Showing papers on "Feedback linearization published in 1998"

Controlling formations of multiple mobile robots

Abstract: We investigate feedback laws used to control multiple robots moving together in a formation. We propose a method for controlling formations that uses only local sensor-based information, in a leader-follower motion. We use methods of feedback linearization to exponentially stabilize the relative distance and orientation of the follower, and show that the zero dynamics of the system are also (asymptotically) stable. We demonstrate in simulation the use of these algorithms to control six robots moving around an obstacle. These types of control laws can be used to control arbitrarily large numbers of robots moving in very general types of formations.

Nonlinear adaptive flight control using neural networks

Abstract: The effectiveness of a controller architecture, which combines adaptive feedforward neural networks with feedback linearization, has been demonstrated on a variety of flight vehicles. The boundedness of tracking error and control signals is guaranteed. The architecture can accommodate both linear-in-the-parameters networks, as well as single-hidden-layer perceptron neural networks. Both theoretical and experimental research is planned to expand and improve the applicability of the approach, and to demonstrate practical utility in the areas of cost reduction and improved flight safety.

Toward improvement of tracking performance nonlinear feedback for linear systems

Abstract: A composite nonlinear feedback tracking control law based on a nominal linear controller is proposed. The design yields nonlinear feedback laws that both increase the speed of the closed-loop system response to the command input and reduce the overshoot, while not imperilling the small signal performance achieved by the nominal linear feedback controller in the face of actuator amplitude saturation. A modern flight control application is used to demonstrate the effectiveness of the design.

Real-time trajectory generation for differentially flat systems

Abstract: This paper considers the problem of real-time trajectory generation and tracking for nonlinear control systems. We employ a two-degree-of-freedom approach that separates the nonlinear tracking problem into real-time trajectory generation followed by local (gain-scheduled) stabilization. The central problem which we consider is how to generate, possibly with some delay, a feasible state space and input trajectory in real time from an output trajectory that is given online. We propose two algorithms that solve the real-time trajectory generation problem for differentially flat systems with (possibly non-minimum phase) zero dynamics. One is based on receding horizon point to point steering, the other allows additional minimization of a cost function. Both algorithms explicitly address the tradeoff between stability and performance and we prove convergence of the algorithms for a reasonable class of output trajectories. To illustrate the application of these techniques to physical systems, we present experimental results using a vectored thrust flight control experiment built at Caltech. A brief introduction to differentially flat systems and its relationship with feedback linearization is also included. © 1998 John Wiley & Sons, Ltd.

A general algorithm for dynamic feedback linearization of robots with elastic joints

Abstract: For a general class of robots with elastic joints, we introduce an inversion algorithm for the synthesis of a dynamic feedback control law that gives input-output decoupling and full state linearization. Control design is performed directly on the second-order robot dynamic equations. The linearizing control law is expressed in terms of the original model components and of their time derivatives, allowing an efficient organization of computations. A tight upper bound for the dimension of the needed dynamic compensator is also obtained.

Robust decentralized control for multimachine power systems

Abstract: In this paper, a new robust linear decentralized controller is proposed to enhance the transient stability of nonlinear multimachine power systems. Only local measurements are required in the proposed controller. The feedback gain of each generator is obtained by solving an algebraic Riccati equation based on the bounds of the machine parameters. The stability analysis shows that the decentralized controller can guarantee the system stability over the whole operating region and regardless of fault locations or parameter uncertainties of the transmission network. Compared with nonlinear controllers, linear controllers are of simpler structure and easier to be implemented. A three-machine power system is considered as an application example. Simulation results show that despite the interconnections between different generators, nonlinearities in the system, different operating points, and different fault locations, the proposed robust decentralized controller can greatly enhance power system transient stability.

A feedback linearizing control scheme for a PWM converter-inverter having a very small DC-link capacitor

Abstract: This paper addresses a control method of reducing the size of the DC link capacitors of a power converter-inverter system. The main idea is to utilise the inverter operation status in the current control of the power converter. Specifically, information on the load power is incorporated in synthesizing the converter current control input so that a proper DC voltage level is maintained. The authors describe the dynamics of load current and apply feedback linearization theory to obtain an input output linearized system. Theoretically, this control strategy is effective in regulating the DC voltage level even though the DC link capacitor is arbitrarily small and load varies abruptly. The superior performance is demonstrated through simulation and experiment. Experiment was performed with a 9 kW PWM power converter-vector inverter system having a 75 /spl mu/F DC-link capacitor.

