Showing papers on "Feedback linearization published in 2001"

Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model

Abstract: This study introduces a fuzzy control design method for nonlinear systems with a guaranteed H/sub /spl infin// model reference tracking performance. First, the Takagi and Sugeno (TS) fuzzy model is employed to represent a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs. The advantage of proposed tracking control design is that only a simple fuzzy controller is used in our approach without feedback linearization technique and complicated adaptive scheme. By the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem (LMIP). The LMIP can be solved very efficiently using the convex optimization techniques. Simulation example is given to illustrate the design procedures and tracking performance of the proposed method.

Non-linear Control for Underactuated Mechanical Systems

Abstract: From the Publisher: This book deals with the application of modern control theory to some important underactuated mechanical systems. It presents modelling and control of the following systems:||- the inverted pendulum||- a convey-crane system||- the pendubot system||- the Furuta pendulum||- the inertia wheel pendulum||- the planar flexible-joint robot||- the planar manipulator with two prismatic and one revolute joints||- the ball & beam system||- the hovercraft model||- the planar vertical and take-off landing (PVTOL) aircraft||- the helicopter model on a platform||- the helicopter model||In every case the model is obtained in detail using either the Euler-Lagrange formulation or the Newton's second law. We develop control algorithms for every particular system using techniques such as passivity, energy-based Lyapunov functions, forwarding, backstepping or feedback linearization techniques.||This book will be of great value for PhD students and researchers in the areas of non-linear control systems.

Nonlinear control of the Reaction Wheel Pendulum

Abstract: In this paper we introduce the Reaction Wheel Pendulum, a novel mechanical system consisting of a physical pendulum with a rotating bob. This system has several attractive features both from a pedagogical standpoint and from a research standpoint. From a pedagogical standpoint, the dynamics are the simplest among the various pendulum experiments available so that the system can be introduced to students earlier in their education. At the same time, the system is nonlinear and underactuated so that it can be used as a benchmark experiment to study recent advanced methodologies in nonlinear control, such as feedback linearization, passivity methods, backstepping and hybrid control. In this paper we discuss two control approaches for the problems of swingup and balance, namely, feedback linearization and passivity based control. We first show that the system is locally feedback linearizable by a local diffeomorphism in state space and nonlinear feedback. We compare the feedback linearization control with a linear pole-placement control for the problem of balancing the pendulum about the inverted position. For the swingup problem we discuss an energy approach based on collocated partial feedback linearization, and passivity of the resulting zero dynamics. A hybrid/switching control strategy is used to switch between the swingup and the balance control. Experimental results are presented.

Towards the design of a biped jogging robot

Abstract: Deals with the design and control of an anthropomorphic autonomous biped robot The objective is to realize a dynamically stable, three-dimensional walking and jogging motion The design, sensors and electronics of the robot are introduced Particular emphasis has been devoted to achieving a high power-to-weight ratio The corresponding methods for weight reduction are presented The control scheme is discussed It is based on the method of feedback linearization employing the equations of motion of the system

A feedback control scheme for reversing a truck and trailer vehicle

Abstract: A control scheme is proposed for stabilization of backward driving along simple paths for a miniaturized vehicle composed of a truck and a two-axle trailer. The paths chosen are straight lines and arcs of circles. When reversing, the truck and trailer under examination can be modeled as an unstable nonlinear system with state and input saturations. The simplified goal of stabilizing along a trajectory (instead of a point) allows us to consider a system with controllable linearization. Still, the combination of instability and saturations makes the task impossible with a single controller. In fact, the system cannot be driven backward from all initial states because of the jack-knife effects between the parts of the multibody vehicle; it is sometimes necessary to drive forward to enter into a specific region of attraction. This leads to the use of hybrid controllers. The scheme has been implemented and successfully used to reverse the radio-controlled vehicle.

Adaptive Control of Nonlinear Attitude Motions Realizing Linear Closed Loop Dynamics

Abstract: An adaptive attitude control law is presented that realizes linear closed-loop dynamics in the attitude error vector. The modified Rodrigues parameters (MRPs) are used as the kinematic variables since they are nonsingular for all possible rotations. The desired linear closed-loop dynamics can be of either PD or PID form. Only a crude estimate of the moment of inertia matrix is assumed to be known. An open-loop nonlinear control law is presented which yields linear closed-loop dynamics in terms of the MRPs. An adaptive control law is developed which asymptotically enforces these desired linear closed-loop dynamics in the presence of large inertia and external disturbance model errors. Since the unforced closed-loop dynamics are nominally linear, standard linear control methodologies can be employed to satisfy design requirements. The adaptive control law is shown to track the desired linear performance asymptotically without requiring a priori knowledge of either the inertia matrix or external disturbance.

