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Control Systems Technology, IEEE Transactions on

Issue 2 • Date March 2009

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Displaying Results 1 - 25 of 27
  • Table of contents

    Publication Year: 2009 , Page(s): C1 - C4
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  • IEEE Transactions on Control Systems Technology publication information

    Publication Year: 2009 , Page(s): C2
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  • A Bottom-Following Preview Controller for Autonomous Underwater Vehicles

    Publication Year: 2009 , Page(s): 257 - 266
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1294 KB) |  | HTML iconHTML  

    This paper describes a solution to the problem of bottom-following for autonomous underwater vehicles (AUVs) that relies on the evaluation of the terrain characteristics ahead of the vehicle using echo sounders. The methodology used poses the problem as a discrete time path following control problem where a conveniently defined error state space model of the plant is augmented with bathymetric (i.e., depth) preview data. A piecewise affine parameter-dependent model representation is adopted that describes the AUV linearized error dynamics for a predefined set of operating regions. For each region, a state feedback H 2 control problem for affine parameter-dependent systems is posed and solved using linear matrix inequalities (LMIs). The resulting nonlinear controller is implemented as a gain-scheduled controller using the D-methodology. Simulation results obtained with a nonlinear dynamic model of the INFANTE AUV in the vertical plane are presented and discussed. View full abstract»

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  • Sensorless Tilt Compensation for a Three-Axis Optical Pickup Using a Sliding-Mode Controller Equipped With a Sliding-Mode Observer

    Publication Year: 2009 , Page(s): 267 - 282
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1395 KB) |  | HTML iconHTML  

    A sliding-mode controller equipped with a sliding-mode observer is synthesized and applied to a novel three-axis four-wire optical pickup for the purpose of sensorless tilt compensation. The three-axis pickup owns the capability to move the lens holder in three directions of focusing, tracking and tilting, which is required particularly for higher data-density optical disks and precision measuring instruments to annihilate nonzero lens tiltings. To achieve the sensorless compensation, Lagrange's equations are first employed to derive equations of motion for the lens holder. A sliding-mode controller is then designed to perform dynamic decoupling and forge control efforts toward the goals of precision tracking, focusing, and zero tilting. Along with the controller, a sliding-mode observer is designed to perform the online tilt estimation of the lens holder. This estimated tilt allows the previously designed sliding-mode controller to be implemented in most existing commercial pickups without additional photodiodes to detect the tilting motion of the lens holder. A full-order high-gain observer is next forged to estimate the moving velocities of the lens holder in order to provide low-noised feedback velocity signals for the designed sliding-mode controller. Simulations are carried out to choose appropriate controller and observer gains. Finally, experiments are conducted to validate the effectiveness of the controller for annihilating lens tilting and the capability of the tilt observer for performing sensorless tilt compensation. View full abstract»

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  • Humidity and Pressure Regulation in a PEM Fuel Cell Using a Gain-Scheduled Static Feedback Controller

    Publication Year: 2009 , Page(s): 283 - 297
    Cited by:  Papers (9)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1456 KB) |  | HTML iconHTML  

    In this paper, the pressure difference between the anode and cathode compartments of a polymer electrolyte membrane (PEM) fuel cell stack is regulated along with the anode and cathode humidities using an anode recirculation system. The pressure regulation requirement stems from membrane safety considerations. The regulation of average humidities in the two compartments is a necessary (although not a sufficient) requirement for stack water management. Two actuators in the anode recirculation system are considered, namely the dry hydrogen flow and the anode back pressure valve. These actuators are adjusted using a static output feedback controller that relies on pressure and humidity measurements on the anode side of the fuel cell stack. As the water mass dynamics and the characteristics of the water transport through the PEM are significantly different between subsaturated conditions (water is present only in vapor phase) and saturated conditions (liquid water along with water vapor), we show that the performance of the static output feedback controller with a fixed set of gains for subsaturated condition deteriorates significantly under a saturated condition. A gain-scheduled controller is therefore developed to compensate for a water-vapor saturated cathode condition. Analysis and simulation provide insights on some of the design and implementation issues for the gain-scheduled output feedback system. View full abstract»