A new approach to dynamic feedback linearization control of an induction motor

Abstract: A new approach to dynamic feedback linearization control of an induction motor is given, Previously, it has been shown that the dynamic model of an induction motor, consisting of speed, stator currents, and rotor flux, is dynamically feedback linearizable. However, the controller and transformation were valid only as long as the motor torque was nonzero and the methodology required switching between two computationally complex transformations. Here it is shown that by considering the direct-quadrature model of the induction motor, a single dynamic feedback linearizing transformation exists and is valid (essentially) as long as the (magnitude of the) rotor flux is nonzero. Furthermore, the resulting control computations are well within the capabilities of contemporary microprocessor technology.

Stability and Control of a Structurally Nonlinear Aeroelastic System

Abstract: The authors examine the stability properties of a class of nonlinear controls derived via feedback linearization techniques for a structurally nonlinear prototypical two-dimensional wing section. In the case in which the wing section has a single trailing-edge control surface, the stability of partial feedback linearization to achieve plunge primary control is studied. It is shown for this case that the zero dynamics associated with the closed-loop system response are locally asymptotically stable for a range of e ow speeds and elastic axis locations. However, there exist locations of the elastic axis and speeds of the subsonic/incompressible e ow for which this simple feedback strategy exhibits a wide range of bifurcation phenomena. Both Hopf and pitchfork bifurcations evolve parametrically in terms of the e ow speed and elastic axis location. In the case in which the wing section has two control surfaces, the global stability of adaptive control techniques derived from full feedback linearization is studied. In comparison with partial or full feedback linearization techniques, the adaptive control strategies presented do not require explicit knowledge of the form of the structural nonlinearity.

Nonlinear control of a series DC motor: theory and experiment

Abstract: The control problem for a series DC motor is considered. Based on a nonlinear mathematical model of a series-connected DC motor, it is shown that the combination of a nonlinear transformation and state feedback (feedback linearization) reduces the nonlinear control design to a linear control design. To demonstrate its effectiveness, an experimental study of this controller is presented. These experimental results are also compared with a simulation of the closed-loop system. Finally, it is shown that a nonlinear observer (with linear error dynamics) for speed and load torque can be constructed based only on measurements of the motor current. Experimental results of this speed and load-torque estimator are also presented.

Entry trajectory tracking law via feedback linearization

Abstract: Asasteptowardextendingthetwo-dimensional(longitudinal)entrypredictive/trackingguidanceschemeusedby the U.S. Space Shuttle Orbitertothreedimensions, a control law fortrackinga three-dimensional entrytrajectory isdesigned. Thetrackinglawcommandstheanglesofattack and of bank thatarerequired tofollow aground track specie ed as a function of energy. Feedback linearization is used to design the tracking law. Some extensions to the existing theory are required to accommodate features of the entry tracking problem. Downrange and crossrange angles serve as output variables for the feedback linearization and lead to state and control transformations that convert the entry dynamics to an equivalent linear system in an approximate sense, which is dee ned. A feedback tracking law is then designed, taking advantage of the linear structure of the system dynamics in the transformed variables. This tracking law is shown to achieve bounded tracking of the output variables. Simulation results indicate the effectiveness of the tracking law in compensating for initial offsets from a reference trajectory. URRENT efforts to develop reusable launch vehicles (RLVs), a space station crew return vehicle, and a military spaceplane provide motivation for investigating potential improvements to the entry guidance capability for a lifting unpowered e ight vehicle.The state of the art is represented by the U.S. Space Shuttle Orbiters' entry guidance, as described by Harpold and Graves. 1 The Shuttle's longitudinal guidance combines predictive guidance, i.e., model- basedreferencetrajectoryplanningwithin-e ightupdating,withref- erence trajectory tracking. Mease and Kremer 2 revisited the Shuttle tracking law derivation in the framework of feedback linearization andshowedthattheShuttlelawisa linearized version ofthepropor- tional integral derivative (PID) type law that the feedback lineariza- tion approach can produce. By not linearizing the tracking law, the nonlinearities in the dynamics can be compensated for, provided they can be adequately modeled. Roenneke and Well 3 simulated a variety of low-lift re-entry eights and showed that the longitudinal PIDtracking lawwith feedback linearization yields uniformly good tracking performance and effectively compensates for 20% errors in air density and large initial position errors. A related nonlinear tracking law has been developed and applied to RLV guidance by Lu. 4 The entry guidance requirements for future unpowered entry ve- hicleswilllikelybe,astheyarefortheShuttle,tosteerthevehicleon afeasibletrajectory,atrajectorywithintheentrycorridor,dee nedby heating, acceleration, dynamic pressure, and controllability limits, thatachievesthe specieedtargetconditionwithin thespecie ederror margin. Additionalrequirements thatdrive our study are eying over specie edwaypointsandincreasedcrossrangecapability.Theformer may be required toavoid e ying over populated areas; the latter may be required for abort scenarios and to reduce the waiting time for returnfromorbit.TheShuttleentryguidancehandlescrossrangetar- getingbybankreversallogic.Crossrangetargetingtakessecondpri- ority todownrange targeting,and some crossrange capability issac- rie ced asa result. The additional requirements suggest that it would be desirable to extend the Shuttle longitudinal predictive/tracking guidance to longitudinal and lateral predictive/tracking guidance. The entry requirements can be met by a guidance scheme com- prising a rapid trajectory planner that generates a feasible ground

