Showing papers on "Feedback linearization published in 1988"

Variable-structure control of spacecraft attitude maneuvers

Abstract: A variable-structure control approach is presented for multiaxial spacecraft attitude maneuvers. Nonlinear sliding surfaces are proposed that result in asymptotically stable, ideal linear decoupled sliding motions of Cayley-Rodrigues attitude parameters, as well as of angular velocities. The resulting control laws are interpreted as more easily implemented and more robust versions of those previously obtained by feedback linearization.

Dynamic control of robots with joint elasticity

Abstract: Reference is made to the problem of controlling the dynamic behavior of robots with rigid links but in presence of joint elasticity. It is shown that use of the more general class of dynamic nonlinear state-feedback allows solving both the feedback linearization and the input-output decoupling problems. A constructive procedure for the decoupling and linearizing feedback is given which is based on generalization system inversion and on the properties of the so-called zero-dynamics of the system. A case study of a planar two-link robot with elastic joints is included. The role of dynamic feedback for this class of robots is discussed. >

Feedback linearization of sampled-data systems

Abstract: It is shown that feedback linearizability of a continuous-time system can be destroyed through the introduction of the usual sample-and-hold devices. A method whereby a feedback linearizable discrete-time model can be recovered is given. >

Feedforward and feedback linearization of nonlinear system and its implementation using internal model control (IMC)

Abstract: Cette strategie, presentee ici theoriquement est appliquee au cas d'un reacteur parfaitement agite