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  • Nonconservative Robust Control: Optimized and Constrained Sensitivity Functions

    Publication Year: 2009 , Page(s): 298 - 308
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (710 KB) |  | HTML iconHTML  

    An automated procedure for optimization of proportional-integral-derivative (PID)-type controller parameters for single-input, single-output (SISO) plants with explicit model uncertainty is presented. Robustness to the uncertainties is guaranteed by the use of Horowitz-Sidi bounds, which are used as constraints when low-frequency performance is optimized in a nonconvex but smooth optimization problem. In the optimization (and hence the parameter tuning), separate criteria are formulated for low-, mid-, and high-frequency (HF) closed-loop properties. The tradeoff between stability margins, control signals, HF robustness, and low-frequency performance is clarified, and the final parameter choice is facilitated. We use a combination of global and local optimization algorithms in the TOMLAB optimization environment and obtain robust convergence without relying on good initial estimates for the controller parameters. The method is applied to a controller structure comparison for a plant with an uncertain mechanical resonance and a plant with uncertain time delay and time constants. For a given control activity, stability margin, and HF robustness, it is shown that a PID controller with a second-order filter and an H infin controller based on loop-shaping achieve approximately the same low-frequency performance. View full abstract»

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  • Optimal Real-Time Scheduling of Control Tasks With State Feedback Resource Allocation

    Publication Year: 2009 , Page(s): 309 - 326
    Cited by:  Papers (7)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (708 KB) |  | HTML iconHTML  

    This paper proposes a new approach for the optimal integrated control and real-time scheduling of control tasks. First, the problem of the optimal integrated control and nonpreemptive off-line scheduling of control tasks in the sense of the H2 performance criterion is addressed. It is shown that this problem may be decomposed into two subproblems. The first subproblem aims at finding the optimal nonpreemptive off-line schedule and may be solved using the branch and bound method. The second subproblem uses the lifting technique to determine the optimal control gains, based on the solution of the first subproblem. Second, an efficient online scheduling algorithm is proposed. This algorithm, called the reactive pointer placement (RPP) scheduling algorithm, uses the plant state information to dispatch the computational resources in a way that improves control performance. Control performance improvements as well as stability guarantees are formally proven. Finally, simulations as well as experimental results are presented in order to illustrate the effectiveness of the proposed approach. View full abstract»

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  • Speed Observer and Reduced Nonlinear Model for Sensorless Control of Induction Motors

    Publication Year: 2009 , Page(s): 327 - 339
    Cited by:  Papers (22)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (600 KB) |  | HTML iconHTML  

    We consider field-oriented speed control of induction motors without mechanical sensors. We augment the traditional approach with a flux observer and derive a sixth-order nonlinear model that takes into consideration the error in flux estimation. A high-gain speed observer is included to estimate the speed from field-oriented currents and voltages. The observer design is independent of the feedback controller design. By high-gain-observer theory, we define a virtual speed output for the sixth-order nonlinear model, which can now be used to design a feedback controller whose performance is recovered by the speed observer when the observer gain is chosen high enough. We then focus on the traditional field oriented control (FOC) approach where the flux is regulated to a constant reference and high-gain current controllers are used. By designing a flux regulator to maintain the flux at a constant reference, and a current regulator to regulate the q-axis current to its command, we derive a third-order nonlinear model that captures the essence of the speed regulation problem. The model has the speed and two flux estimation errors as the state variables, the q -axis current as the control input, and the virtual speed as the measured output. It enables us to perform rigorous analysis of the closed-loop system under different controllers, and under uncertainties in the rotor and stator resistances and the load torque. In this paper, we emphasize the design of feedback controllers that include integral action. The analysis reveals an important role played by the steady-state product of the flux frequency and the q-axis current in determining the control properties of the system. The conclusions arrived at by using the reduced-order model are collaborated by simulation and experimental results. View full abstract»