Estimation for nonlinear stochastic differential equations by a local linearization method 1

Abstract: This paper proposes a new local linearization method which approximates a nonlinear stochastic differential equation by a linear stochastic differential equation. Using this method, we can estimate parameters of the nonlinear stochastic differential equation from discrete observations by the maximum likelihood technique. We conduct the numerical experiments to evaluate the finite sample performance of identification of the new method, and compare it with the two known methods: the original local linearization method and the Euler methods. From the results of experiments, the new method shows much better performance than the other two methods particularly when the sampling interval is large

Control of flat systems by quasi-static feedback of generalized states

Abstract: Generalized states, the state representations of which depend on time derivatives of the input, are naturally used in the control design for flat systems. Quasi-static feedback of these generalized states, which involves time derivatives of the closedloop input, is shown to allow control of all flat systems by feedback linearization of the tracking error dynamics. This is then used in a method proposed for the analysis and design by subsystems of certain flat series connections. The results are illustrated on a gantry crane example.

Differential-geometric methods for control of electric motors

Abstract: SUMMARY The di⁄erential-geometric techniques of nonlinear control developed over the last 20 years or so include static and dynamic feedback linearization, input—output linearization, nonlinear state observers and disturbance decoupling. The theory has now reached a level of maturity where control practicioners are making e⁄ective use of the techniques for electric motors. Indeed, DC and AC motors have well-defined nonlinear mathematical models which often satisfy the structural conditions required of the di⁄erential-geometric theory. In this paper, the application of various di⁄erential-geometric methods of nonlinear control is shown by way of examples including DC motors (series, shunt and separately excited), induction motors, synchronous motors and DC—DC converters. A number of contributions are surveyed which show the benefits of the methods for the design of global control laws by systematic means. ( 1998 John Wiley & Sons, Ltd.

Feedback Control Theory for Dynamic Traffic Assignment

Abstract: Modelling and Problem Formulation.- Dynamic Traffic Routing Problem in Distributed Parameter Setting.- Fuzzy Feedback Control for Dynamic Traffic Routing.- Feedback Linearization for Dynamic Traffic Routing.- Sliding Mode Control for Dynamic Traffic Routing.- Network Level problem: System Optimal.- Network Level Problem: User Equilibrium.

A finite-difference method for linearization in nonlinear estimation algorithms

Abstract: Linearizations of nonlinear functions that are based on Jacobian matrices often cannot be applied in practical applications of nonlinear estimation techniques. An alternative linearization method is presented in this paper. The method assumes that covariance matrices are determined on a square root factored form. A factorization of the output covariance from a nonlinear vector function is directly determined by perturbing the nonlinear function with the columns of the factored input covariance, without explicitly calculating the linearization and with no differentiations involved. The output covariance is more accurate than that obtained with the ordinary Jacobian linearization method. It also has an advantage that Jacobian matrices do not have to be derived symbolically.

Robust stability analysis and design method for the fuzzy feedback linearization regulator

Abstract: A robust stability analysis and design method for a fuzzy feedback linearization regulator is presented. The well-known Takagi-Sugeno fuzzy model is used as the nonlinear plant model. Uncertainties and disturbance are assumed to be included in the model structure with known bounds. For these structured uncertainties, stability robustness of the closed system is analyzed in both input-output sense and Lyapunov sense. The robust stability conditions are proposed using multivariable circle criterion and the relationship between input-output stability and Lyapunov stability. Also, based on the stability analysis, a systematic design procedure for the fuzzy feedback linearization regulator is provided. The effectiveness of the proposed analysis and design method is illustrated by a simple example.

