Showing papers on "Feedback linearization published in 2012"

Survey of State-Dependent Riccati Equation in Nonlinear Optimal Feedback Control Synthesis

Abstract: A EROSPACE engineering applications greatly stimulated the development of optimal control theory during the 1950s and 1960s, where the objective was to drive the system states in such a way that some defined cost was minimized. This turned out to have very useful applications in the design of regulators (where some steady state is to be maintained) and in tracking control strategies (where some predetermined state trajectory is to be followed). Among such applications was the problem of optimal flight trajectories for aircraft and space vehicles. Linear optimal control theory in particular has been very well documented and widely applied, where the plant that is controlled is assumed linear and the feedback controller is constrained to be linear with respect to its input. However, the availability of powerful low-cost microprocessors has spurred great advantages in the theory and applications of nonlinear control. The competitive era of rapid technological change, particularly in aerospace exploration, now demands stringent accuracy and cost requirements in nonlinear control systems. This has motivated the rapid development of nonlinear control theory for application to challenging, complex, dynamical real-world problems, particularly those that bear major practical significance in aerospace, marine, and defense industries. Infinite-time horizon nonlinear optimal control (ITHNOC) presents a viable option for synthesizing stabilizing controllers for nonlinear systems by making a state-input tradeoff, where the objective is to minimize the cost given by a performance index. The original theory of nonlinear optimal control dates from the 1960s. Various theoretical and practical aspects of the problem have been addressed in the literature over the decades since. In particular, the continuous-time nonlinear deterministic optimal control problem associated with autonomous (time-invariant) nonlinear regulator systems that are affine (linear) in the controls has been studied by many authors. The long-established theory of optimal control offers quite mature and well-documented techniques for solving this control-affine nonlinear optimization problem, based on dynamic programming or calculus of variations, but their application is generally a very tedious task. Bellman’s dynamic programming approach reduces to solving a nonlinear first-order partial differential equation (PDE), expressed by the Hamilton–Jacobi–Bellman (HJB) equation. The solution to the HJB equation gives the optimal performance/cost value (or storage) function and determines an optimal control in feedback form under some smoothness assumptions. Alternatively, in the classical calculus of variations, optimal control problems can be characterized locally in terms of the Hamiltonian dynamics arising from Pontryagin’s minimum principle. These are the characteristic equations of the HJB PDE, which result in a nonlinear, constrained two-point boundary value problem (TPBVP) that, in general, can only be solved by successive approximation of the optimal control input using iterative numerical techniques for each set of initial conditions. Numerically, even though the nonlinear TPBVP is somewhat easier to solve than the HJBPDE, control signals can only be determined offline and are thus best suited for feedforward control of plants for which the state trajectories are known a priori. Therefore, contrary to the dynamic programming approach, the resultant control law is not generally in feedback form. Open-loop control, however, is sensitive to random disturbances and requires that the initial state be on the optimal trajectory. In contrast, nonlinear optimal feedback has inherent robustness properties (inherent in the sense that it is obtained by ignoring uncertainty and disturbances). The potential difficulty with the HJB approach is that no efficient algorithm is available to solve the PDE when it is nonlinear and the problem dimension is high, making it impossible to derive exact expressions for optimal controls for most nontrivial problems of interest. The optimal can only be computed in special cases, such as linear dynamics and quadratic cost, or very low-dimensional systems. In particular, if the plant is linear time invariant (LTI) and the (infinite-time) performance index is quadratic, then the corresponding HJB equation for this infamous linear-quadratic regulator (LQR) problem reduces to an algebraic Riccati equation (ARE). Contrary to the well-developed and widely applied theory and computational tools for theRiccati equation (for example, see [1]), theHJB equation is difficult, if not impossible, to solve for most practical applications. The exact solution for the optimal control policies is very complex

LVRT Scheme of PMSG Wind Power Systems Based on Feedback Linearization

Abstract: This paper proposes a low-voltage ride-through scheme for the permanent magnet synchronous generator (PMSG) wind power system at the grid voltage sag. The dc-link voltage is controlled by the generator-side converter instead of the grid-side converter (GSC). Considering the nonlinear relationship between the generator speed ωm and the dc-link voltage Vdc , a dc-link voltage controller is designed using a feedback linearization theory. The GSC controls the grid active power for a maximum power point tracking. The validity of this control algorithm has been verified by simulation and experimental results for a reduced-scale PMSG wind turbine simulator.