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  • Adaptive Control of Electrostatic Microactuators With Bidirectional Drive

    Publication Year: 2009 , Page(s): 340 - 352
    Cited by:  Papers (18)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (988 KB) |  | HTML iconHTML  

    In this paper, adaptive control is presented for a class of single-degree-of-freedom (1DOF) electrostatic microactuator systems which can be actively driven bidirectionally. The control objective is to track a reference trajectory within the air gap without knowledge of the plant parameters. Both full-state feedback and output feedback schemes are developed, the latter being motivated by practical difficulties in measuring velocity of the moving plate. For the full-state feedback scheme, the system is transformed to the parametric strict feedback form, for which adaptive backstepping is performed to achieve asymptotic output tracking. Analogously, the output feedback design involved transformation to the parametric output feedback form, followed by the use of adaptive observer backstepping to achieve asymptotic output tracking. To prevent contact between the movable and fixed electrodes, special barrier functions are employed in Lyapunov synthesis. All closed-loop signals are ensured to be bounded. Extensive simulation studies illustrate the performance of the proposed control. View full abstract»

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  • Identification of a Managed River Reach by a Bayesian Approach

    Publication Year: 2009 , Page(s): 353 - 365
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1121 KB) |  | HTML iconHTML  

    This paper considers the problem of identification, and more particularly of time-delay estimation, of a river reach managed to produce hydroelectric power. Difficulties lie in the obligation to use data collected during a combined feedback/feedforward control carried out by a human operator. We propose a Bayesian identification method, non-supervised and simple to implement, estimating jointly the time-delay and a finite-impulse response (FIR). It is based on the detection of an abrupt change in the FIR at a time equal to the time-delay. Experimental results show the effectiveness of the proposed method to estimate the river reach time-delay from data collected in imposed experimental conditions. View full abstract»

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  • Online References Reshaping and Control Reallocation for Nonlinear Fault Tolerant Control

    Publication Year: 2009 , Page(s): 366 - 379
    Cited by:  Papers (16)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (621 KB) |  | HTML iconHTML  

    In this paper, we consider the problem of graceful performance degradation, for affine nonlinear systems. The method is an optimization based scheme, that gives a constructive way to reshape online the output reference for the post-fault system, and explicitly take into account the actuators and states saturations. The online output reference reshaping is associated with an online, model predictive control (MPC)-based, controller reconfiguration, that forces the post-fault system to track the new output reference. The effect of fault detection and diagnosis (FDD) uncertainties on the online controller reconfiguration stability are studied, to ensure at least boundedness of the closed-loop system's states. The reshaping and reconfiguration schemes are applied to the Caltech ducted fan numerical example, which is described by a non-minimum phase nonlinear model. View full abstract»

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  • Optimal Control of a Variable Geometry Turbocharged Diesel Engine Using Neural Networks: Applications on the ETC Test Cycle

    Publication Year: 2009 , Page(s): 380 - 393
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2029 KB) |  | HTML iconHTML  

    Modern diesel engines are typically equipped with variable geometry turbo-compressor, exhaust gas recirculation (EGR) system, common rail injection system, and post-treatment devices in order to increase their power while respecting the emissions standards. Consequently, the control of diesel engines has become a difficult task involving five to ten control variables that interact with each other and that are highly nonlinear. Actually, the control schemes of the engines are all based on static lookup tables identified on test-benches; the values of the control variables are interpolated using these tables and then, they are corrected, online, by using the control techniques in order to obtain better engine's response under dynamic conditions. In this paper, we are interested in developing a mathematical optimization process that search for the optimal control schemes of the diesel engines under static and dynamic conditions. First, we suggest modeling a turbocharged diesel engine and its opacity using the mean value model which requires limited experiments; the model's simulations are in excellent agreement with the experimental data. Then the created model is integrated in a dynamic optimization process based on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The optimization results show the reduction of the opacity while enhancing the engine's effective power. Finally, we proposed a practical control technique based on the neural networks in order to apply these control schemes online to the engine. The neural controller is integrated into the engine's simulations and is used to control the engine in real time on the European transient cycle (ETC). The results confirm the validity of the neural controller. View full abstract»

