Frequent and large load changes are often encountered in chemical processes. This can be lead to erroneous results in system identification especially for the fully automated identification procedure in autotuners. Relatively speaking, the relay feedback test is less sensitive to load disturbance (e.g., as compared to the step test). However, as the magnitude of load increases, the estimates of ultimate gain and ultimate frequency deteriorate exponentially. In this work, the causes of errors are analyzed using a describing function and a remedial action is devised. Since load disturbance leads to asymmetric output responses, an output-biased relay is employed to restore symmetric output response. Furthermore, instead of a trial-and-error procedure, the bias value can be calculated immediately following system responses. Subsequently, an identification procedure is proposed to maintain the quality of the model in the face of load changes. Linear and nonlinear systems are used to test the effectiveness of t...

Autotune identification under load disturbance

Using averaging methods of the theory of differential equations, the effects of the injection of high frequency signals, known as dithers, in non-linear systems is studied. The behaviour of the dithered system is compared with that of a smoothed one, whose non-linearity is the convolution of the dither distribution function and the original non-linearity. It is proved that if over a given time interval the smoothed system has a bounded solution, then so does the dithered system, provided that the dither frequency is high enough, and the output of the two systems can be made as close as desired. Moreover, if the trajectories of the smoothed system are asymptotically attracted to a compact set, for example a stable orbit or singular point, then the trajectories of the dithered system can be made to remain close to this set. In particular, a satisfactory explanation of quenching of limit cycldes is botained in this way. The analysis takes account of certain disturbances which might arise due to the injection...

Application of a method of averaging to the study of dithers in non-linear systems

Robust control for servo-mechanisms under inexact friction compensation

Preface and Introduction F years ago the structures of a linearized theory of servomechanisms and a linearized theory of aircraft dynamics were substantially complete. Combination and extension of the two subjects, accumulation of favorable experimental evidence, an increased general understanding, and the continuing challenge of complex and stringent requirements have made aircraft flight control a useful predictive science and a recognized engineering specialty. This much is no news to readers of the Journal of Guidance, Control, and Dynamics. Before we begin to congratulate ourselves, however, the editors have thought it appropriate to reflect on the perennial question from the floor: "What about nonliriearities?" The question is often facile and impertinent. A considered response is, of necessity, complicated, extensive but not comprehensive, and invariably controversial. No general response is possible^ Nevertheless, we may hope that reconsideration of specific topics will elucidate the matter and we have been persuaded to make the attempt. Our approach is historical. No new research results are presented, but our interpretation may disturb the conventional wisdom. The earliest, more or less successful, automatic flight control systems were highly nonlinear in their sensing and actuating elements (see Fig. 1, taken from Ref. 1). Analysis, however, was at that time disdained, and performance was achieved by cut and try methods. We have told elsewhere the story of the synthesis of the art of the " tinker er-in vent or" and the science of the "theoretician" in connection with aircraft flight control.' The confluence of techniques was well developed by about 1952.' This included the experimental and theoretical study of significant nonlinearities. But the litera-

Retrospective essay on nonlinearities in aircraft flight control

This survey paper presents a comprehensive review of work in the field of non-linear oscillations. A brief discussion of second-order systems is followed by a presentation of exact criteria, approximate analytical methods and computational techniques for limit cycles in single variable systems. Multivariate systems are then covered from an analogous viewpoint which allows the reader to clearly identify both how single variable methods have been extended and the possibilities for further research. Particular emphasis is placed on describing function methods since it is believed that, where exact solutions are not possible, the approach may not only give approximate solutions but provides good insight for further computational or simulation studies. The coverage is essentially restricted to continuous lumped parameter systems and includes both free and forced oscillations. Several applications of the theories in various fields of engineering and science are discussed and indicate the broad interest in non-l...

R. C. Boyer

Papers

Effects of Extra Sinusoidal Inputs to Nonlinear Systems