Modeling and control of a quadrotor UAV with tilting propellers

Abstract: Standard quadrotor UAVs possess a limited mobility because of their inherent underactuation, i.e., availability of 4 independent control inputs (the 4 propeller spinning velocities) vs. the 6 dofs parameterizing the quadrotor position/ orientation in space. As a consequence, the quadrotor pose cannot track an arbitrary trajectory over time (e.g., it can hover on the spot only when horizontal). In this paper, we propose a novel actuation concept in which the quadrotor propellers are allowed to tilt about their axes w.r.t. the main quadrotor body. This introduces an additional set of 4 control inputs which provides full actuation to the quadrotor position/orientation. After deriving the dynamical model of the proposed quadrotor, we formally discuss its controllability properties and propose a nonlinear trajectory tracking controller based on dynamic feedback linearization techniques. The soundness of our approach is validated by means of simulation results.

A Derivative-Free Kalman Filtering Approach to State Estimation-Based Control of Nonlinear Systems

Abstract: For nonlinear systems, subject to Gaussian noise, the extended Kalman filter (EKF) is frequently applied for estimating the system's state vector from output measurements. The EFK is based on linearization of the systems' dynamics using a first-order Taylor expansion. Although EKF is efficient in several problems, it is characterized by cumulative errors due to the gradient-based linearization it performs, and this may affect the accuracy of the state estimation or even risk the stability of the state estimation-based control loop. To overcome the flaws of EKF, it has been proposed to use the unscented Kalman filter (UKF) as a method for nonlinear state estimation, which does not introduce linearization errors. Aiming also at finding more efficient implementations of nonlinear Kalman filtering, this paper introduces a derivative-free Kalman filtering approach, which is suitable for state estimation-based control of a class of nonlinear systems. The considered systems are first subject to a linearization transformation, and next state estimation is performed by applying the standard Kalman filter to the linearized model. Unlike EKF, the proposed method provides estimates of the state vector of the nonlinear system without the need for derivatives and Jacobians calculation and without using linearization approximations. The proposed derivative-free Kalman filtering approach has been compared to EKF and UKF in the case of state estimation-based control for a nonlinear DC motor model.

Dynamic Stability of Three-Phase Grid-Connected Photovoltaic System Using Zero Dynamic Design Approach

Abstract: This paper presents a new approach to control the grid current and dc-link voltage for maximum power point tracking and improvement of the dynamic response of a three-phase grid-connected photovoltaic (PV) system. To control the grid current and dc-link voltage, the zero dynamic design approach of feedback linearization is used, which linearizes the system partially and enables controller design for reduced-order PV system. This paper also describes the zero dynamic stability of the three-phase grid-connected PV system, which is a key requirement for the implementation of such controllers. Simulation results on a large-scale grid-connected PV system show the effectiveness of the proposed control scheme in terms of delivering maximum power into the grid.

Fuzzy Adaptive Tracking Control of Wheeled Mobile Robots With State-Dependent Kinematic and Dynamic Disturbances

Abstract: Unlike most works based on pure nonholonomic constraint, this paper proposes a fuzzy adaptive tracking control method for wheeled mobile robots, where unknown slippage occurs and violates the nonholononomic constraint in the form of state-dependent kinematic and dynamic disturbances. These disturbances degrade tracking performance significantly and, therefore, should be compensated. To this end, the kinematics with state-dependent disturbances are rigorously derived based on the general form of slippage in the mobile robots, and fuzzy adaptive observers together with parameter adaptation laws are designed to estimate the state-dependent disturbances in both kinematics and dynamics. Because of the modular structure of the proposed method, it can be easily combined with the previous controllers based on the model with the pure nonholonomic constraint, such that the combination of the fuzzy adaptive observers with the previously proposed backstepping-like feedback linearization controller can guarantee the trajectory tracking errors to be globally ultimately bounded, even when the nonholonomic constraint is violated, and their ultimate bounds can be adjusted appropriately for various types of trajectories in the presence of large initial tracking errors and disturbances. Both the stability analysis and simulation results are provided to validate the proposed controller.

