Showing papers on "Feedback linearization published in 2013"

Distributed Cooperative Secondary Control of Microgrids Using Feedback Linearization

Abstract: This paper proposes a secondary voltage control of microgrids based on the distributed cooperative control of multi-agent systems. The proposed secondary control is fully distributed; each distributed generator only requires its own information and the information of some neighbors. The distributed structure obviates the requirements for a central controller and complex communication network which, in turn, improves the system reliability. Input-output feedback linearization is used to convert the secondary voltage control to a linear second-order tracker synchronization problem. The control parameters can be tuned to obtain a desired response speed. The effectiveness of the proposed control methodology is verified by the simulation of a microgrid test system.

Stable Decentralized Control of a Platoon of Vehicles With Heterogeneous Information Feedback

Abstract: The problem of controlling a string of vehicles moving in one dimension is considered so that they all follow a lead vehicle with constant spacing between successive vehicles. Due to practical design and implementation, the negative effect of the tracking lag parameter is taken into account. A hierarchical platoon controller design framework is established comprising a feedback linearization controller at the first layer and a decentralized bidirectional control controller at the second layer. The stability criterion is examined by using a partial differential equation approximation in the limit of the number of vehicles subjected to unequal asymmetry in position and velocity feedback. For disturbance attenuation, string stability analysis is also examined. At the end of the paper, simulations are given to show the efficiency of the proposed results.

Quantitative Feedback Design of Linear and Nonlinear Control Systems

Abstract: Preface. Acknowledgements. Abbreviations Notation and Symbols. 1. Introduction. Part I: Linear Systems. 2. Basics of SISO Feedback Controlled Systems. 3. Synthesis of LTI Controllers for MISO LTI Plants. 4. Synthesis of LTI Controllers for MIMO LTI Plants. Part II: Nonlinear Systems. 5. Synthesis of LTI Controllers for Nonlinear SISO Plants. 6. Synthesis of LTV Controllers for Nonlinear SISO Plants. 7. Synthesis of LTI Controllers for Nonlinear MIMO Plants. 8. Synthesis of LTV Controllers for Nonlinear MIMO Plants. Index.

Neural-Adaptive Control of Single-Master–Multiple-Slaves Teleoperation for Coordinated Multiple Mobile Manipulators With Time-Varying Communication Delays and Input Uncertainties

Abstract: In this paper, adaptive neural network control is investigated for single-master-multiple-slaves teleoperation in consideration of time delays and input dead-zone uncertainties for multiple mobile manipulators carrying a common object in a cooperative manner. Firstly, concise dynamics of teleoperation systems consisting of a single master robot, multiple coordinated slave robots, and the object are developed in the task space. To handle asymmetric time-varying delays in communication channels and unknown asymmetric input dead zones, the nonlinear dynamics of the teleoperation system are transformed into two subsystems through feedback linearization: local master or slave dynamics including the unknown input dead zones and delayed dynamics for the purpose of synchronization. Then, a model reference neural network control strategy based on linear matrix inequalities (LMI) and adaptive techniques is proposed. The developed control approach ensures that the defined tracking errors converge to zero whereas the coordination internal force errors remain bounded and can be made arbitrarily small. Throughout this paper, stability analysis is performed via explicit Lyapunov techniques under specific LMI conditions. The proposed adaptive neural network control scheme is robust against motion disturbances, parametric uncertainties, time-varying delays, and input dead zones, which is validated by simulation studies.

Exact Tracking Using Backstepping Control Design and High-Order Sliding Modes

Abstract: In this technical note, a controller ensuring exponential exact tracking in the presence of matched and unmatched disturbances for the nonlinear systems in the block controllable form is proposed. The controller is designed using the backstepping procedure and combines the feedback linearization technique with the high-order sliding-modes. The matched and unmatched disturbances are compensated by the injection of a continuous term generated by the robust exact high-order sliding-modes differentiator. The obtained control law is differentiable and can be applied directly to the system. Simulations verify the performance of the proposed controller.

