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Journal ArticleDOI

Non-linear design for cost of feedback reduction in systems with large parameter uncertainty †

01 Jun 1975-International Journal of Control (Taylor & Francis Group)-Vol. 21, Iss: 6, pp 977-1001
TL;DR: In this paper, a non-linear first-order reset element (FORE) is used to reduce the feedback loop transmission bandwidth of linear, minimum-phase plants with large parameter uncertainty.
Abstract: Feedback systems containing linear, minimum-phase plants with large parameter uncertainty may be designed to achieve specified performance tolerances over the entire range of parameter uncertainty. The principal ‘cost of feedback’ is in the feedback loop bandwidth, which is generally much larger than that of the system as a whole. This makes the system very sensitive to sensor noise and high-frequency parasitics. It is shown how a non-linear ‘first-order reset element’ (FORE) may be used to drastically decrease the feedback loop transmission bandwidth. One is logically led to FORE by simple, linear feedback frequency response concepts. The paper assumes that the primary design problem is to satisfy quantitative response tolerances to command inputs. However, disturbances at the plant are not neglected, but the specification on such disturbances is in the damping of the step response. An important feature of the non-linear design is that the system response to command inputs is almost exactly that of a lin...
Citations
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Journal ArticleDOI
TL;DR: It is shown that it is possible to find realizations for any given family of controller transfer matrices so that the closed-loop system remains stable, no matter how the authors switch among the controller.

457 citations


Cites methods from "Non-linear design for cost of feedb..."

  • ...The idea of reseting part of the controller state dates as far back as the 1950s with the Clegg Integrator (Clegg, 1958) and later with Horowitz and Rosenbaum’s 4rst-order reset elements (FORE) (Horowitz & Rosenbaum, 1975)....

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Journal ArticleDOI
TL;DR: This paper considers more general reset structures than previously considered, allowing for higher-order controllers and partial-state resetting, and gives a testable necessary and sufficient condition for quadratic stability and links it to both uniform bounded-input bounded-state stability and steady-state performance.

299 citations


Cites background from "Non-linear design for cost of feedb..."

  • ...As mentioned, Horowitz and his coworkers (for example, see [6]) incorporated FOREs into control system design by advocating a twostep process in which a linear controller was first designed followed by selection of the FORE’s pole....

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  • ...In [6], specific guidelines were provided which explicitly link the design of the FORE to the linear compensation....

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Journal ArticleDOI
TL;DR: In this paper, the authors propose an engineering design theory devoted to the practical design of feedback control systems, which they call QFT, where the amount of feedback needed is tuned to the (,,, ) sets.
Abstract: QFT is an engineering design theory devoted to the practical design of feedback control systems. The foundation of QFT is that feedback is needed in control only when plant (P), parameter and/or disturbance (D) uncertainties (sets ={P}, ={D}) exceed the acceptable (A) system performance uncertainty (set ={A}). The principal properties of QFT are as follows. (1) The amount of feedback needed is tuned to the (, , ) sets. If ‘exceeds’ (, ), feedback is not needed at all. (2) The simplest modelling is used: (a) command, disturbance and sensor noise inputs, and (b) the available sensing points and the defined outputs. No special controllability test is needed in either linear or non-linear plants. It is inherent in the design procedure. There is no observability problem because uncertainty is included. The number of independent sensors determines the number of independent loop transmissions (Li), the functions which provide the benefits of feedback. (3) The simplest mathematical tools have been found most use ful—primarily frequency response. The uncertainties are expressed as sets in the complex plane. The need for the larger , sets to be squeezed into the smaller set results in bounds on the Li(jω) in the complex plane. In the more complex systems a key problem is the division of the ‘feedback burden’ among the available Li(jω). Point-by-point frequency synthesis tremendously simplifies this problem. This is also true for highly uncertain non-linear and time-varying plants which are converted into rigorously equivalent linear time invariant plant sets and/or disturbance sets with respect to the acceptable output set . Fixed point theory justifies the equivalence. (4) Design trade-offs are highly transparent in the frequency domain: between design complexity and cost of feedback (primarily bandwidth), sensor noise levels, plant saturation levels, number of sensors needed, relative sizes of , and cost of feedback. The designer sees the trade-offs between these factors as he proceeds and can decide according to their relative importance in his particular situation. QFT design techniques with these properties have been developed step by step for: (i) highly uncertain linear time invariant (LTI) SISO single- and multiple-loop systems, MIMO single-loop matrix and multiple-loop matrix systems; and (ii) non-linear and time-varying SISO and MIMO plants, and to a more limited extent for plants with distributed control inputs and sensors. QFT has also been developed for single- and multiple-loop dithered non-linear (adaptive) systems with LTI plants, and for a special class (FORE) of non-linear compensation. New techniques have been found for handling non-minimum-phase (NMP) MIMO plants, plants with both zeros and poles in the right half-plane and LTI plants with incidental hard non-linearities such as saturation.

290 citations

Journal ArticleDOI
TL;DR: Lyapunov based results for verifying L"2 and exponential stability of reset systems are presented and can be easily modified to cover L"p stability for arbitrary [email protected]?[1,~].

265 citations


Cites background or methods from "Non-linear design for cost of feedb..."

  • ...Several examples illustrate that introducing resets in a linear system may reduce the L2 gain if the reset controller parameters are carefully tuned. c© 2008 Elsevier Ltd....