Functional Adaptive Control: An Intelligent Systems Approach

Abstract: I. Introduction.- 1. Introduction.- 1.1 Intelligent Control Systems.- 1.2 Approaches to Intelligent Control.- 1.2.1 Contribution of Adaptive Control.- 1.2.2 Contribution of Artificial Intelligence.- 1.2.3 Confluence of Adaptive Control and AI: Intelligent Control.- 1.3 Enhancing the Performance of Intelligent Control.- 1.3.1 Multiple Model Schemes: Dealing with Complexity.- 1.3.2 Stochastic Adaptive Control: Dealing with Uncertainty.- 1.4 The Objectives and their Rationale.- II. Deterministic Systems.- 2. Adaptive Control of Nonlinear Systems.- 2.1 Introduction.- 2.2 Continuous-time Systems.- 2.2.1 Control by Feedback Linearization.- 2.2.2 Control by Backstepping.- 2.2.3 Adaptive Control.- 2.3 Discrete-time Systems.- 2.3.1 Affine Approximations and Feedback Linearization.- 2.3.2 Adaptive Control.- 2.4 Summary.- 3. Dynamic Strueture Networks for Stahle Adaptive Control.- 3.1 Introduction.- 3.2 Problem Formulation.- 3.3 Fixed-structure Network Solutions.- 3.4 Dynamic Network Structure.- 3.5 The Control Law and Error Dynamies.- 3.6 The Adaptive System.- 3.7 Stability Analysis.- 3.8 Evaluation of Control Parameters and Implementation.- 3.8.1 The Disturbanee Bound.- 3.8.2 Choice of the Boundary Layer.- 3.8.3 Comments.- 3.8.4 Implementation.- 3.9 Simulation Examples.- 3.9.1 Example 1.- 3.9.2 Example 2.- 3.10 Summary.- 4. Composite Adaptive Control of Continuous-Time Systems.- 4.1 Introduetion.- 4.2 Problem Formulation.- 4.3 The Neural Networks.- 4.4 The Control Law.- 4.5 Composite Adaptation.- 4.5.1 The Identifieation Model.- 4.5.2 The Adaptation Law.- 4.6 Stability Analysis.- 4.7 Determination of the Disturbanee Bounds.- 4.8 Simulation Examples.- 4.8.1 Example 1.- 4.8.2 Example 2.- 4.9 Summary.- 5. Funetional Adaptive Control of Discrete-Time Systems.- 5.1 Introduetion.- 5.2 Problem Formulation.- 5.3 The Neural Network.- 5.4 The Control Law.- 5.5 The Adaptive System.- 5.6 Stability Analysis.- 5.7 Traeking Error Convergenee.- 5.8 Simulation Examples.- 5.8.1 Example 1.- 5.8.2 Example 2.- 5.9 Extension to Adaptive Sliding Mode Control.- 5.9.1 Definitions of a Discrete-time Sliding Mode.- 5.9.2 Adaptive Sliding Mode Control.- 5.9.3 Problem Formulation.- 5.9.4 The Control Law.- 5.9.5 The Adaptive System.- 5.9.6 Stability Analysis.- 5.9.7 Sliding and Tracking Error Convergence.- 5.9.8 Simulation Example.- 5.10 Summary.- III. Stochastic Systems.- 6. Stochastic Control.- 6.1 Introduction.- 6.2 FUndamental Principles.- 6.3 Classes of Stochastic Control Problems.- 6.4 Dual Control.- 6.4.1 Degrees of Interaction.- 6.4.2 Solutions to the Implementation Problem.- 6.5 Conclusions.- 7. Dual Adaptive Control of Nonlinear Systems.- 7.1 Introduction.- 7.2 Problem Formulation.- 7.3 Dual Controller Design.- 7.3.1 GaRBF Dual Controller.- 7.3.2 Sigmoidal MLP Dual Controller.- 7.3.3 Analysis of the Control Laws.- 7.4 Simulation Examples and Performance Evaluation.- 7.4.1 Example 1.- 7.4.2 Example 2.- 7.5 Summary.- 8. Multiple Model Approaches.- 8.1 Introduction.- 8.2 Basic Formulation.- 8.2.1 Multiple Model Adaptive Contro!..- 8.2.2 Jump Systems.- 8.3 Adaptive IO Models.- 8.3.1 Scheduled Mode Transitions.- 8.4 Summary.- 9. Multiple Model Dual Adaptive Control of Jump Nonlinear Systems.- 9.1 Introduction.- 9.2 Problem Formulation.- 9.3 The Estimation Problem.- 9.3.1 Known Mode Case.- 9.3.2 Unknown Mode Case.- 9.4 Self-organized Allocation of Local Models.- 9.5 The Control Law.- 9.5.1 Known Mode Case.- 9.5.2 Unknown Mode Case.- 9.6 Simulation Examples and Performance Evaluation.- 9.6.1 Example 1.- 9.6.2 Example 2.- 9.7 Summary.- 10. Multiple Model Dual Adaptive Control of Spatial Multimodal Systems.- 10.1 Introduction.- 10.2 Problem Formulation.- 10.3 The Modular Network.- 10.4 The Estimation Problem.- 10.4.1 Local Model Parameter Estimation.- 10.4.2 Validity Function Estimation.- 10.5 The Control Law.- 10.5.1 Known System Case.- 10.5.2 Unknown System Case.- 10.6 Simulation Examples and Performance Evaluation.- 10.6.1 Example 1.- 10.6.2 Example 2.- 10.6.3 Performance Evaluation.- 10.7 Summary.- IV. Conclusions.- 11. Conclusions.- References.

