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Feedback Theory (feedback + theory)
Selected AbstractsPointing control design for a high precision flight telescope using quantitative feedback theoryINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2001Anthony E. Bentley Abstract A pointing control system is developed and tested for a flying gimbaled telescope. The two-axis pointing system is capable of sub-microradian pointing stability and high accuracy in the presence of large host vehicle jitter. The telescope also has high agility , it is capable of a 50° retarget (in both axes simultaneously) in less than 2 s. To achieve the design specifications, high-accuracy, high-resolution, two-speed resolvers were used, resulting in gimbal-angle measurements stable to 1.5 µrad. In addition, on-axis inertial angle displacement sensors were mounted on the telescope to provide host-vehicle jitter cancellation. The inertial angle sensors are accurate to about 100 nrad, but do not measure low-frequency displacements below 2 Hz. The gimbal command signal includes host-vehicle attitude information, which is band-limited. This provides jitter data below 20 Hz, but includes a variable latency between 15 and 25 ms. One of the most challenging aspects of this design was to combine the inertial-angle-sensor data with the less perfect information in the command signal to achieve maximum jitter reduction. The optimum blending of these two signals, along with the feedback compensation were designed using Quantitative Feedback Theory. Copyright © 2001 John Wiley & Sons, Ltd. [source] Some ideas for QFT researchINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2003Isaac Horowitz Feedback theory is much less popular now than 5 years ago. However, there is little question that the problem of achieving desired system tolerances from uncertain plants, at minimum cost of feedback, will remain an important, enduring one for many future generations. Although much progress has been made, it is minuscule in comparison with the extent of the problem. The purpose here is to suggest some significant QFT research problems, some tantalizingly on the boundary of the unknown. There have been in the past many suggestions for improvements in feedback synthesis. Most e.g. the Smith Regulator (Int. J. Control 1983;38:977) have been illusory, because they were formulated in a qualitative context, without the disciplines of quantitative uncertainty and performance specifications, degrees of freedom, sensor noise, plant modification, etc. Without such disciplines, it is impossible to properly evaluate competing techniques. The reader is referred to the 1991 Survey paper for some background, Horowitz (Int. J. Control 1991;53(2):255). Copyright © 2003 John Wiley & Sons, Ltd. [source] Non-diagonal MIMO QFT controller design reformulationINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2009Mario Garcia-Sanz Abstract This paper presents a reformulation of the full-matrix quantitative feedback theory (QFT) robust control methodology for multiple-input,multiple-output (MIMO) plants with uncertainty. The new methodology includes a generalization of previous non-diagonal MIMO QFT techniques; avoiding former hypotheses of diagonal dominance; simplifying the calculations for the off-diagonal elements, and then the method itself; reformulating the classical matrix definition of MIMO specifications by designing a new set of loop-by-loop QFT bounds on the Nichols Chart, which establish necessary and sufficient conditions; giving explicit expressions to share the load among the loops of the MIMO system to achieve the matrix specifications; and all for stability, reference tracking, disturbance rejection at plant input and output, and noise attenuation problems. The new methodology is applied to the design of a MIMO controller for a spacecraft flying in formation in a low Earth orbit. Copyright © 2008 John Wiley & Sons, Ltd. [source] Improvements on the computation of boundaries in QFTINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2006José Carlos Moreno Abstract Quantitative feedback theory (QFT) is an engineering design technique of uncertain feedback systems that uses frequency domain specifications. A key step in QFT is the mapping of these specifications into regions of the Nichols plane, whose borders are usually referred to as boundaries. Boundaries computation is a key design step, thus a precise and efficient computation is critical for both obtaining low bandwidth feedback compensators and simplification of the design process. In this work, the problem of boundaries computation is analysed, introducing a new algorithm based on the computation of level curves of a three-dimensional surface. Besides magnitude boundaries, associated with some specification over the magnitude of a closed-loop transfer function, phase boundaries are also considered. In addition, comparison with previous published algorithms is done in terms of precision and computational efficiency. Copyright © 2006 John Wiley & Sons, Ltd. [source] The Liapunov's second method for continuous time