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  • ...First systematic procedures for controller design exploiting the Clegg integrator were proposed in Horowitz and Rosenbaum (1975) and Krishnan and Horowitz (1974)....

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Journal ArticleDOI
TL;DR: In this article, the authors present a QFT-based design of feedback control systems, where the amount of feedback needed is tuned to the (P,D,A); sets.
Abstract: QFT is an engineering design theory devoted to the practical design of feedback control systems. The foundation of QFT is that feedback is needed in control only when plant (P), parameter and/or disturbance (D) uncertainties (sets P; = {P}, D = {D}) exceed the acceptable (A) system performance uncertainty (set A ={A}). The principal properties of QFT are as follows. (1) The amount of feedback needed is tuned to the (P,D,A); sets. If A/ 'exceeds’ (P,D)feedback is not needed at all. (2) The simplest modelling is used: (a) command, disturbance and sensor noise inputs, and (b) the available sensing points and the defined outputs. No special controllability test is needed in either linear or non-linear plants. It is inherent in the design procedure. There is no observability problem because uncertainty is included. The number of independent sensors determines the number of independent loop transmissions (Li,,), the functions which provide the benefits of feedback. (3) The simplest mathematical tools h...

234 citations

References
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Book
01 Jan 1968
TL;DR: The theory of automatic control has been advanced in important ways during recent years, particularly with respect to stability and optimal control, but these theories do not, however, lay to rest all questions of importance to the control engineer.
Abstract: ABRAMSON Information theory and coding BATTIN Astronautical guidance BLACHMAN Noise and its effect on communication BREMER Superconductive devices BROXMEYER Inertial navigation systems GELB AND VANDER VELDE Multiple-input describing functions and nonlinear system design GILL Introduction to the theory of finite-state machines HANCOCK AND WINTZ Signal detection theory HUELSMAN Circuits, matrices, and linear vector spaces KELSO Radio ray propagation in the ionosphere MERRIAM Optimization theory and the design of feedback control systems MUUM Biological control systems analysis NEWCOMB Linear multiport synthesis PAPOULIS The fourier integral and its applications R. N. BRACEWELL) STEINBERG AND LEQUEUX (TRANSLATOR Radio astronomy WEEKS Antenna engineering PREFACE The theory of automatic control has been advanced in important ways during recent years, particularly with respect to stability and optimal control. These are significant contributions which appeal to many workers, including the writers, because they answer important questions and are both theoretically elegant and practically useful. These theories do not, however, lay to rest all questions of importance to the control engineer. The designer of the attitude control system for a space vehicle booster which, for simplicity, utilizes a rate-switched engine gimbal drive, must know the characteristics of the limit cycle oscillation that the system will sustain and must have some idea of how the system will respond to attitude commands while continuing to limit-cycle. The designer of a chemical process control system must be able to predict the transient oscillations the process may experience during start-up due to the limited magnitudes of important variables in the system. The designer of a radar antenna pointing system with limited torque capability must be able to predict the rms pointing error due to random wind disturbances on the antenna, and must understand how these random disturbances will influence the behavior of the system in its response to command inputs. But more important than just being able to evaluate how a given system will behave in a postulated situation is the fact that these control engineers must design their systems to meet specifications on important characteristics. Thus a complicated exact analytical tool, if one existed, would be of less value to the designer than an approximate tool which is simple enough in application to give insight into the trends in system behavior as a function of system parameter values or possible compensations, hence providing the basis for system design. As an analytical tool to answer questions such as these in a way …

1,244 citations

Book
01 Jan 1963
TL;DR: Synthesis of feedback systems, Synthesis of Feedback Systems, this article, synthesis of feedback system, feedback system synthesis, feedback synthesis, synthesizing feedback systems, مرکز فناوری اطلاعات و اسلاز رسانی
Abstract: Synthesis of feedback systems , Synthesis of feedback systems , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

1,036 citations

Journal ArticleDOI
TL;DR: The design procedure is quite transparent, providing the designer with the insight to make necessary tradeoffs, at every step in the design process, based on frequency response concepts.
Abstract: There is given a minimum-phase plant transfer function, with prescribed bounds on its parameter values The plant is imbedded in a two-degree-of freedom feedback system, which is to be designed such that the system time response to a deterministic input lies within specified boundaries Subject to the above, the design should be such as to minimize the effect of sensor noise at the input to the plant This report presents a design procedure for this purpose, based on frequency response concepts The time-domain tolerances are translated into equivalent frequency response tolerances The latter lead to bounds on the loop transmission function in the form of continuous curves on the Nichols chart The properties of the loop transmission function which satisfy these bounds with minimum effect of sensor noise, are derived

457 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the use of the nonlinear device known as the Clegg integrator in the design of a nonlinear feedback system, which minimizes the effect of white sensor noise on the input to the plant.
Abstract: The problem considered is the design of a feedback system containing a linear, time invariant, minimum phase plant, whose parameters are known only within given bounds, such that the time response of the system remains within specified limits. A quasi-optimal design, for given design constraints, is one which minimizes the effect of white sensor noise on the input to the plant. An investigation was conducted on the use of the non linear device known as the Clegg integrator in the design of such a system. The describing function of the Clegg integrator has the same magnitude characteristic, apart from a scale factor, as the linear integrator, but has 52 deg less phase-lag, at all frequencies, than the linear integrator; thus, when used in a feedback system, it provides a larger stability margin than the linear integrator. This property allows the nonlinear feedback system to be designed so that the sensor noise is attenuated more than in the linear design.

182 citations