Showing papers on "Feedback linearization published in 1989"
TL;DR: In this article, the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs is studied and necessary and sufficient conditions for the existence of the linearization transformation are derived.
Abstract: This paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs. Necessary and sufficient conditions for the existence of the linearization transformation are derived. For nonlinear systems without inputs, the conditions are shown to be corrections to an existing result. A computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented.
423 citations
TL;DR: In this paper, an adaptive update law which counteracts the effects of unknown parameters is shown to be robust to the unmodeled dynamics, and conditions are given for global stability of an adaptive control law designed for the reduced-order model of a class of nonlinear plants.
Abstract: A feedback linearization design is presented which includes unknown parameters and unmodeled dynamics. An adaptive update law which counteracts the effects of unknown parameters is shown to be robust to the unmodeled dynamics. The proposed design methodology is based on a conceptually simple stability analysis. Conditions are given for global stability of an adaptive control law designed for the reduced-order model of a class of nonlinear plants. In the presence of unmodeled dynamics, the regulation property is preserved in a stability region. The size of the region is estimated using bounds that not only prove robustness, but also allow a comparison between adaptive and nonadaptive nonlinear controls. >
400 citations
TL;DR: In this paper, the authors derive globally stabilizing state feedback laws for broad classes of nonlinear systems and present an example of a globally stabilizable nonlinear feedback system which cannot be stabilized, even locally, by any output feedback law -in particular, by a high gain law.
347 citations
TL;DR: In this article, the problem of transforming a nonlinear multi-input system into a linear controllable one via nonsingular dynamic feedback and (extended) state space diffeomorphism is addressed.
269 citations
13 Dec 1989
TL;DR: In this paper, a feedback linearization design of the mechanical link dynamics with that of the electrical motor dynamics is proposed to improve the control accuracy of a brushless actuator with an asymptotic approximation of the integral manifold.
Abstract: The present trend toward the development of gearless robots aims to eliminate mechanical complexity where possible. Consistent with this objective is the increasing use of brushless motors as joint actuators. These electronically commutated motors do have the required characteristic of high torque at low-speed, but pose a challenge for accurate torque control at the joints. It is shown that by coordinating the feedback linearization design of the mechanical link dynamics with that of the electrical motor dynamics, greater control accuracy can be achieved. The feedback linearization is applied to a reduced-order model which accounts for the electrical dynamics with an asymptotic approximation of the integral manifold. A first-order correction to the current commands of joint actuators improves the torque tracking accuracy of the robot. >
79 citations
TL;DR: In this paper, a sliding-mode technique is applied to achieve a robust feedback linearization of the highly non-linear dynamic equation of the arm, and pole placement is then used to attain good dynamic response.
Abstract: This paper is concerned with the application of sliding control’ to the regulation of a one-link flexible robot arm, with an arbitrary number of flexible modes. Slidingmode technique is applied to achieve a robust feedback linearization of the highly non-linear dynamic equation of the arm. Pole placement is then used to attain good dynamic response. An example is given to demonstrate the potential of the sliding method. This work serves as a first step towards a practical solution in the feedback control of flexible arms using the sliding technique.
56 citations
13 Dec 1989
TL;DR: The application of modern nonlinear control theory to the fast and accurate positioning of stepping motors is discussed and control algorithms based on a feedback linearization approach are presented and contrasted with current techniques.
Abstract: The application of modern nonlinear control theory to the fast and accurate positioning of stepping motors is discussed. The mathematical model of a permanent magnet stepper motor is presented. Control algorithms based on a feedback linearization approach are presented and contrasted with current techniques. Methods to determine the unknown motor parameters in real-time and normal operation are also discussed. These allow for straightforward extensions of the control algorithms to adaptive control. An experimental setup to evaluate the performance of the overall system is described. >
53 citations
TL;DR: A reduction procedure is applied in order to reduce the problem to the stabilization of a first-order control system by a C 2 feedback function and sufficient conditions are given for the solution of the last problem and of the first problem as well.
47 citations
13 Dec 1989
TL;DR: In this article, an approach for the approximate input-output linearization of nonlinear systems, particularly those for which relative degree is not well defined, is presented, and the authors demonstrate some properties of the accuracy of the approximation and, in the context of the ball and beam example, show it to be far superior to the Jacobian approximation.