Adaptive nonlinear output-feedback control with unknown high-frequency gain sign

Abstract: A global adaptive output-feedback control scheme, which does not require a priori knowledge of high-frequency gain sign, is proposed for general nonlinear systems in output-feedback form. Unlike in Ding (1998), the removal of a priori knowledge of the high-frequency gain sign is not at the price of making growth restrictions on system nonlinearities, and furthermore, only the minimal number of parameters needs to be updated.

Hybrid control using recurrent fuzzy neural network for linear induction motor servo drive

Abstract: A hybrid control system using a recurrent fuzzy neural network (RFNN) is proposed to control a linear induction motor (LIM) servo drive. First, feedback linearization theory is used to decouple the thrust force and the flux amplitude of the LIM. Then, a hybrid control system is proposed to control the mover of the LIM for periodic motion. In the hybrid control system, the RFNN controller is the main tracking controller, which is used to mimic a perfect control law, and the compensated controller is proposed to compensate the difference between the perfect control law and the RFNN controller. Moreover, an online parameter training methodology, which is derived using the Lyapunov stability theorem and the gradient descent method is proposed to increase the learning capability of the RFNN. The effectiveness of the proposed control scheme is verified by both the simulated and experimental results. Furthermore, the advantages of the proposed control system are indicated in comparison with the sliding mode control system.

Mechanical Engineer's Handbook

Abstract: Preface Contributors 1. Statics Vector Algebra Centroids and Surface Properties Moments and Couples Equilibrium Dry Friction 2. Dynamics Fundamentals Kinematics of a Point Dynamics of a Particle Planar Kinematics of a Rigid Body Dynamics of a Rigid Body 3. Mechanics of Materials Stress Deflection and Stiffness Fatigue 4. Theory of Mechanisms Fundamentals Position Analysis Velocity and Acceleration Analysis Kinetostatics 5. Machine Components Screws Gears Springs Rolling Bearings Lubrication and Sliding Bearings 6. Theory of Vibration Introduction Linear Systems with One Degree of Freedom Linear Systems with Finite Numbers of Degrees of Freedom Machine-Tool Vibrations 7. Principles of Heat Transfer Heat Transfer Thermodynamics Conduction Heat Transfer Convection Heat Transfer 8. Fluid Dynamics Fluids Fundamentals Hydraulics 9. Control Introduction Signals Transfer Functions Connection of Elements Poles and Zeros Steady-State Error Time-Domain Performance Frequency-Domain Performances Stability of Linear Feedback Systems Design of Closed-Loop Control Systems by Pole-Zero Methods Design of Closed-Loop Control Systems by Frequential Methods State Variable Models Nonlinear Systems Nonlinear Controllers by Feedback Linearization Sliding Control Appendix: Differential Equations and Systems of Differential Equations Index

Stable model reference adaptive fuzzy control of a class of nonlinear systems

Abstract: In this paper, we propose a new adaptive fuzzy control scheme called model reference adaptive fuzzy control (MRAFC). The MRAFC scheme employs a reference model to provide closed-loop performance feedback for generating or modifying a fuzzy controller's knowledge base. The MRAFC scheme grew from ideas in conventional model reference adaptive control (MRAC). The MRAFC scheme is developed to perform adaptive feedback linearization to a class of nonlinear systems. A class of fuzzy controllers, which can be expressed in an explicit form, is used as the primary controller. Based on Lyapunov's second method, we have developed MRAFC schemes and derived fuzzy rule adaptive laws. Hence, not only the stability of the system can be assured but also the performance, such as the issues of robustness and parameter convergence, of the MRAFC system can be analyzed explicitly. We showed that in the case of no modeling error, the state error converges to zero asymptotically. In the case that persistent excitation is satisfied, we showed that the MRAFC system is asymptotically stable. By considering the periodic signal as reference input signal, we showed that the square wave can make the MRAFC system be persistently excited. The feasibility of applying these techniques has been demonstrated by considering the control of an inverted pendulum in following a reference model response.

Dynamics and control of multi-converter DC power electronic systems

Abstract: In multi-converter power electronic systems, different power electronic converters are integrated together to form a complex and extensively interconnected system. In general, there are two kinds of loads in these systems. One group is conventional loads, which have positive incremental impedance characteristics. They are mainly considered as constant voltage loads that require regulated voltage for their operation. The other group is tightly regulated power electronic converters and motor drives sinking constant power from their input buses. The purpose of this paper is to present an assessment of the dynamic interactions between these loads in the multi-converter DC power electronic systems. Furthermore, a nonlinear robust stabilizing controller based on the feedback linearization technique for DC/DC PWM converters is presented.