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  • Nonlinear Control Allocation for Non-Minimum Phase Systems

    Publication Year: 2009 , Page(s): 394 - 404
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (335 KB) |  | HTML iconHTML  

    In this brief, we propose a control allocation method for a particular class of uncertain over-actuated affine nonlinear systems, with unstable internal dynamics. Dynamic inversion technique is used for the commanded output to track a smooth output reference trajectory. The corresponding control allocation law has to guarantee the boundedness of the states, including the internal dynamics, and satisfy control constraints. The proposed method is based on a Lyapunov design approach with finite-time convergence to a given invariant set. The derived control allocation is in the form of a dynamic update law which, together with a sliding mode control law, guarantees boundedness of the output tracking error as well as of the internal dynamics. The effectiveness of the control law is tested on a numerical model of the non-minimum phase planar vertical take-off and landing (PVTOL) system. View full abstract»

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  • Coordination Planning: Applying Control Synthesis Methods for a Class of Distributed Agents

    Publication Year: 2009 , Page(s): 405 - 415
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (331 KB) |  | HTML iconHTML  

    This brief proposes a new multi-agent planning approach to logical coordination synthesis that views a class of distributed agents as discrete-event processes. The coordination synthesis problem involves finding a coordination module for every agent, using which their coordinated interactions would never violate some specified inter-agent constraint. This brief first shows explicitly that, though conceptually different, the well-researched problem of supervision in control science and the problem of distributed agent coordination planning in computer agents science are mathematically related. This basic result enables the application of the vast body of knowledge and associated synthesis tools already founded in discrete-event control theory for automatic coordination synthesis of distributed agents. Within this logical framework, a basic planning methodology applying the discrete-event control synthesis methods is proposed and illustrated using TCT, a software design tool implementing these methods. A simple example demonstrates how it supports formal synthesis of coordination modules for distributed agents. Discussions in relation to previous work examine the relative significance of the new multi-agent planning framework. View full abstract»

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  • Active Joint Synchronization Control for a 2-DOF Redundantly Actuated Parallel Manipulator

    Publication Year: 2009 , Page(s): 416 - 423
    Cited by:  Papers (14)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (246 KB) |  | HTML iconHTML  

    This brief applies the synchronization to solve control problem of redundantly actuated parallel manipulators. With the synchronization method, a new controller termed active joint-synchronization (AJ-S) controller is developed for a 2-degree-of-freedom (DOF) redundantly actuated parallel manipulator. The dynamic model of the parallel manipulator is formulated in the active joint space, in which the internal force is calculated by the projection method and the friction is depicted with the Coulomb + viscous friction model. By defining the tracking error, synchronization error, coupled error, and the referenced trajectory vector of the active joints, the AJ-S controller based on the dynamic model is designed. And the AJ-S controller is proven to guarantee asymptotic convergence to zero of both tracking and synchronization errors by the Barbalat's lemma. The AJ-S controller is implemented in the trajectory tracking experiments of an actual 2-DOF redundantly actuated parallel manipulator, and the superiority of the AJ-S controller over the well-known tracking controller is studied. View full abstract»

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  • Velocity Estimation: Assessing the Performance of Non-Model-Based Techniques

    Publication Year: 2009 , Page(s): 424 - 433
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (516 KB) |  | HTML iconHTML  

    The performance of modern motion control systems is strongly related to the resolution of the position sensor and to the digital filtering algorithm used to estimate the velocity. This brief discusses a systematic approach to analyze and assess the performance of non-model-based estimators. A new methodology for the analytical characterization of the velocity estimation error, both in the time and in the frequency domains, is proposed. A case study illustrates how this methodology can be exploited in the analysis of existing velocity measurement systems and/or in the design of a new one. View full abstract»