Abstract: The authors present an approach for the approximate input-output linearization of nonlinear systems, particularly those for which relative degree is not well defined. They show that there is a great deal of freedom in the selection of an approximation and that, by designing a tracking controller based on the approximating system, tracking of reasonable trajectories can be achieved with small error. The approximating system is itself a nonlinear system, with the difference that it is input-output linearizable by state feedback. The authors demonstrate some properties of the accuracy of the approximation and, in the context of the ball and beam example, show it to be far superior to the Jacobian approximation. The results are focused on finding regular SISO systems which are close to systems which are not regular and controlling these approximate regular systems. >
44 citations
13 Dec 1989
TL;DR: In this article, an adaptive controller for nonlinear, linearly parameterized systems is presented, where parameter estimation is performed on the scalar Lyapunov equation instead of the n-dimensional equation of the system itself.
Abstract: An adaptive controller for nonlinear, linearly parameterized systems is presented. The new features introduced in the design are: (1) parameter estimation is performed on the scalar Lyapunov equation instead of the n-dimensional equation of the system itself. This allows non-Lipschitz uncertainties to be tolerated, especially when the stabilizing laws are not feedback linearization plus linear control. (2) Double estimation is used. One estimate is used for the stabilizing control, and the other is used to cancel the perturbation terms introduced by the adaptation, if possible. This is proposed to solve the problem of the implicit definition of the controller which arises when one tries to do this cancellation. >
38 citations
TL;DR: In this paper, the application of recently developed feedback linearization techniques to controlling the powertrain of an automobile is discussed, where the objective is to regulate the output torque of the engine and transmission system to achieve a desired longitudinal acceleration of the vehicle.
Abstract: The application of recently developed feedback linearization techniques to controlling the powertrain of an automobile is discussed. The objective of powertrain control is to regulate the output torque of the engine and transmission system to achieve a desired longitudinal acceleration of the vehicle. With higher model order and increasing system complexity, the design process for feedback linearization becomes harder and more tedious. However, the design process can be simplified for a class of nonlinear systems including the automobile powertrain. Simplification of the design process is accomplished by incorporating the single perturbation technique into the input-output linearization technique. Furthermore, the controller obtained by the simplified linearization technique is computationally simpler than the one obtained by the conventional linearization technique. Nonetheless, it provides good dynamic performance for the powertrain system. >
TL;DR: Linearizable nonlinear discrete-time systems are described as a composition of diffeomorphisms in this paper, where linearizability of a general nonlinear system is obtained as an extension of linearization of the system expressed in terms of the diffeomorphic elements.
Abstract: Linearizable nonlinear discrete-time systems are described as a composition of diffeomorphisms. Linearizability of a general nonlinear system is obtained as an extension of linearizability of the system expressed in terms of the diffeomorphisms. >
TL;DR: In this paper, a set of generalized transformed variables are derived for a single pass shell and tube heat exchanger using this technique, which reduce the apparent nonlinear behavior of single pass heat exchangers.
Abstract: The use of partial linearization by nonlinear state variable feedback has been proposed as a means of reducing the detrimental effects of system nonlinearities upon the performance of linear control schemes used with nonlinear systems. In this paper a set of generalized transformed variables are derived for a single pass shell and tube heat exchanger using this technique. The implementation of these generalized transformed variables, which reduce the apparent nonlinear behavior of single pass heat exchangers, eliminates the need to rederive a nonlinear transformation for each heat exchanger controller design. As shown by open loop transient behavior of the system, the transformed variables reduce the nonlinear characteristics of the system response. The closed loop performance of the heat exchanger system has been evaluated for both servo and regulator control, and the effect of model error upon the robustness of the closed loop controller performance has been investigated.
TL;DR: In this article, the authors show that, while straightforward application of the linearization theory to a non-minimum phase system results in a system with a linear input-output response but unstable internal dynamics, designing a feedback control based on a minimum phase approximation to the true system with desirable properties such as bounded tracking and asymptotic stability is possible.
01 Jan 1989
TL;DR: This Chapter shall see how the theory developed for single-input single output systems can be extended to nonlinear systems having many inputs and many outputs.