Nonlinear state feedback controller for nonlinear systems: Stability analysis and design based on fuzzy plant model

Abstract: This paper presents the stability analysis of a fuzzy-model-based control system consisting of a nonlinear plant and a nonlinear state feedback controller and the design of the nonlinear gains of the controller. The nonlinear plant is represented by a fuzzy model having p rules. A nonlinear state feedback controller is designed to close the feedback loop. Under this design, the stability condition is reduced to p linear matrix inequalities. An application example on stabilizing a mass-spring-damper system will be given.

Control problems in underactuated manipulators

Abstract: We discuss some recent control techniques for underactuated manipulators - a special instance of mechanical systems having fewer input commands than degrees of freedom. This class includes robots with passive joints, elastic joints, or flexible links. Structural system properties are investigated showing that robots with passive joints are the most difficult to control. With reference to these, solutions are proposed for the typical problems of trajectory planning and tracking, and of set-point regulation. The relevance of nonlinear control techniques such as dynamic feedback linearization and iterative state steering is clarified through illustrative examples.

Speed nonlinear control of DC motor drive with field weakening

Abstract: In this paper, the authors show that it is feasible to apply nonlinear multiple-input multiple-output feedback linearization technique to a separately excited DC motor system that is operated in the high-speed field-weakening regime. Load-adaptive and sensorless control techniques to improve dynamic speed performance are proposed and compared. Also, application results are presented to verify theoretical ones.

Three-Axes Missile Autopilot Design: From Linear to Nonlinear Control Strategies

Abstract: A three-axes skid-to-turn missile autopilot design is presented. The modeling is that of a missile developed by AerospatialeMatraMissiles.Variouscontrollawshavebeencomparedinordertoestimatetheirpotentialandtheir applicability: classical linear time-invariant control and static and dynamic approximate input-output linearizing feedbacks. The robustness is studied, and the best results, in terms of stability, performance, and robustness, are shown to be obtained by using a special type of nonlinear dynamic control. The simulation results are explained using a table of comparison.

Nonlinear control strategy applied to a shunt active power filter

Abstract: This paper presents a new nonlinear decoupling control method of a three-phase three-wire voltage source shunt active filter. The currents injected by the active filter are controlled in the synchronous orthogonal dq frame using a decoupled feedback linearization control method. The reference currents are extracted from the sensed nonlinear load currents by applying the synchronous reference frame method. The voltage level of the DC side is regulated using an output feedback linearization control. Integral compensators are added in both current and voltage loops in order to eliminate the steady state errors due to system parameters uncertainty. Simulation results confirm the performance considered theoretically for the shunt active filter.

Control for an Integrated Suspension System via Parameterized Linear Matrix Inequality Characterizations

Abstract: The automotive hydro-pneumatic integrated suspen- sion model is nonlinear with large dimension. As a consequence, the nonlinear control methodology based on the traditional Hamilton-Jacoby-Isaacs equation is impractical in this appli- cation. An alternative so-called parameterized linear matrix inequality (PLMI) approach is proposed for solving this hard nonlinear control problem. The validity of the proposed approach is confirmed not only by detailed and realistic simula- tions but also by extensive experiments. Specifically, the proposed nonlinear control method outperforms the more classical feedback linearization control technique.

Autopilot Design for the Stanford DragonFly UAV: Validation through Hardware-in-the-Loop Simulation*

Abstract: We present an embedded autopilot design for the Stanford DragonFly Unmanned Aerial Vehicle (UAV) of which the digital computer in the avionics is only capable of processing sampled data and executing discrete-time control policies. We demonstrate that linear control design is not sufficient to satisfy performance requirements for specified high performance maneuvers at slow sample rates. We design a new nonlinear digital controller using an approximate feedback linearization. The sampled nonlinear dynamics for the feedback linearization is obtained using the Adams-Bashforth method, and the resulting control law is augmented with the discrete disturbance accommodation control to improve the performance and stability of the controlled system. The control law is implemented on a Hardware-in-the-Loop Simulation, which is a testbed platform that provides a faithful laboratory representation of the DragonFly UAV in flight: sensor and actuator packet delay and communication constraints in the control, are included in this testbed. We evaluate the control law using different sample rates and present our results. Keyword: UAV flight control, discrete-time control policy, approximate feedback linearization, disturbance accommodation, embedded systems.

On controlling aircraft formations

Abstract: We describe a framework for controlling a group of unmanned aerial vehicles (UAVs) flying in close formation. We first present a nonlinear dynamical model which includes the induced rolling moment by the lead aircraft on the wing of the following aircraft. Then, we outline two methods for trajectory generation of the leading aircraft, based on interpolation techniques on the Euclidean group, SE(3). Two formation controllers that allow each aircraft to maintain its position and orientation with respect to neighboring UAVs are derived using input-output feedback linearization. Numerical simulations illustrate the application of these ideas and demonstrate the validity of the proposed framework.