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  • Feedforward Control of Shape Memory Alloy Actuators Using Fuzzy-Based Inverse Preisach Model

    Publication Year: 2009 , Page(s): 434 - 441
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (493 KB) |  | HTML iconHTML  

    This brief investigates a possible application of the inverse Preisach model in combination with the feedforward and feedback control strategies to control shape memory alloy actuators. In the feedforward control design, a fuzzy-based inverse Preisach model is used to compensate for the hysteresis nonlinearity effect. An extrema input history and a fuzzy inference is utilized to replace the inverse classical Preisach model. This work allows for a reduction in the number of experimental parameters and computation time for the inversion of the classical Preisach model. A proportional-integral-derivative (PID) controller is used as a feedback controller to regulate the error between the desired output and the system output. To demonstrate the effectiveness of the proposed controller, real-time control experiment results are presented. View full abstract»

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  • Vision-Based Range Regulation of a Leader-Follower Formation

    Publication Year: 2009 , Page(s): 442 - 448
    Cited by:  Papers (8)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (709 KB) |  | HTML iconHTML  

    This brief describes a single-vehicle tracking algorithm relying on active contours for target extraction and an extended Kalman filter for relative position estimation. The primary difficulty lies in the estimation and regulation of range using monocular vision. The work represents a first step towards treating the problem of the control of several unmanned vehicles flying in formation using only local visual information. In particular, allowing only onboard passive sensing of the external environment, we seek to study the achievable closed-loop performance under this model. View full abstract»

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  • Moving Horizon {cal H}_{\infty } Tracking Control of Wheeled Mobile Robots With Actuator Saturation

    Publication Year: 2009 , Page(s): 449 - 457
    Cited by:  Papers (13)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (271 KB) |  | HTML iconHTML  

    This brief considers the dynamic tracking control of wheeled mobile robots (WMR), in the presence of both actuator saturations and external disturbances. A computationally tractable moving horizon H infin tracking scheme is presented, where a constrained H infin control problem is solved at each sampling time with the update of not only the initial condition but also the prediction model. Closed-loop tracking properties inclusive of L 2 disturbance attenuation are discussed in the framework of dissipation theory. Simulation results are given. View full abstract»

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  • An Adaptive Controller for the Shunt Active Filter Considering a Dynamic Load and the Line Impedance

    Publication Year: 2009 , Page(s): 458 - 464
    Cited by:  Papers (11)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (807 KB) |  | HTML iconHTML  

    This brief presents a controller for an active filter to compensate reactive power and current harmonic distortion in a single phase system, i.e., to guarantee a power factor close to unity. The proposed controller considers the deleterious effects caused by the interaction between load and line impedances, which may lead to instabilities when the controller is enabled. The rationale behind the solution consists in the introduction of a lead compensator with a gain that is adjusted by adaptation, which replaces the conventional proportional term. This modification improves the stability conditions when the load and source impedances are non-negligible. In particular, the scheme provides a solution in the critical scenario, when the load is composed by a capacitor connected in parallel to a distorted current source. Special attention is given to the current control loop because it is precisely in this loop where the instability problems are generated. Realistic numerical results are provided to illustrate the benefits of the proposed solution. View full abstract»

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  • Analog Active Control of Acoustic Noise at a Virtual Location

    Publication Year: 2009 , Page(s): 465 - 472
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (773 KB) |  | HTML iconHTML  