State‐feedback stabilization for a class of stochastic time‐delay nonlinear systems

Abstract: SUMMARY This paper investigates the problem of state-feedback stabilization for a class of lower-triangular stochastic time-delay nonlinear systems without controllable linearization. By extending the adding-a-power-integrator technique to the stochastic time-delay systems, a state-feedback controller is explicitly constructed such that the origin of closed-loop system is globally asymptotically stable in probability. The main design difficulty is to deal with the uncontrollable linearization and the nonsmooth system perturbation, which, under some appropriate assumptions, can be solved by using the adding-a-power-integrator technique. Two simulation examples are given to illustrate the effectiveness of the control algorithm proposed in this paper.Copyright © 2011 John Wiley & Sons, Ltd.

A critical review of the most popular types of neuro control

Abstract: In this review article, the most popular types of neural network control systems are briefly introduced and their main features are reviewed. Neuro control systems are defined as control systems in which at least one artificial neural network (ANN) is directly involved in generating the control command. Initially, neural networks were mostly used to model system dynamics inversely to produce a control command which pushes the system towards a desired or reference value of the output (1989). At the next stage, neural networks were trained to track a reference model, and ANN model reference control appeared (1990). In that method, ANNs were used to extend the application of adaptive reference model control, which was a well-known control technique. This attitude towards the extension of the application of well-known control methods using ANNs was followed by the development of ANN model-predictive (1991), ANN sliding mode (1994) and ANN feedback linearization (1995) techniques. As the first category of neuro controllers, inverse dynamics ANN controllers were frequently used to form a control system together with other controllers, but this attitude faded as other types of ANN control systems were developed. However, recently, this approach has been revived. In the last decade, control system designers started to use ANNs to compensate/cancel undesired or uncertain parts of systems' dynamics to facilitate the use of well-known conventional control systems. The resultant control system usually includes two or three controllers. In this paper, applications of different ANN control systems are also addressed. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Modeling and control of a spherical rolling robot: A decoupled dynamics approach