Abstract: In this Chapter we shall see how the theory developed for single-input single output systems can be extended to nonlinear systems having many inputs and many outputs. In particular, in the first three sections we shall consider a special class of multivariable nonlinear systems, those for which there is a meaningful multivariable analogue of the notion of relative degree. For these systems it is an easy matter to extend — in a straightforward way — most of the design procedures illustrated in Chapter 4. Then, in section 5.4, we shall proceed to the study of more general classes of multivariable systems. In order to avoid unnecessary complications, we shall restrict our analysis to the consideration of systems having the same number m of input and output channels. Occasionally, we shall specify how the results should be adapted in order to include systems having a different number of inputs and outputs.
TL;DR: In this paper, a finite element formulation for a class of nonlinear viscoelastic continua subjected to stochastic excitation is developed by means of a linear equivalent linearization technique, which minimizes the expected value of the square of the difference between nonlinear and linearized auxiliary equations.
Abstract: A finite element formulation for a class of nonlinear viscoelastic continua subjected to stochastic excitation is developed by means of a stochastic equivalent linearization technique. The nonlinear viscoelastic properties of the continua are modeled in terms of the constitutive equation which linearly involves the hysteretic tensor and in terms of the auxiliary equation which describes a nonlinear relationship among the strain and hysteretic tensors and their time derivatives. This auxiliary equation is linearized with the aid of a stochastic linearization technique which minimizes the expected value of the square of the difference between the nonlinear and linearized auxiliary equations. The linearized boundary value problem then involves a set of two linearization coefficients which are functions of space and time. With the aid of the weighted residuals method, the boundary value problem developed for the continuum is transformed into that in the finite element formulation. In integrating the equation ...
21 Jun 1989
TL;DR: In this paper, the authors compare feedback linearization and singular perturbation control techniques for flexible joint robots, which can be controlled using a globally decoupled linear system theory.
Abstract: Analytical and experimental results comparing feedback linearization and singular perturbation control techniques for flexible joint robots are presented. The feedback linearization approach results in a globally decoupled linear system which can be controlled using techniques of linear system theory. The singular perturbation approach exploits a natural time-scale separation that results from large joint stiffness to compute a composite control law to damp the joint oscillations while exploiting the desirable properties of rigid robot dynamics.
13 Dec 1989
TL;DR: The feedback linearization properties of a class of multilink manipulators with one flexible link are studied and it is shown that the input-output equations are feedback linearizable when the output variable is chosen appropriately.
Abstract: The feedback linearization properties of a class of multilink manipulators with one flexible link are studied. This class includes the 5-bar-linkage and the elbow manipulator. It is shown that the input-output equations are feedback linearizable when the output variable is chosen appropriately. It is shown that the input-state equations are not feedback linearizable. Alternate methods of controlling these manipulators must be studied. >
TL;DR: In this paper the concept of slow manifold theory is applied to a class of nonlinear singularly perturbed systems to achieve external linearization for the “full system” via reduced order decompositions into exact slow and fast subsystems.
TL;DR: The methods of Gaussian linearization along with a new Gaussian Criterion used in the prediction of the stationary output variances of stable nonlinear oscillators subjected to both stochastic parametric and external excitations are presented.
Abstract: The methods of Gaussian linearization along with a new Gaussian Criterion used in the prediction of the stationary output variances of stable nonlinear oscillators subjected to both stochastic parametric and external excitations are presented. The techniques of Gaussian linearization are first derived and the accuracy in the prediction of the stationary output variances is illustrated. The justification of using Gaussian linearization a priori is further investigated by establishing a Gaussian Criterion. The non-Gaussian effects due to system nonlinearities and/or large noise intensities in a Duffing oscillator are also illustrated. The validity of employing the Gaussian Criterion test for assuring accuracy of Gaussian linearization is supported by performing the Chi-square Gaussian goodness-of-fit test.
13 Dec 1989
TL;DR: In this article, all nonlinear systems which can be transformed by change of coordinates to time-varying linear systems with output injection are characterized, and all of them can be represented as linear systems.
Abstract: All nonlinear systems which can be transformed by change of coordinates to time-varying linear systems with output injection are characterized. >
13 Dec 1989
TL;DR: In this paper, a state feedback law for an affine nonlinear system that makes a compact set containing the equilibrium of interest globally attractive is designed by designing a so-called control Lyapunov function.