Simplified Feedback Linearization Control of Three-Phase Photovoltaic Inverter With an LCL Filter

Abstract: The conventional grid-connected photovoltaic (PV) inverter is controlled by a dual-loop control strategy in synchronous reference frame, and the controllers are designed for steady-state operating point based on the small signal model by neglecting the high-order and coupling terms. However, in an LCL filter, the coupling terms are complicated due to the dq transformation which will affect the dynamic performance. In this paper, an innovative simplified feedback linearization (SFL) control strategy is proposed for the PV inverter with the LCL filter, which offers satisfactory performance, particularly, in decoupling the control system, improving the dynamic performance, and enhancing the adaptability. Furthermore, the SFL controllers are simpler than the high-order tracking controllers used in conventional feedback linearization control. The detailed simplification process and accurate transfer functions for SFL control strategy have been presented, and the performance comparisons between the proposed SFL control strategy and the classical dual-loop method are carried out to show the characteristics of the proposed control algorithm. Finally, a laboratory prototype of a 150-kW PV inverter with the LCL filter has been implemented to test the feasibility and effectiveness of the proposed strategy. The proposed SFL control strategy can also be applied to a higher order system or other power converters.

A Homogeneous Domination Approach to State Feedback of Stochastic High-Order Nonlinear Systems With Time-Varying Delay

Abstract: The homogeneous domination approach is introduced to solve the state feedback stabilization problem for stochastic high-order nonlinear systems with time-varying delay. Under the weaker conditions on the drift and diffusion terms, by using the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability.

Robust control of robot manipulators based on uncertainty and disturbance estimation

Abstract: SUMMARY In this work, uncertainty and disturbance estimation (UDE) based robust trajectory tracking controller for rigid link manipulators was proposed. The UDE was employed to estimate the composite uncertainty that comprises the effects of system nonlinearities, external disturbances, and parametric uncertainties. A feedback linearization based controller was designed for trajectory tracking, and the same was augmented by the UDE-estimated uncertainties to achieve robustness. The resulting controller however required measurement of joint velocities apart from the joint positions. To address the issue, an observer that employed the UDE-estimated uncertainties for robustness was proposed, giving rise to the UDE-based controller–observer structure. Closed-loop stability of the overall system was established. The notable feature of the proposed design was that it neither required accurate plant model nor any information about the uncertainty. Also, the design needed only joint position measurements for its implementation. To demonstrate the effectiveness, simulation results of the proposed approach as applied to the trajectory tracking control of two-link robotic manipulator and comparison of its performance with some of the well-known existing controllers were presented. Lastly, hardware implementation of the proposed design for trajectory control of Quanser's single-link flexible joint module was carried out, and it was shown that the proposed strategy offered a viable approach for designing implementable robust controllers for robots. Copyright © 2011 John Wiley & Sons, Ltd.

Towards the Unification of Locomotion and Manipulation through Control Lyapunov Functions and Quadratic Programs

Abstract: This paper presents the first steps toward unifying locomotion controllers and algorithms with whole-body control and manipulation A theoretical framework for this unification will be given based upon quadratic programs utilizing control Lyapunov functions In particular, we will first consider output based feedback linearization strategies for locomotion together with whole-body control methods for manipulation We will show that these two traditionally disjoint methods are equivalent through the correct choice of controller We will then present a method for unifying these two methodologies through the use of control Lyapunov functions presented in the form of a quadratic program In addition, it will be shown that these controllers can be combined with force-based control to achieve locomotion and force-based manipulation in a single framework Finally, simulation results will be presented demonstrating the validity of the proposed framework

A Review of Piecewise Linearization Methods

Abstract: Various optimization problems in engineering and management are formulated as nonlinear programming problems. Because of the nonconvexity nature of this kind of problems, no efficient approach is available to derive the global optimum of the problems. How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory. In the last few decades, piecewise linearization methods have been widely applied to convert a nonlinear programming problem into a linear programming problem or a mixed-integer convex programming problem for obtaining an approximated global optimal solution. In the transformation process, extra binary variables, continuous variables, and constraints are introduced to reformulate the original problem. These extra variables and constraints mainly determine the solution efficiency of the converted problem. This study therefore provides a review of piecewise linearization methods and analyzes the computational efficiency of various piecewise linearization methods.