Analysis and Optimization of Systems

Abstract: Relations between H? and risk sensitive controllers.- Duality for linear time invariant finite dimensional systems.- Calculation of maximal stability domains using an optimality property of kharitonov polynomials.- Optimal regulator for linear systems with delays in state and control - spectrum decomposition and prediction approach.- Sous-espaces invariants des operateurs lineatres. Point de vue et methodes numberiques nouveaux.- From fractality to non integer derivation : A fundamental idea for a new process control strategy.- Optimal robust multi-purpose general feedback systems.- Vibrational stabilization of linear systems with time delay.- Quantitative feedback theory (QFT): A natural tool for active vibration control synthesis.- An H ? method for the design of linear time-invariant multivariable sampled-data control systems.- Theory and method for designing feedback controllers of siso descriptor systems with H?-optimal sensitivity.- A note on distrubance decoupling with stability for nonlinear systems.- Dynamic decoupling of voltage frequency controlled induction motors.- State space realizations of nonlinear systems defined by input-output differential equations.- Strong controllability for series cascade of polynomial control systems.- Sur quelques problemes concernant les systemes lineaires generalises.- An observer design for nonlinear control systems.- Two sufficient conditions for dynamic feedback linearization of nonlinear systems.- Sur la commande digitale d'un systeme non lineaire a dephasage minimal.- Controlabilite des systems bilineaires generaux et homogenes dans R2.- Commande non-interactive d'un reacteur chimique non-lineaire apport de la logique flour pour amelioration de la robustesse.- On inverse problem of nonlinear system dynamics.- On the stabilizability of homogeneous control systems.- Linear model matching with prescribed tracking error and internal stability for nonlinear systems.- Almost disturbance decoupling for multivariable nonlinear systems: A sufficient condition.- A sufficient condition for extremality.- Robustesse des systemes lineaires boucles aux perturbations non-lineaires.- An implementation of the method of analytic centers.- A step-size selection procedure for equality constrained optimization.- Strong variation algorithm for minimax control.- A non-clustering multistart algorithm for global optimization.- Free time optimal control problems with unilateral state constraints.- An angular open mapping theorem.- Variable end points problems in the calculus of variations : Coupled points.- Necessary conditions for infinite dimensional control problems.- Optimal control of quasilinear multistate elliptic systems.- Finite rank, relatively bounded perturbations of semi-groups generators.- Shape optimization of a nonshallow arch towards critical buckling load.- Algorithmes pour l'implementation de la commande optimale avec critere quadratique des systemes bilineaires.- Algorithme de commande pour les systemes energetiques "presque bilineaires" distribues (SPB) conductifs - convectifs - radiatifs.- Analytic methods for the modeling of flexible structures.- Asymptotic behaviour of the solutions to wave equation with nonlinear damping on the boundary.- Stabilisation d'une classe de systemes distribues hyperboliques.- Feedback control of vibrations in an extendible cantilever sweptback wing.- Boundary control of hyperbolic system with boundary condition involving a time delay.- Dynamical boundary control of two-dimensional petrovsky system: Vibrating rectangular plate.- Distributed control approximation of pointwise control for hyperbolic systems.- Implementing stability results in solving large scale convex programming problems.- Quasi-decentralized multimodel estimation of linear systems.- Decentralized stabilization of nonlinear large-scale system with singular perturbations.- Solution of coupled riccati equations occurring in nash games.- The solution to a kind of stackelberg game systems with multi-follower: Coordinative and incentive.- Simultaneous design of communication and control strategies for stochastic systems with feedback.- An alternative method to solve a variational inequality applied to an air traffic control example.- Resolution numerique d'equations d'hamilton-jacobi-bellman au moyen d'algorithmes multigrilles et d'iterations sur les politiques.- Deterministic and stochastic control problems with identical optimal cost functions.- Chaos, determinism and stochasticity.- The conditional adjoint process.- Optimality conditions for continuous time systems with controlled jump Markov disturbances: Application to an FMS planning problem.- Multiple time scale analysis of manufacturing systems.- Controle optimal semi-actif de suspension de vehicule.- Optimal control laws for a two-level linear quadratic problem.- Application of RKH space methods to the filtering problem forlinear hereditary systems.- Piecewise linear filtering with small observation noise.- Approximate filtering of random fields.- Asymptotic analysis for piecewise linear filtering.- A class of adaptive controllers with application to robust adaptive control.- Set valued solutions to control problems and their approximations.- A robust discrete adaptive control approach based on passivity results for non-linear systems.- On predictiye control: A comparison and some extensions.- Robustness of pole placement direct adaptive control for time-varying plants.- Avoiding the non-admissible region of the parameter space in indirect adaptive control algorithms.- Partial state LQ and GPC adaptive control: An experimental evaluation.- Robust adaptive control - Averaging gradient algorithm.- A class of reduced order filters designed for state dependent noise.- Approximate wiener-kolmogorov filters.- Linear dynamic errors in variables models: Some structure theory.- Analyse et surveillance vibratoire d'Une machine en rotation.- Lissage-detection de signaux non stationnaires.- Variational methods of piecewise approximation.- The application of likelihood ratio based derivative estimates in interpolation approximations for queueing systems.- Optimization of stochastic dynamical systems in the frequency domain.- Perturbation analysis and augmented markov chains for discrete event systems.- Sensitivity analysis from sample paths using the method of likelihoods.- A simple interpretation of perturbation analysis.- Finitely generated Moduloids.- Layout method of manufacturing workshop.- Optimization of a multi-reservoir water network using a conjugate gradient technique. A case study.- A generalization of little's law to moments of queue lengths and waiting times in closed, product form queueing networks.- Reduction de modele preservant la stabilite : un algorithme base sur l'approximation stochastique dans les espaces de hardy.- Parametrization of MIMO systems in closed-loop balanced representation.- Identifiability of a model of compartmentation of serotonin in human platelets.- The uncertainty principle of mathematical modelling.- A summary of parametrization results on the rational interpolation problem.- Inputs, outputs and states in the representation of time series.- Deterministic Markovian 2-D systems.- A graph metric for a class of MIMO linear distributed systems.- The application of the canonical correlation concept to the identification of linear state space models.- Detection of gastric signals from cutaneous abdominal measurements.- The ill- conditionning in stereotaxic irradiation: Optimization of isodoses arrays distribution using the singular values decomposition.- Hopf bifurcation point detection. application of a continuation method to optimization of multistate systems.- Structure des modeles mathematiques en biologie.- Une commande nonlineaire de bioprocedes fedbatch.

Exact Linearization of Nonlinear Systems with Outputs

Abstract: This paper discusses the problem of using feedback and coordinates transformation in order to transform a given nonlinear system with outputs into a controllable and observable linear one. We discuss separately the effect of change of coordinates and, successively, the effect of both change of coordinates and feedback transformation. One of the main results of the paper is to show what extra conditions are needed, in addition to those required for input-output-wise linearization, in order to achieve full linearity of both state-space equations and output map.

