Showing papers on "Feedback linearization published in 1980"

On the stabilization of nonlinear systems using state detection

Abstract: In this paper, we study the problem of stabilizing a nonlinear control system by means of a feedback control law, in cases where the entire state of the system is not available for measurement. The proposed method of stabilization consists of three parts: 1) determine a stabilizing control law based on state feedback, assuming the state vector x(t) can be measured; 2) construct a state detection mechanism, which generates a vector z(t) such that z(t)-x(t)\rightarrow 0 as t\rightarrow \infty and 3) apply the previously determined control law to z(t) . This scheme is well established for linear time-invariant systems, and its global convergence has previously been studied in the case of nonlinear systems. Hence, the contribution of this paper is in showing that such a scheme works in the absence of any linearity assumptions, and in studying both local asymptotic stability and global asymptotic stability.

Foundations of feedback theory for nonlinear dynamical systems

Abstract: We study the fundamental properties of feedback for nonlinear, time-varying, multi-input muldt-output, distributed systems. The classical Black formula is generalized to the nonlinear case. Achievable advantages and limitations of feedback in nonlinear dynamical systems are classified and studied in five categories: desensitization, disturbance attenuation, linearizing effect, asymptotic tracking and disturbance rejection, stabilization. Conditions under which feedback is beneficial for nonlinear dynamical systems are derived. Our results show that if the appropriate linearized inverse return difference operator is small, then the nonlinear feedback system has advantages over the open-loop system. Several examples are proyided to illustrate the results.

Decoupling of invertible nonlinear systems with state feedback and precompensation

Abstract: For a class of nonlinear invertible systems considered by Hirschorn [1], a decoupling control synthesis using state feedback and precompensation is presented. Two examples which include decoupling of vertical and horizontal path angles of a terrain-following airplane are presented.

A two-stage Lyapunov-Bellman feedback design of a class of nonlinear systems

Abstract: The composite control proposed in an earlier paper for a class of singularly perturbed nonlinear systems is now shown to possess properties essential for near-optimal feedback design. It asymptotically stabilizes the desired equilibrium and produces a finite cost which tends to the optimal cost for a slow problem as the singular perturbation parameter tends to zero. Thus, the well-posedness of the full regulator problem is established. The stability results are also applicable to two-time-scale systems which are not singularly perturbed, and the paper does not assume the knowledge of singular perturbation techniques.

Design of nonlinear feedback controllers

Abstract: This paper shows how the design of feedback controllers for nonlinear systems may be formulated as an optimization problem with infinite dimensional constraints for which known algorithms may be employed. An important aspect is a method for reducing the time interval, required to ensure stability, to a finite value.

A linearization technique for the dynamic response of nonlinear continua

Abstract: The efforts of this dissertation are directed toward the development of a technique for understanding the dynamic response of structural elements governed by nonlinear partial differential equations. This technique is based on the concepts of the equivalent linearization method which relies on obtaining an optimal linear set of equations to model the original nonlinear set. In this method, the linearization is performed at the continuum level. At this level, the equivalent linear stiffness and damping parameters are physically realizable and are defined in such a way that the method can be easily be incorporated into finite element computer codes. Three different approaches to the method are taken with each approach based on the minimization of a distinct difference between the nonlinear system and its linear replacement, Existence and uniqueness properties of the minimizat4on solutions are established. The method is specialized for the treatment of steady-state solutions to harmonic excitation and of stationary response to random excitation. Procedures for solving the equivalent linearization are also discussed. The method is applied to three specific examples: one dimensional, hysteretic shear beams, thin plates governed by nonlinear equations of motion and the same nonlinear thin plates but with cutouts. Solutions via the equivalent linearization method using the stress difference minimization compare well with Galerkin's method and numerical integration. The last example is easily handled by the continuum equivalent linearization technique, whereas other methods prove to be inadequate.

Pole assignment in single-input linear systems

Abstract: A computationally attractive procedure is given for calculating the feedback gain matrix required to place the poles of a single-input linear system at arbitrary locations. The method, applicable to uncontrollable as well as controllable ones, requires no explicit transformation of coordinates, nor does it require an a priori knowledge of the open-loop characteristic polynomial.

Feedback Design of Closed Contour Servomechanisms

Abstract: Two-dimensional (x, y) profile or curve tracers are considered in terms of position errors and peripheral velocity errors as the servomechanism follows a closed contour without introducing external forcing functions. The servo system is implemented using standard position controls with nonlinear cross-axis feedback terms, which are generated analytic functions of the pattern. Each axis essentially serves as a feedback path for the other axis in this system. Linearization enables one to design the system dynamics and test the controls. A machine tool using the nonlinear feedback system was constructed and tested. Performance was excellent, and an example of the results is presented.

The two-channel non-linear feedback system

Abstract: In a feedback system containing a non-linear non-inertial link followed by a low-pass filter, the feedback is limited by the high-frequency noise components of a sensor and input stage. A method is presented which uses a non-linear auxiliary feedback loop in order to increase the feedback and reduce the sensitivity of the output signal to the parameters of filter and power stage. The system satisfies the absolute stability criterion. A numerical example is presented with an increase of 40 dB in the feedback gain.