    In this brief, an analog virtual microphone control system in application to noise reduction for a phone is designed. It aims at generating a zone of quiet at a virtual microphone location corresponding to the eardrum. Such location is different than the real microphone location. The idea of the control system is based on the assumption that the primary acoustic noise is the same at these two locations. The first constraint is formulated to guarantee a sufficient stability margin. Another constraint protects against excessive noise reinforcement for any frequency. Controller parameters are found by solving the optimization problem. Due to its high nonlinearity the exhaustive search method is used. It follows a preliminary analysis of the solution space. Additionally, a feedforward filter compensating for influence of the control system on the transmitted speech is designed. The overall control system is implemented using chips with switched capacitors, what makes the tuning and maintenance easy. The system is verified by means of simulations and real-world experiments. It is shown that road noise is satisfactorily reduced. Both measurement results and subjective impressions confirm that the system meets the requirements. View full abstract»

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  • A Systematic Method for Gain Selection of Robust PID Control for Nonlinear Plants of Second-Order Controller Canonical Form

    Publication Year: 2009 , Page(s): 473 - 483
    Cited by:  Papers (10)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1045 KB) |  | HTML iconHTML  

    A systematic method to select gains of a discrete proportional-integral-derivative (PID) controller is presented. The PID controller with the gains obtained by the proposed method can robustly control nonlinear multiple-input-multiple-output (MIMO) plants in a second-order controller canonical form, such as robot dynamics. This method has been made possible by the finding that the discrete PID control is equivalent to the discrete form of time-delay control (TDC), a robust control method for nonlinear plants with uncertainty. By using this equivalence relationships are obtained between PID gains and parameters of TDC, which enable a systematic method for the select PID gains. In addition, based on the systematic method, a simple and effective method is proposed to tune PID gains applicable to nonlinear plants with inaccurate models. This method incorporates a set of independent tuning parameters that is far less than those for conventional methods for PID gain selection. The usefulness of the proposed methods is verified through the ease and simplicity of determining PID gains for six degrees-of-freedom (DOF) programmable universal machine for assembly (PUMA)-type robot manipulator; the effectiveness of these PID gains is confirmed by the adequate and robust performance through experimentation on the robot. View full abstract»

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  • Decentralized Detection of a Class of Non-Abrupt Faults With Application to Formations of Unmanned Airships

    Publication Year: 2009 , Page(s): 484 - 493
    Cited by:  Papers (5)  |  Patents (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (430 KB) |  | HTML iconHTML  

    We propose a decentralized non-abrupt fault detection (DNaFD) scheme for leader-to-follower formations of unmanned airships. Non-abrupt faults are those that result in slow performance degradation and in undesirable drift, which can propagate from one vehicle to another, and therefore can adversely affect mission integrity, potentially destabilizing multivehicle formations, while being difficult to detect. As opposed to model-based fault detectors, which are typically insensitive to non-abrupt faults, the proposed signal-based DNaFD enables the detection of slowly degrading vehicle performance by performing a statistical test on heading angle trajectories. Here, the formation of unmanned airships is assumed stabilized by a distributed formation guidance scheme that uses neighboring vehicle information. High-fidelity, nonlinear 6-degrees-of-freedom (DOF) simulations of formation flying airships show that the proposed DNaFD scheme combined with a simple guidance adaptation technique enable detection of a class of non-abrupt faults and formation recovery, despite mild winds and parametric uncertainties, while preserving a requirement on formation geometry. View full abstract»

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  • Noniterative {cal H}_{\infty } -Based Model Order Reduction of LTI Systems Using LMIs

    Publication Year: 2009 , Page(s): 494 - 501
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (422 KB) |  | HTML iconHTML  

    This brief addresses the model order reduction problem for linear time invariant (LTI) systems. The problem is to minimize the H infin norm of the error between the original system and the reduced system, which is known to be a nonconvex optimization problem. Based on this, the brief proposes a convex suboptimal solution which is expressed in terms of linear matrix inequalities (LMIs). The performance of the proposed method is assessed through application to several large order systems and compared with the well-known Hankel Norm model order reduction method. View full abstract»

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  • IEEE copyright form

    Publication Year: 2009 , Page(s): 502 - 503
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    Freely Available from IEEE

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