New nonlinear control algorithms for multiple robot arms

Abstract: Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space. >

Load Balancing and Closed Chain Multiple Arm Control

Abstract: We give the general dynamical equations for several rigid link manipulators rigidly grasping a commonly held rigid object. It is shown that the number of lost arm configuration degrees of freedom due to imposing the closed loop kinematic constraints is the same as the number of degrees of freedom gained for controlling the internal forces of the closed chain system. This number is equal to the dimension of the kernel of the Jacobian operator which transforms contact forces to the net forces acting on the held object, and it is shown that this kernel can be identified with the subspace of controllable internal forces of the closed chain system. Control of these forces allows one to regulate the grasping forces imparted to the held object or to control the load taken by each arm. It is shown that the internal forces can be influenced without affecting the control of the configuration degrees of freedom, and that this fact is independent of control law choice and involves only kinematical information about each arm. Control laws of feedback linearization type are shown to be useful for controlling the location and attitude of a frame fixed with respect to the held object, while simultaneously controlling the internal forces of the closed chain system. Since the kernel describing the internal forces subspace depends only on the relative location of arm tip contact points, force feedback can be used to feedback linearize and control the system even when the held object has unknown mass properties.

A Lyapunov approach for robust nonlinear state feedback synthesis

Abstract: The authors apply the input/output linearization approach for nonlinear state feedback synthesis. The model uncertainty under consideration is a class of state model perturbations that satisfy appropriate matching conditions. The controller design uses a Lyapunov-based approach to guarantee uniform ultimate boundedness of the states and the output. >

Feedback linearization in the presence of uncertainties

Abstract: After a brief review of feedback linearization, several approaches to the problem of parametric uncertainty are outlined, and the adaptive approach to both SISO and MIMO plants is discussed in detail. Based on experience with adaptive control of linear plants, two parameter update laws are chosen for nonlinear plants according to their relative degrees. The simpler of the two adaptive laws is applicable to plants with relative degree one. For plants with higher relative degree the adaptive scheme is more complex, but a simple update law can still be employed in the special case when the state diffeomorphism, required for linearization, does not depend on uncertain parameters. The simpler adaptive scheme is shown to be robust with respect to unmodelled dynamics.

Input/output linearization: A nonlinear analog of placing poles at process zeros

Abstract: This paper deals with SlSO nonlinear processes and their control with nonlinear static state feedback. The Byrnes-lsidori concept of nonlinear zeros is first reviewed and illustrated with two chemical engineering examples. This concept is then used to interpret input/output linearizing state feedback as a nonlinear analog of placing poles at the process zeros. This interpretation leads to closed-loop internal stability conditions for nonlinear processes under input /output linearizing state feedback.

Feedback control of multiinput nonlinear systems by extended linearization

Abstract: Control of a nonlinear system is addressed by considering its family of linearizations. Given that a family of linear state-feedback controllers has been designed to meet some (linear) control objective, it is shown how these controllers can be pieced together into an overall, nonlinear, state-feedback controller. The resulting closed-loop system has the property that its linearizations are equal to the desired linearly controlled systems. A similar approach can be used to design nonlinear state estimators. The approach is illustrated by applying it to the control of a planar two-link manipulator. >

On the feedback linearization of robots with elastic joints

Abstract: Robotic manipulators in which the joints exhibit a certain amount of elasticity are considered. Necessary and sufficient conditions are given under which these systems can be linearized by state feedback and suitable change of coordinates. Conditions which allow an approximate feedback linearization are also derived. Simulation results for a three-degree-of-freedom robot are presented. >

Robust stabilization of feedback linearizable systems

Abstract: An examination is made of the robust stabilization of a class of uncertain nonlinear systems for which the uncertainties are not required to satisfy the so-called structure matching conditions. Sufficient conditions for two systems belonging to this class to be both feedback linearizable are obtained. In the case of models with unknown parameters entering linearly, an adaptive control law is synthesized based on the exact linearization of the model system. >