An Adaptive Voltage Control Strategy of Three-Phase Inverter for Stand-Alone Distributed Generation Systems

Abstract: This paper proposes an adaptive control method of three-phase inverters for stand-alone distributed generation systems (DGSs). The proposed voltage controller includes two control terms: an adaptive compensating term and a stabilizing term. The adaptive compensating control term is constructed to avoid directly calculating the time derivatives of state variables. Meanwhile, the stabilizing control term is designed to asymptotically stabilize the error dynamics of the system. Also, a fourth-order optimal load current observer is proposed to reduce the number of current sensors and enhance the system reliability and cost effectiveness. The stability of the proposed voltage controller and the proposed load current observer is fully proven by using Lyapunov theory. The proposed control system can establish good voltage regulation such as fast dynamic response, small steady-state error, and low total harmonic distortion under sudden load change, unbalanced load, and nonlinear load. Finally, the validity of the proposed control strategy is verified through simulations and experiments on a prototype DGS test bed with a TMS320F28335 DSP. For a comparative study, the control scheme of feedback linearization for multi-input and multioutput is implemented, and its results are presented in this paper.

Dynamics of Underactuated Multibody Systems: Modeling, Control and Optimal Design

Abstract: 1 Introduction 2 Multibody Systems 3 Feedback Linearization and Model Inversion of Nonlinear Systems 4 Trajectory Tracking of Multibody Systems 5 Model Inversion Using Servo-Constraints 6 Trajectory Tracking of Flexible Multibody Systems 7 Optimal System Design 8 Concluding Remarks Index

LMI-Based Gain Synthesis for Simple Robust Quadrotor Control

Abstract: In this paper, we present a method for using linear matrix inequalities (LMIs) to synthesize controller gains for a quadrotor system. The controller is based on approximate feedback linearization and is structured to allow for tuning similar to proportional-integral-derivative (PID) controllers. The synthesis procedure generates suboptimal gains with respect to mixed H2 and H∞ performance cost functions and a pole placement region constraint. The basic procedure is extended to account for dynamic external disturbances, inexact nonlinearity cancellation, multiplicative actuator uncertainty, and saturated integrators in the control loop. The controller is tested in a real-world flight using 10 Hz position updates with 2 cm standard deviation noise to approximate GPS or vision-based control scenarios.

Nonlinear and Adaptive Control Systems

Abstract: An adaptive system for linear systems with unknown parameters is a nonlinear system. The analysis of such adaptive systems requires similar techniques to analyse nonlinear systems. Therefore it is natural to treat adaptive control as a part of nonlinear control systems. Nonlinear and Adaptive Control Systems treats nonlinear control and adaptive control in a unified framework, presenting the major results at a moderate mathematical level, suitable for MSc students and engineers with undergraduate degrees. Topics covered include introduction to nonlinear systems; state space models; describing functions for common nonlinear components; stability theory; feedback linearization; adaptive control; nonlinear observer design; backstepping design; disturbance rejection and output regulation; and control applications, including harmonic estimation and rejection in power distribution systems, observer and control design for circadian rhythms, and discrete-time implementation of continuous-time nonlinear control laws.

Model Predictive Formation Control Using Branch-and-Bound Compatible With Collision Avoidance Problems

Abstract: This paper presents a model predictive control (MPC) approach for multivehicle formation taking into account collision avoidance and velocity limitation with reduced computational burden. The first part of the paper constructs a formation control law using feedback linearization with MPC in order to reduce the optimal control problem to a mixed-integer quadratic programming problem for a group of unicycles. The second part constructs a new branch-and-bound (B& B) -based algorithm for collision-avoidance problems. Numerical examples and experiments show that the proposed method significantly reduces computation time.

Path Following for a Class of Mechanical Systems

Abstract: Path following entails having the output of a control system approach a path and traverse it without a priori time parameterization of the motion along the path. We design path-following controllers for a class of mechanical control systems applicable to closed and nonclosed paths. Our approach uses transverse feedback linearization (TFL) to partially meet our objective by putting the system into a convenient normal form for control design. To meet the remaining control requirements, we present a method of refining the TFL normal form. Our approach is demonstrated experimentally on a five-bar robotic manipulator and in simulation on a nonminimum phase robotic manipulator with a flexible link.