Abstract: This paper presents the results of a study on the dynamical modeling, analysis, and control of a spherical rolling robot. The rolling mechanism consists of a 2-DOF pendulum located inside a spherical shell with freedom to rotate about the transverse and longitudinal axis. The kinematics of the model has been investigated through the classical methods with rotation matrices. Dynamic modeling of the system is based on the Euler-Lagrange formalism. Nonholonomic and highly nonlinear equations of motion have then been decomposed into two simpler subsystems through the decoupled dynamics approach. A feedback linearization loop with fuzzy controllers has been designed for the control of the decoupled dynamics. Rolling of the controlled mechanism over linear and curvilinear trajectories has been simulated by using the proposed decoupled dynamical model and feedback controllers. Analysis of radius of curvature over curvilinear trajectories has also been investigated.

Feedback Linearization-Based Position Control of an Electrohydraulic Servo System With Supply Pressure Uncertainty

Abstract: Electrohydraulic servo systems (EHSS) are used for several engineering applications, and in particular, for efficient handling of heavy loads. proportional-integral-differential (PID) control is used extensively to control EHSS, but the closed-loop performance is limited using this approach, due to the nonlinear dynamics that characterize these systems. Recent studies have shown that feedback linearization is a viable control design technique that addresses the nonlinear dynamics of EHSS; however, it is important to establish the robustness of this method, given that hydraulic system parameters can vary significantly during operation. In this study, we focus on supply pressure variations in a rotational electrohydraulic drive. The supply pressure appears in a square-root term in the system model, and thus, standard adaptive techniques that require uncertain parameters to appear linearly in the system equations, cannot be used. A Lyapunov approach is used to derive an enhanced feedback-linearization-based control law that accounts for supply pressure changes. Simulation results indicate that standard feedback-linearization based control is robust to EHSS parameter variations, providing significant improvement over PID control, and that the performance can be further improved using the proposed control law.

Robust Nonlinear Controls of Model-Scale Helicopters Under Lateral and Vertical Wind Gusts

Abstract: A helicopter maneuvers naturally in an environment where the execution of the task can easily be affected by atmospheric turbulence, which leads to variations of its model parameters. This paper discusses the nature of the disturbances acting on the helicopter and proposes an approach to counter the effects. The disturbance consists of vertical and lateral wind gusts. A 7-degrees-of-freedom (DOF) nonlinear Lagrangian model with unknown disturbances is used. The model presents quite interesting control challenges due to nonlinearities, aerodynamic forces, under actuation, and its non-minimum phase dynamics. Two approaches of robust control are compared via simulations with a Tiny CP3 helicopter model: an approximate feedback linearization and an active disturbance rejection control using the approximate feedback linearization procedure. Several simulations show that adding an observer can compensate the effect of disturbances. The proposed controller has been tested in a real-time application to control the yaw angular displacement of a Tiny CP3 mini-helicopter mounted on an experiment platform.

Partial feedback linearization control of overhead cranes with varying cable lengths

Abstract: Overhead cranes are under-actuated mechanical systems with three degrees-of-freedom (trolley displacement, cable length, and cargo swing angle) and only two actuators: one for cargo hoisting and another for trolley driving. An overhead crane transfers the trolley to a desired position, hoists the cargo up and down until the desired cable length is achieved while keeping the cargo swing angle small during the transfer process. The rope should no longer have a swing angle at the load destination. In this research, a nonlinear controller is proposed for an overhead crane system, in which partial feedback linearization technique is used. To show the effectiveness of the proposed controller, we perform both simulation and experimental study. The simulation and experimental results show that the crane system with the proposed controller is asymptotically stable. Furthermore, all state trajectories of the system reach a steady state within a considerably short time even if the inherent structure of the system is changed.

