Wilson J. Rugh

Survey Research on gain scheduling

Current research on gain scheduling is clarifying customary practices as well as devising new approaches and methods for the design of nonlinear control systems.

Gain scheduling for H-infinity controllers: a flight control example

A new approach to gain scheduling linear dynamic controllers is illustrated for a pitch-axis autopilot design problem. In this application the linear controllers are designed at distinct operating conditions by H/sup infinity / methods. The gain scheduling procedure uses particular features of both the linear dynamic controllers and the controller configuration to remove so-called hidden coupling terms that can occur in scheduled controllers. Potential performance improvement is demonstrated by comparing simulation results to those for a naive gain scheduled controller that ignores the coupling terms. >

On a nonlinear multivariable servomechanism problem

Abstract Multivariable nonlinear plants with both measured and unmeasured vector disturbance signals are considered. Output-feedback, dynamic control laws are designed for the problem of tracking a constant or slowly-varying reference input while rejecting constant or slowly-varying disturbances.

Gain scheduling dynamic linear controllers for a nonlinear plant

For a general type of nonlinear tracking problem, we consider gain scheduling based on a family of linear dynamic controllers designed for a family of plant linearizations about constant operating points. A necessary and sufficient condition for the existence of gain scheduled controllers satisfying appropriate requirements is presented. Using this condition, the impact of linear controller configuration on the existence of a gain scheduled controller can be assessed, and ad hoc approaches to scheduling can be analyzed.

Decoupling in a Class of Nonlinear Systems by State Variable Feedback

For a class of nonlinear systems we derive a necessary and sufficient condition for the existence of a state variable feedback control law which accomplishes decoupling, as well as some conditions which characterize the class of decoupling control laws. Several examples are presented to illustrate the application of these results. For a special subclass which includes the so-called bilinear systems, we give two equivalent forms of the necessary and sufficient condition.

An approximation method for the nonlinear servomechanism problem

An analysis of the nonlinear servomechanism problem by the authors (1992) is shown to lead naturally to a straightforward and practical method for solving the problem in an approximate sense. The results are based on a kth-order approximate solution for the plant zero-error manifold, and corresponding control law constructions are shown to yield kth-order asymptotic tracking and disturbance rejection properties for the closed-loop system. The approach is illustrated by application to the ball and beam system. >

Brief Stability preserving interpolation methods for the synthesis of gain scheduled controllers

Synthesis of gain scheduled controllers for nonlinear plants often requires that a parameter-varying controller be generated from a finite set of linear time-invariant controllers. We propose interpolation methods for this task with the property that stability of the linearized closed-loop system is preserved for all values of the scheduling parameter. In addition, slow-variation arguments are presented that establish local stability of the nonlinear closed-loop system with gain scheduled controller.

Complete identification of a class of nonlinear systems from steady-state frequency response

A solution to the identification problem for a class of nonlinear systems, based on steady-state frequency response, is presented. This class is composed of certain interconnections of stable linear dynamic systems and integer power nonlinearities. Two kinds of measurements are considered. The first involves obtaining the amplitude and relative phase of each harmonic of the steady-state frequency response, while the second involves measuring the amplitudes only. In each case we find the number of measurements sufficient to identify a system for which the highest power present and the bounds on the dimensions of the linear subsystems are known.

Input-output pseudolinearization for nonlinear systems

An input-output pseudolinearized system has the property that its family of linearizations about constant operating points has input-output behavior that is independent of the operating point. We develop a necessary and sufficient condition for existence of a state feedback and state coordinate change that transforms a given system into a pseudo-normal form that is input-output pseudolinearized. These ideas are applied to obtain new approaches to approximate tracking and approximate inversion of nonlinear systems. >

On the pseudo-linearization problem for nonlinear systems

Abstract Based on well-known results for linear systems, an alternate treatment of tthe pseudo-linearization problem of Reboulet and Champetier is given. Sufficient conditions for pseudo-linearization are obtained in the general case, and these are shown to be satisfied under mild hypothesis by systems with one or two inputs. Advantages of the new approach include the simplicity of the derivation, and a more explicit representation for a pseudo-linearizing transformation.