Fuzzy sliding mode control design for a class of nonlinear systems with structured and unstructured uncertainties

Abstract: This paper presents controlling of a class of nonlinear systems with struc- tured and unstructured uncertainties using fuzzy sliding mode control. First known dy- namics of the system are eliminated through feedback linearization and then fuzzy sliding mode controller is designed using TS method, based on the Lyapunov method, which is capable of handling uncertainties. There are no signs of the undesired chattering phenom- enon in the proposed method. The globally asymptotic stability of the closed-loop system is mathematically proved. Finally, this method of control is applied to the inverted pendu- lum system as a case study. Simulation results show the system performance is desirable. Keywords: Nonlinear systems, Structure uncertainties, Unstructured uncertainties, Fuzzy, Sliding mode control

Design Novel Fuzzy Robust Feedback Linearization Control with Application to Robot Manipulator

Abstract: First three degree of six degree of freedom robotic manipulator is controlled by a new fuzzy sliding feedback linearization controller. The robot arm has six revolute joints allowing the corresponding links to move horizontally. When developing a controller using conventional control methodology (e.g., feedback linearization methodology), a design scheme has to be produced, usually based on a system’s dynamic model. The work outline in this research utilizes soft computing applied to new conventional controller to address these methodology issues. Feedback linearization controller (FLC) is influential nonlinear controllers to certain systems which this method is based on compute the required arm torque using nonlinear feedback control law. When all dynamic and physical parameters are known FLC works superbly; practically a large amount of systems have uncertainties and fuzzy feedback linearization controller (FFLC) reduce this kind of limitation. Fuzzy logic provides functional capability without the use of a system dynamic model and has the characteristics suitable for capturing the approximate, varying values found in a MATLAB based area. To increase the stability and robustness new mathematical switching sliding mode methodology is applied to FFLC. Based on this research model free mathematical tunable gain new sliding switching feedback linearization controller applied to robot manipulator is presented to have a stable and robust nonlinear controller and have a good result compared with conventional and pure fuzzy logic controllers.

Concurrent Learning Adaptive Model Predictive Control

Abstract: A concurrent learning adaptive-optimal control architecture for aerospace systems with fast dynamics is presented. Exponential convergence properties of concurrent learning adaptive controllers are leveraged to guarantee a verifiable learning rate while guaranteeing stability in presence of significant modeling uncertainty. The architecture switches to online-learned model based Model Predictive Control after an online automatic switch gauges the confidence in parameter estimates. Feedback linearization is used to reduce a nonlinear system to an idealized linear system for which an optimal feasible solution can be found online. It is shown that the states of the adaptively feedback linearized system stay bounded around those of the idealized linear system, and sufficient conditions for asymptotic convergence of the states are presented. Theoretical results and numerical simulations on a wing-rock problem with fast dynamics establish the effectiveness of the architecture.

Neural network-based adaptive event-triggered control of nonlinear continuous-time systems

Abstract: In this paper, a neural network (NN) based adaptive event-triggered control is developed for a single input and single output (SISO) uncertain nonlinear continuous time system. An explicit design of the event-triggered controller using NN approximation and feedback linearization is presented. The controller dynamics are approximated by using two single layer NNs. In addition, novel weight update laws are derived for the NNs in the context of event-triggered transmission, i.e., weights are updated only at the triggering instants, hence, aperiodic in nature. The closed loop stability analysis using Lyapunov approach for impulsive dynamical system is carried out to show the uniform ultimate boundedness (UUB) of the NN weight estimation errors as well as system states. Numerical results are included for validating the design.

Reference command tracking control for an air-breathing hypersonic vehicle with parametric uncertainties

Abstract: For the longitudinal model of an air-breathing hypersonic vehicle (AHV) subject to high nonlinearity, uncertain parameters and input constraints, this paper designs a controller for reference command tracking control. Firstly, the feedback linearization method is employed for a modified AHV model with uncertain parameters. Secondly, dynamical effect caused by the uncertain parameters on the linearized model is analyzed, which reveals that the linearized model is affected by disturbance and affine parameter-dependent matrices. Thirdly, a robust controller is designed using H ∞ method, which addresses input constraints of the AHV by additional linear matrix inequalities (LMIs). Simulations on the nonlinear AHV model demonstrate that the designed controller achieves desired tracking performance with well robustness.

