multi area LFC-DR model

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    It is well known that Load Frequency Control (LFC) model plays a vital role in electric power system design and operation. In the literature, much research works has stated on the advantages and realization of DR (Demand Response), which has proved to be an important part of the future smart grid. In an interconnected power system, if a load   demand changes randomly, both frequency and tie line power varies. LFC-DR model is tuned by standard controllers like PI, PD, PID controllers, as they have constant gains. Hence, they are incapable of acquiring desirable dynamic performance for an extensive variety of operating conditions and various load changes. This paper presents the idea of introducing a DR control loop in the traditional Multi area LFC model (called LFC -DR) using LQR- Fuzzy Logic Control. The effect of DR-CDL i.e. (Demand Response Communication Delay Latency) in the design is also considered and is linearized using Padé approximation. Simulation results shows that the addition of DR control loop with proposed controller guarantees stability of the overall closed-loop LFC-DR system which effectively improves the system dynamic performance and is superior over a classical controller at different operating scenarios

    Stability analysis of linear ODE-PDE interconnected systems

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    Les systèmes de dimension infinie permettent de modéliser un large spectre de phénomènes physiques pour lesquels les variables d'états évoluent temporellement et spatialement. Ce manuscrit s'intéresse à l'évaluation de la stabilité de leur point d'équilibre. Deux études de cas seront en particulier traitées : l'analyse de stabilité des systèmes interconnectés à une équation de transport, et à une équation de réaction-diffusion. Des outils théoriques existent pour l'analyse de stabilité de ces systèmes linéaires de dimension infinie et s'appuient sur une algèbre d'opérateurs plutôt que matricielle. Cependant, ces résultats d'existence soulèvent un problème de constructibilité numérique. Lors de l'implémentation, une approximation est réalisée et les résultats sont conservatifs. La conception d'outils numériques menant à des garanties de stabilité pour lesquelles le degré de conservatisme est évalué et maîtrisé est alors un enjeu majeur. Comment développer des critères numériques fiables permettant de statuer sur la stabilité ou l'instabilité des systèmes linéaires de dimension infinie ? Afin de répondre à cette question, nous proposons ici une nouvelle méthode générique qui se décompose en deux temps. D'abord, sous l'angle de l'approximation sur les polynômes de Legendre, des modèles augmentés sont construits et découpent le système original en deux blocs : d'une part, un système de dimension finie approximant est isolé, d'autre part, l'erreur de troncature de dimension infinie est conservée et modélisée. Ensuite, des outils fréquentiels et temporels de dimension finie sont déployés afin de proposer des critères de stabilité plus ou moins coûteux numériquement en fonction de l'ordre d'approximation choisi. En fréquentiel, à l'aide du théorème du petit gain, des conditions suffisantes de stabilité sont obtenues. En temporel, à l'aide du théorème de Lyapunov, une sous-estimation des régions de stabilité est proposée sous forme d'inégalité matricielle linéaire et une sur-estimation sous forme de test de positivité. Nos deux études de cas ont ainsi été traitées à l'aide de cette méthodologie générale. Le principal résultat obtenu concerne le cas des systèmes EDO-transport interconnectés, pour lequel l'approximation et l'analyse de stabilité à l'aide des polynômes de Legendre mène à des estimations des régions de stabilité qui convergent exponentiellement vite. La méthode développée dans ce manuscrit peut être adaptée à d'autres types d'approximations et exportée à d'autres systèmes linéaires de dimension infinie. Ce travail ouvre ainsi la voie à l'obtention de conditions nécessaires et suffisantes de stabilité de dimension finie pour les systèmes de dimension infinie.Infinite dimensional systems allow to model a large panel of physical phenomena for which the state variables evolve both temporally and spatially. This manuscript deals with the evaluation of the stability of their equilibrium point. Two case studies are treated in particular: the stability analysis of ODE-transport, and ODE-reaction-diffusion interconnected systems. Theoretical tools exist for the stability analysis of these infinite-dimensional linear systems and are based on an operator algebra rather than a matrix algebra. However, these existence results raise a problem of numerical constructibility. During implementation, an approximation is performed and the results are conservative. The design of numerical tools leading to stability guarantees for which the degree of conservatism is evaluated and controlled is then a major issue. How can we develop reliable numerical criteria to rule on the stability or instability of infinite-dimensional linear systems? In order to answer this question, one proposes here a new generic method, which is decomposed in two steps. First, from the perspective of Legendre polynomials approximation, augmented models are built and split the original system into two blocks: on the one hand, a finite-dimensional approximated system is isolated, on the other hand, the infinite-dimensional truncation error is preserved and modeled. Then, frequency and time tools of finite dimension are deployed in order to propose stability criteria that have high or low numerical load depending on the approximated order. In frequencies, with the aid of the small gain theorem, sufficient stability conditions are obtained. In temporal, with the aid of the Lyapunov theorem, an under estimate of the stability regions is proposed as a linear matrix inequality and an over estimate as a positivity test. Our two case studies have been treated with this general methodology. The main result concerns the case of ODE-transport interconnected systems, for which the approximation and stability analysis using Legendre polynomials leads to exponentially fast converging estimates of stability regions. The method developed in this manuscript can be adapted to other types of approximations and exported to other infinite-dimensional linear systems. Thus, this work opens the way to obtain necessary and sufficient finite-dimensional conditions of stability for infinite-dimensional systems
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