Abstract: A state feedback law for an affine nonlinear system that makes a compact set containing the equilibrium of interest globally attractive is designed. The problem is solved by designing a so-called control Lyapunov function, using Z. Artstein's theorem (1983). Such a design is obtained for a nonlinear system which has already been maximally linearized by feedback and diffeomorphism. >
13 Dec 1989
TL;DR: The possibility of globally stabilizing, by means of a smooth state feedback, systems obtained by cascading a linear controllable system and a general nonlinear system is studied in this article.
Abstract: The possibility of globally stabilizing, by means of a smooth state feedback, systems obtained by cascading a linear controllable system and a general nonlinear system is studied. In general, stabilizing the linear part with very negative eigenvalues does not suffice to stabilize the whole system, because of the peaking phenomenon: for a linear controllable system it is always possible to choose a feedback that will have poles with a very negative real part, but in general the resulting trajectories go far away before they go to zero. This poses an obstruction to the stabilization of globally minimum phase systems that can be compensated for if the derivatives of the nonlinear part have sufficiently slow growth. Theorems giving sufficient conditions for stabilizability in terms of such growth conditions are proved. >
TL;DR: In this paper, an approach to the control of voltage-fed induction motors, which takes explicitly into account the nonlinear multivariable nature of the model and the presence of uncertainties in the motor inductances, is discussed.
TL;DR: In this article, active large angle slewing maneuvers of a multi-body flexible dynamic system are investigated, where closed-loop feedback algorithms are implemented to perform slewing maneuver, while simultaneously suppressing flexural vibrations of the system.
Abstract: Active large angle slewing maneuvers of a multi-body flexible dynamic system are investigated. An appropriate state variable transformation and a feedback linearization technique are employed to transform the dynamics of the nonlinear system to a new state that is more amenable to control design procedures. Closed-loop feedback algorithms are implemented to perform slewing maneuvers, while simultaneously suppressing flexural vibrations of the system. Stability of this class of nonlinear systems is also investigated, whereby a sufficient condition for asymptotic stability of the system is established. Numerical examples are presented to demonstrate the proposed active control algorithms.
13 Dec 1989
TL;DR: In this article, the design of robust stabilizing controllers for uncertain nonlinear systems which are feedback-equivalent to controllable linear systems is studied. But the design method does not necessarily require structure matching conditions between the real plant and the nominal model of the plant.
Abstract: A study is made of the design of robust stabilizing controllers for uncertain nonlinear systems which are feedback-equivalent to controllable linear systems. Uncertainty is considered to be parametric and is caused by unknown or time-varying modeled parameters. Uncertainties due to unmodeled dynamics are not addressed. The proposed design method does not necessarily require structure matching conditions between the real plant and the nominal model of the plant. The problem reduces to the design of linear controllers for a linear system perturbed by uncertainties which lie in the range of the control input operator only when the matching conditions are satisfied. The design approach is based on the second method of Lyapunov, wherealgebraic Riccati equations need to be solved. >
TL;DR: In this paper, the authors present sufficient conditions for dynamic feedback linearization via a restricted class of dynamic compensators, made of simple chains of integrators followed by static feedback on the extended state space.
14 Aug 1989
TL;DR: The stability and control problems associated with twinlift helicopter configurations are analyzed and a nonlinear control scheme based on feedback linearization is presented for the resulting closed-loop systems.
Abstract: The stability and control problems associated with twinlift helicopter configurations are analyzed. For the two twin-lift configurations viz. twin-lift with spreader bar and twin-lift without spreader bar, a nonlinear control scheme based on feedback linearization is presented. The performance of the resulting closed-loop systems in terms of trim attitudes and required control travel for carrying out a typical twin-lift mission is evaluated through nonlinear simulation. Also, the effect of controller and sensor degradations on the overall system performance is discussed.
21 Jun 1989
TL;DR: In this paper, the role of singular perturbation analysis for design of nonlinear control for rapid slewing of a rigid body with attached flexible appendage is investigated, and various options for robust control implementation are discussed.
Abstract: In this paper we consider the practical application of methods for feedback linearization of multibody systems with elasitic interactions. We investigate the role of singular perturbation analysis for design of nonlinear control for rapid slewing of a rigid body with attached flexible appendage. Similar problems arise in elastic models for appendage deployment and fast, lightweight robotic arms. Although such models cannot be exactly linearized by C? transformation of the system state and feedback the nominal models can be partially linearized with respect to primary system orientation variables. Models are developed and various options for robust control implementation are discussed.