Attitude Control of Spacecraft with Actuator Uncertainty

Abstract: A LTHOUGH safe-mode transition is a technique widely applied to handle component faults of spacecraft, it is not an option during critical phases. To increase onboard autonomy in fault management fault-tolerant-control (FTC) design without ground intervention has attracted increasing attention [1,2]. Feedback linearization control was developed for automated attitude recovery of spacecraft [3]. An FTC attitude control was presented in [4] to accommodate reaction-wheel faults. In particular, sliding mode control (SMC) is becoming an effective approach to tackle with uncertainty and external disturbance. SMC is successfully applied to design FTC for spacecraft. In [5] an SMC-based lawwas synthesized to stabilize attitudewith actuator outage fault. In [6] an adaptive SMC scheme was proposed to tolerate thruster failures. Accommodating partial loss of actuator effectiveness without angular-velocity measurements was discussed in [7]. In [8] rapid reorientation was studied in the absence of control along either roll or yaw axes. The preceding FTC schemes assume that actuators are free of misalignments. However, finite manufacturing tolerance or warping of structure may introduce actuator alignment errors. This issue may cause performance degradation of the attitude-control system. To address this problem an adaptive-control law was developed to handle small gimbals’ alignment error of variable speed-control moment gyros [9]. In [10] a model reference adaptive controller was tested with alignment errors up to 15 deg. An extended Kalman filter was used for on-orbit alignment calibration [11]. Unknown inertia parameters and actuator uncertainty were investigated in [12]. In [13] an adaptive-control law was presented to compensate for thrustmagnitude error and misalignment. This study investigates attitude stabilization with external disturbance, unknown inertia parameters, and actuator uncertainties including fault and misalignment. An adaptive control is proposed to render the closed-loop system input-to-state stable and is organized as follows: Sec. II presents a mathematical model of a rigid spacecraft, Sec. III presents main results, and simulation results are given in Sec. IV followed by the conclusions in Sec. V.

Digital Control of a Shunt Hybrid Power Filter Adopting a Nonlinear Control Approach

Abstract: This paper proposes a nonlinear derivative-less control approach for controlling a three-phase shunt hybrid power filter (SHPF). The dynamic model of the SHPF system is first elaborated in the stationary frame and then transformed into a “dq” reference frame. The control system is divided into two separate loops, namely the two current dynamics inner loop and the dc voltage dynamic outer loop. The exact feedback linearization technique is used to decouple the inner loop variables. Proportional-integral controllers are utilized to control the SHPF input currents and dc-bus voltage. The proposed nonlinear control is first simulated and then validated on a 2.5-kVA laboratory prototype supported by the DS 1104 digital real-time controller board of dSPACE. Satisfactory results, such as low-ac-current total harmonic distortion, fast step response, and high robustness under load variation, are obtained. Significantly high correlation between the experimental results and the theoretical model, implemented with SIMULINK/Matlab, is obtained.

Nonlinear model predictive control using Feedback Linearization and local inner convex constraint approximations

Abstract: Model predictive control (MPC) is one of the most popular advanced control techniques and is used widely in industry The main drawback with MPC is that it is fairly computationally expensive and this has so far limited its practical use for nonlinear systems To reduce the computational burden of nonlinear MPC, Feedback Linearization together with linear MPC has been used successfully to control nonlinear systems The main drawback is that this results in an optimization problem with nonlinear constraints on the control signal In this paper we propose a method to handle the nonlinear constraints that arises using a set of dynamically generated local inner polytopic approximations The main benefits of the proposed method is guaranteed recursive feasibility and convergence

Navigation of an Autonomous Car Using Vector Fields and the Dynamic Window Approach

Abstract: This work presents a safe navigation approach for a car-like robot. The approach relies on a global motion planning based on velocity vector fields along with a dynamic window approach for avoiding unmodeled obstacles. Basically, the vector field is associated with a kinematic, feedback linearization controller whose outputs are validated, and eventually modified, by the dynamic window approach. Experiments with a full-size autonomous car equipped with a stereo camera show that the vehicle was able to track the vector field and avoid obstacles in its way.

Control of Nonprehensile Rolling Manipulation: Balancing a Disk on a Disk

Abstract: This paper presents feedback stabilization control of a rolling manipulation system called the disk-on-disk. The system consists of two disks in which the upper disk (object) is free to roll on the lower disk (hand) under the influence of gravity. The goal is to stabilize the object at the unstable upright position directly above the hand. We show that it is possible to stabilize the object at the upright position, while the hand or object rotates to a specific orientation or spins at a constant velocity. We use full-state feedback linearization to derive control laws. We present simulation as well as experimental results demonstrating the controllers.