Design Robust Backstepping on-line Tuning Feedback Linearization Control Applied to IC Engine

Abstract: Design a nonlinear controller for second order nonlinear uncertain dynamical systems (e.g., Internal Combustion Engine) is one of the most important challenging works. This paper focuses on the design of a robust backstepping adaptive feedback linearization controller (FLC) for internal combustion (IC) engine in presence of uncertainties. In order to provide high performance nonlinear methodology, feedback linearization controller is selected. Pure feedback linearization controller can be used to control of partly unknown nonlinear dynamic parameters of IC engine. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, Mamdani’s performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is applied to pure feedback linearization controller. The results demonstrate that the error-based fuzzy feedback linearization controller is a model-free controllers which works well in certain and partly uncertain system. Pure feedback linearization controller and error-based feedback linearization like controller with have difficulty in handling unstructured model uncertainties. To solve this problem applied backstepping-based tuning method to error-based fuzzy feedback linearization controller for adjusting the feedback linearization controller gain ( ). This controller has acceptable performance in presence of uncertainty (e.g., overshoot=1%, rise time=0.48 second, steady state error = 1.3e-9 and RMS error=1.8e-11).

A survey of control algorithms for Quadrotor Unmanned Helicopter

Abstract: Basic structure of Quadrotor Unmanned Helicopter (QUH) and its practical application values are introduced as well as several control algorithms, such as, intelligent PID algorithm, linear quadratic LQR algorithm, H∞ loop-shaping algorithm, sliding mode control algorithm, feedback linearization control algorithm, adaptive control algorithm and backstepping design algorithm and then analyses merits and drawbacks of above control algorithms. At last, our research prospects the major research aspects and development direction on future researches of QUH.

Fault Ride-Through Enhancement of DFIG-Based Wind Generation Considering Unbalanced and Distorted Conditions

Abstract: A control strategy is proposed to enhance the operation, under network disturbances, of a wind turbine driven doubly fed induction generator (DFIG). The scheme allows us to overcome low voltages, imbalances, and harmonic distortions at the point of common coupling. The control law is designed using a feedback linearization approach plus resonant filters; this law directly controls the DFIG stator powers from the rotor voltages, unlike the most used nested two-loop approaches. An accurate control of the active and reactive powers delivered to the grid permits us to fulfill severe grid code requirements and to improve the fault ride-through capability. Under unbalanced conditions, the reference currents of both grid- and rotor-side converters are coordinately chosen to simultaneously eliminate the double-frequency pulsations in the total active power and electromagnetic torque. Several tests and disturbances to provide a realistic assessment and validation have been performed, showing the adequacy of the proposed controller. Comparisons with other control approaches with different objectives are also presented to illustrate the advantages regarding elimination of the double-frequency ripples and harmonic rejection capability.

Decoupling control for spatial six-degree-of-freedom electro-hydraulic parallel robot

Abstract: This paper presents a decoupling controller equipped with cross-coupling pre-compensation for an electro-hydraulic parallel robot, in order to weaken system dynamic coupling effects usually ignored on the design of advanced controllers and improve system control performance. The mathematical model of the electro-hydraulic parallel robot is built using the Kane method and a hydromechanics approach, and the kinematical model is established with a closed-form solution and the Newton-Raphson method. The feedback linearization theory is applied to reduce coupling effects stemmed from system dynamics of the parallel robot via incorporating force-velocity control with cross-coupling pre-compensations. The control performance involving stability, accuracy, and robustness of the proposed controller for spatial 6-DOF parallel robot is analyzed in theory and experiment. The experimental results illustrate that the proposed controller can highly improve the control performance by weakening system dynamic coupling effects of the electro-hydraulic parallel robot, especially for trajectory tracking performance.

Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances

Abstract: In this paper, the composite nonlinear feedback control method is considered for robust tracking and model following of uncertain linear systems. The control law guarantees that the tracking error decreases asymptotically to zero in the presence of time varying uncertain parameters and disturbances. For performance improvement of the dynamical system, the proposed robust tracking controller consists of linear and nonlinear feedback parts without any switching element. The linear feedback law is designed to allow the closed loop system have a small damping ratio and a quick response while the nonlinear feedback law increases the damping ratio of the system as the system output approaches the output of the reference model. A new collection of different nonlinear functions used in the control law are offered to improve the reference tracking performance of the system. The proposed robust tracking controller improves the transient performance and steady state accuracy simultaneously. Finally, the simulations are provided to verify the theoretical results.