Geometry of feedback and optimal control

Abstract: Symplectic methods for optimization and control singular trajectories, feedback equivalence and time optimal control problem controllability of generic systems on surfaces recent advances in the stabilization problem for low dimensional systems asymptotic stabilization via homogeneous approximation critical Hamiltonians and feedback invariants optimal control problems on lie groups - crossroads between geometry and mechanics nonlinear control and combinatorics of words feedback classification of nonlinear control systems on R2R3 time-optinal feedback control for nonlinear systems - a geometric approach qualitative behaviour control problem and stabilization of dynamical systems an introduction to the co-ordinate-free maximum principle.

Output Feedback Variable Structure Adaptive Control of an Aeroelastic System

Abstract: The paper presents an application of the variable structure model reference adaptive control theory to control of aeroelastic systems with structural nonlinearity. Interestingly, the design approach does not require any knowledge of the parameters of the system and the nonlinear functions, and only output feedback is used for the synthesis of the control systems. Control laws for the trajectory tracking of pitch angle and plunge displacement are derived. In the closed-loop system, the state vector asymptotically converges to the origin. Control laws are discontinuous functions of the tracking error, and modulation functions of the relays are generated on-line using bounds on uncertain functions and certain auxiliary signals. Digital simulation results are presented which show that in the closed-loop system, pitch angle and plunge displacement are smoothly regulated to zero in spite of the uncertainty and unmodeled functions in the system using only output feedback.

Gain-scheduled controller design: An analytic framework directly incorporating non-equilibrium plant dynamics

Abstract: A velocity-based linearization framework is employed to develop a novel rigorous approach to gain-scheduling design. The proposed approach enables knowledge concerning the plant dynamics at non-equilibrium operating points to be incorporated directly into the controller design. Since the velocity-based linearization framework supports the analysis of the transient response, performance considerations can be accommodated. The approach retains continuity with linear methods, which is central to the existing conventional gain-scheduling methodology, and, since a single type of linearization is employed throughout, the design procedure is both straightforward and conceptually appealing.

Helicopter Blade Response and Aeromechanical Stability with a Magnetorheological Fluid Based Lag Damper

Abstract: This paper explores the feasibility of using Magnetorheological (MR) fluid-based dampers for lag damping augmentation in helicopters. An MR damper model is integrated with a rotor aeromechanical model. Two different control schemes are presented-namely the On-Off scheme and the Feedback Linearization scheme. In the On-Off scheme, two criteria are used to obtain equivalent linear damping for the nonlinear MR damper as a function of the size of perturbation and the applied field. The Feedback Linearization scheme uses a feedback controller to linearize the force output of the MR damper. The two control schemes are compared for lag transient response in ground resonance and their ability to reduce periodic damper loads in forward flight. It is shown that an MR damper of a size comparable to an elastomeric damper can provide sufficient damping for ground resonance stabilization and can significantly reduce periodic damper loads with ajudicious choice of operation scheme.

The design of stabilizing controls for shipboard DC-to-DC buck choppers using feedback linearization techniques

Abstract: Motivated by the Navy's interest in developing a DC zonal electrical distribution system, the authors have formulated a DC-to-DC buck chopper nonlinear control law to guarantee local asymptotic stability for a range of admissible constant power, variable input capacitance loads. Constant power nonlinearity is eliminated by pseudolinearization.

Adaptive vehicle cruise control system and methodology

Abstract: Disclosed herein is a headway control for an adaptive cruise control system based on a basic headway control law derived from feedback linearization techniques. The usefulness of the linear approximations is demonstrated, and basic attributes of data which are believed important to system response are introduced. Certain modifications to a basic headway controller for enabling system performance to better meet driver expectations under real road conditions are made as a result of empirical information.

A neural approach for control of nonlinear systems with feedback linearization

Abstract: Several schemes for feedback linearization using neural networks have been investigated and compared. Then an approach to design a neurocontroller in the sense of feedback linearization is introduced. The contents include: (1) full input-output linearization when a system has relative degree n; (2) partial input-output linearization when a system has relative degree r (r