Feedforward and feedback linearization of non-linear systems with disturbances

Abstract: The problem of transforming non-linear systems with input disturbances to their linear equivalents is investigated. A characterization of the class of non-linear systems with disturbances that are equivalent to controllable quasi-linear systems with disturbances, z = Az + bv + ξ(z) d, is given. The necessary transformations (state-space coordinate changes and control input-space coordinate changes by non-linear feedforward and feedback) are presented and their implications for control system synthesis are discussed. Finally a numerical example is given,

Robot arm force control through system linearization by nonlinear feedback

Abstract: Based on a differential geometric feedback linearization technique for nonlinear time-varying systems, a dynamic force control method for robot arms is developed. It uses active force-moment measurements at the robot wrist. The controller design fully incorporates the robot-arm dynamics and is so general that it can be reduced to pure position control, hybrid position/force control, and pure force control. The controller design is independent of the tasks to be performed. Computer simulations show that the controller improves the position error by a factor of ten in cases in which position errors generate force measurements. A theorem on linearization of time-varying system is also presented. >

Two sufficient conditions for dynamic feedback linearization of nonlinear systems

Abstract: We address the problem of transforming a nonlinear multi-input system into a linear controllable one via dynamic state feedback and (extended) state space diffeomorphism We give sufficient conditions for two classes of multi-input systems to be dynamic feedback linearizable

Tracking and disturbance rejection in nonlinear systems: the integral manifold approach

Abstract: The authors study the tracking and disturbance rejection problem of a class of time-invariant nonlinear systems which are linear equivalent to controllable linear systems By using a nonlinear feedback control and a slowly varying integral control, the closed-loop system asymptotically tracks a reference input and rejects disturbances which are both unknown and slowly varying The integral manifold concept is used to design a nonlinear controller >

On equivalent Harmonic and Stochastic Linearization for Nonlinear Shock-Absorbers

Abstract: Many dynamical systems can be described by mainly linear mechanical models with some isolated nonlinear elements. If only the system’s overall dynamic response is of interest, these isolated nonlinear elements can often be taken care of by equivalent linearization techniques.

Dynamic Feedback Linearization of a Hydraulic Valve-Actuator Combination

Abstract: This paper considers linearization of a hydraulic valve-actuator combination using dynamic feedback.

Dynamic feedback linearization with application to aircraft control

Abstract: The authors study the problem of the linearization of a nonlinear system by dynamic state feedback. A necessary condition and a sufficient condition are presented and are shown to apply to a general aircraft model. >

Invariants for feedback equivalence and Cauchy characteristic multifoliations of nonlinear control systems

Abstract: Linearization of a nonlinear feedback control system under nonlinear feedback is treated as a problem of equivalence-under the Lie pseudogroup of feedback transformations-of distributions on the product manifold of the state and control variables. The new feature of this paper is that it introduces the Cauchy characteristic sub-distributions of these distributions and their derived distributions. These Cauchy characteristic distributions are involutive and nested, hence define a Multifoliate Structure. A necessary condition for feedback equivalence of two nonlinear control systems is that these multifoliations be transformed under the feedback pseudogroup. For linear systems, this Cauchy characteristic multifoliate structuee is readily computed in terms of the (A, B)-matrix that defines the linear system. Assuming that the conditions for local feedback linearization are satisfied, the existence of a global feedback linearizing transformation is dependent on computing an element of the first cohomology group of the space with coefficients in the sheaf of groupoid of infinitesimal feedback automorphisms of the linear system. The theorem quoted above about the Cauchy characteristic multifoliations provides some information about this groupoid. It is computed explicitly and directly for control systems with one- or two-state dimensions. Finally, these Cauchy characteristic sub-distributions must inevitably play a role in the numerical or symbolic computational analysis of the Hunt-Su partial differential equations for the feedback-linearizing transformation.

Transient response of joint-dominated space structures - A new linearization technique

Abstract: The linearization method presented for calculating the transient responses of nonlinear systems due to initial disturbances is an extension of the 'describing function' approach, in which the system's steady-state response is calculated by representing such nonlinear elements as space structure joints with impedances that are functions of response amplitude. It is shown that, for the transient case, the steady-state impedances can be averaged over the range of responses in order to furnish equivalent values of stiffness and damping; these, for a given set of initial displacements, may be treated as constant during calculations of system response.