Uncertainty modeling and robust minimax LQR control of multivariable nonlinear systems with application to hypersonic flight

Abstract: For a class of multi-input and multi-output nonlinear uncertainty systems, a novel approach to design a nonlinear controller using minimax linear quadratic regulator (LQR) control is proposed. The proposed method combines a feedback linearization method with the robust minimax LQR approach in the presence of time-varying uncertain parameters. The uncertainties, which are assumed to satisfy a certain integral quadratic constraint condition, do not necessarily satisfy a generalized matching condition. The procedure consists of feedback linearization of the nominal model and linearization of the remaining nonlinear uncertain terms with respect to each individual uncertainty at a local operating point. This two-stage linearization process, followed by a robust minimax LQR control design, provides a robustly stable closed loop system. To demonstrate the effectiveness of the proposed approach, an application study is provided for a flight control problem of an air-breathing hypersonic flight vehicle (AHFV), where the outputs to be controlled are the longitudinal velocity and altitude, and the control variables are the throttle setting and elevator deflection. The proposed method is used to derive a linearized uncertainty model for the longitudinal motion dynamics of the AHFV first, and then a robust minimax LQR controller is designed, which is based on this uncertainty model. The controller is synthesized considering seven uncertain aerodynamic and inertial parameters. The stability and performance of the synthesized controller is evaluated numerically via single scenario simulations for particular cruise conditions as well as a Monte-Carlo type simulation based on numerous cases. It is observed that the control scheme proposed in this paper performs better, especially from the aspect of robustness to large ranges of uncertainties, than some controller design schemes previously published in the literature. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Harmonic reduction in capacitive micromachined ultrasonic transducers by gap feedback linearization

Abstract: The nonlinear relationship between the electrical input signal and electrostatic force acting on the capacitive micromachined ultrasonic transducer (CMUT) membrane limits its harmonic imaging performance. Several input shaping methods were proposed to compensate for the nonlinearity originating from the electrostatic force's dependence on the square of the applied voltage. Here, we analyze harmonic generation in CMUTs with a time-domain model. The model explains the basis of the input shaping methods and suggests that the nonlinearity resulting from gap dependence of the electrostatic force is also significant. It also suggests that the harmonic distortion in the output pressure can be eliminated by subharmonic ac-only excitation of the CMUT in addition to scaling the input voltage with the instantaneous gap. This gap feedback configuration can be approximated by the simple addition of a series impedance to the CMUT capacitance. We analyze several types of series impedance feedback topologies for gap feedback linearization. We show that for subharmonic ac excitation, although resistive and capacitive impedances result in a trade-off between input voltage and harmonic distortion for a desired pressure output, harmonic generation can be suppressed while increasing the Pa/V transmit sensitivity for proper series inductance and resistance feedback. We experimentally demonstrate the feedback method by reducing harmonic generation by 10 dB for the same output pressure at the fundamental frequency by using a simple series resistor feedback with a CMUT operating at a center frequency of 3 MHz. The proposed methods also allow for utilization of the full CMUT gap for transmit operation and, hence, should be useful in high-intensity ultrasonic applications in addition to harmonic imaging.

Design and control of novel tri-rotor UAV

Abstract: Tri-rotor UAVs are more efficient compared to quadrotors in regard to the size and power requirement, yet, tri-rotor UAVs are more challenging in terms of control and stability. In this paper, we propose the design and control of a novel tri-rotor UAV. The proposed platform is designed to achieve six degree of freedom using a thrust vectoring technique with the highest level of flexibility, manoeuvrability and minimum requirement of power. The proposed tri-rotor has a triangular shape of three arms where at the end of each arm, a fixed pitch propeller is driven by a DC motor. A tilting mechanism is employed to tilt the motor-propeller assembly and produce thrust in the desired direction. The three propellers can be tilted independently to achieve full authority of torque and force vectoring. A feedback linearization associated with ℋ ∞ loop shaping design is used to synthesize a controller for the system. The results are verified via simulation.

A Feedback Linearization Control Scheme for the Integration of Wind Energy Conversion Systems Into Distribution Grids

Abstract: This paper focuses on the development of a control strategy for integration of wind energy conversion systems (WECS) into the electrical distribution networks with particular attention to the combined provision of energy and ancillary services. Typically, a WECS is composed by a variable speed wind turbine coupled with a direct driven permanent magnet (DDPM) synchronous generator. This configuration offers a considerable flexibility in design and operation of the power unit, as its output is delivered to the grid through a fully controlled frequency converter. Here, a new control scheme to regulate electrical and mechanical quantities of such generation unit is proposed, aimed both at reaching optimal performances in terms of power delivered to the grid and at providing the voltage support ancillary service at the point of common coupling. The control scheme is derived resorting to the feedback linearization (FBL) technique, which allows both decoupling and linearization of a non linear multiple input multiple output system. Several numerical simulations are then performed in order to show how the flexibility of the DDPM wind generator can be fully exploited, thanks to the use of the FBL approach, which assures independent control of each variable and significant simplifications in controller synthesis and system operation, thus making it easier to integrate WECS into modern day smart grids.

Damping of Low Frequency Oscillations of Multi-Machine Multi-UPFC Power Systems, Based on Adaptive Input-Output Feedback Linearization Control

Abstract: In this paper, damping of the low frequency oscillations of multi-machine multi-UPFC power systems is investigated based on adaptive input-output feedback linearization control (AIFLC) approach. Considering a three-phase symmetrical fault, ignoring the subtransient states of the synchronous machines, the nonlinear state equations of the system are derived in order to obtain the UPFC reference control signals as well as the system parameters estimation laws. The stability of the system controller is proved by Lyapunov theory. Moreover using the six reduced order model of synchronous machine, some simulation results are presented in order to verify the validity and effectiveness of the proposed control approach.

Stochastic stability for nonlinear systems driven by Lévy noise

Abstract: This paper is to investigate the stochastic stability for nonlinear systems with Levy process based on Lyapunov exponents. A method of equivalent linearization is proposed to reduce and simplify the original systems. And the mean square responses are carried out to verify the effectiveness of the proposed approach. Then the Lyapunov exponents will be defined and derived to explore the stochastic stability, and two examples are presented to demonstrate the procedure of equivalent linearization and stochastic stability is considered for these two special examples. The results show that the technique of equivalent linearization can be used to study nonlinear systems excited by Levy noise.

Composite adaptive fuzzy control for synchronizing generalized Lorenz systems

Abstract: This paper presents a methodology of asymptotically synchronizing two uncertain generalized Lorenz systems via a single continuous composite adaptive fuzzy controller (AFC). To facilitate controller design, the synchronization problem is transformed into the stabilization problem by feedback linearization. To achieve asymptotic tracking performance, a key property of the optimal fuzzy approximation error is exploited by the Mean Value Theorem. The composite AFC, which utilizes both tracking and modeling error feedbacks, is constructed by introducing a series-parallel identification model into an indirect AFC. It is proved that the closed-loop system achieves asymptotic stability under a sufficient gain condition. Furthermore, the proposed approach cannot only synchronize two different chaotic systems but also significantly reduce computational complexity and implemented cost. Simulation studies further demonstrate the effectiveness of the proposed approach.

Integrated mechanical and control design of underactuated multibody systems

Abstract: Multibody systems are called underactuated if they have less control inputs than degrees of freedom, e.g. due to passive joints or body flexibility. For trajectory tracking of underactuated multibody systems often advanced modern nonlinear control techniques are necessary. The analysis of underactuated multibody systems might show that they possess internal dynamics. Feedback linearization is only possible if the internal dynamics remain bounded, i.e. the system is minimum phase. Also feed-forward control design for minimum phase systems is much easier to realize than for non-minimum phase systems. However, often the initial design of an underactuated multibody system is non-minimum phase. Therefore, in this paper a procedure for integrated mechanical and control design is proposed such that minimum phase underactuated multibody systems are obtained. Thereby an optimization-based design process is used, whereby the geometric dimensions and mass distribution of the multibody systems are altered.