difference equationsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2003P. PepeArticle first published online: 10 OCT 200 Abstract Among many other cases such as economic and lossless propagation models, continuous time difference equations are encountered as the internal dynamics in a class of non-linear time delay systems, when controlled by a suitable state feedback which drives the output exponentially to zero. The Liapunov's second method for these infinite dimensional systems has not been extensively investigated in the literature. This paper has the aim of filling this gap. Liapunov's second method theorems for checking the stability and the asymptotic stability of this class of infinite dimensional systems are built up, in both a finite and an infinite dimensional setting. In the finite dimensional setting, the Liapunov function is defined on finite dimensional sets. The conditions for stability are given as inequalities on continuous time. No derivatives are involved, as in the dynamics of the studied systems. In the infinite dimensional setting, the continuous time difference equation is transformed into a discrete time system evolving on an infinite dimensional space, and then the classical Liapunov theorem for the system in the new form is written. In this paper the very general case is considered, that is non-linear continuous time difference equations with multiple non commensurate delays are considered, and moreover the functions involved in the dynamics are allowed to be discontinuous, as well as the initial state. In order to study the stability of the internal dynamics in non-linear time delay feedback systems, an exogenous disturbance is added, which goes to zero exponentially as the time goes to infinity. An example is considered, from non-linear time delay feedback theory. While the results available in the literature are inconclusive as far as the stability of that example is concerned, such stability is proved to hold by the theorems developed in this paper, and is validated by simulation results. Copyright © 2003 John Wiley & Sons, Ltd. [source] Survey of quantitative feedback theory (QFT),INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2001Isaac Horowitz 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(j,) in the complex plane. In the more complex systems a key problem is the division of the ,feedback burden' among the available Li(j,). 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. [source] Pointing control design for a high precision flight telescope using quantitative feedback theoryINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2001Anthony E. Bentley Abstract A pointing control system is developed and tested for a flying gimbaled telescope. The two-axis pointing system is capable of sub-microradian pointing stability and high accuracy in the presence of large host vehicle jitter. The telescope also has high agility , it is capable of a 50° retarget (in both axes simultaneously) in less than 2 s. To achieve the design specifications, high-accuracy, high-resolution, two-speed resolvers were used, resulting in gimbal-angle measurements stable to 1.5 µrad. In addition, on-axis inertial angle displacement sensors were mounted on the telescope to provide host-vehicle jitter cancellation. The inertial angle sensors are accurate to about 100 nrad, but do not measure low-frequency displacements below 2 Hz. The gimbal command signal includes host-vehicle attitude information, which is band-limited. This provides jitter data below 20 Hz, but includes a variable latency between 15 and 25 ms. One of the most challenging aspects of this design was to combine the inertial-angle-sensor data with the less perfect information in the command signal to achieve maximum jitter reduction. The optimum blending of these two signals, along with the feedback compensation were designed using Quantitative Feedback Theory. Copyright © 2001 John Wiley & Sons, Ltd. [source] Linear time computation of feasible regions for robust compensatorsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2001M. Sami Fadali Abstract We introduce an application of computational geometry, including figures of merit standard in the analysis of algorithms, to the design of robust control systems. With respect to system transfer function magnitude, we show how to compute feasible regions for compensators whose plant transfer function is the ratio of uncertain interval polynomials. Our solution sweeps the Minkowski quotient set of the corresponding Kharitonov rectangles. Enumerating the winding numbers of Minkowski sum convolution curves, we obtain optimal, linear time algorithms that eliminate three factors from the execution inefficiency of traditional gridding approaches. We illustrate with examples pertinent to quantitative feedback theory (QFT). Copyright © 2001 John Wiley & Sons, Ltd. [source] Some results in nonlinear QFTINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 2 2001A. Bańos Abstract Nonlinear QFT (quantitative feedback theory) is a technique for solving the problem of robust control of an uncertain nonlinear plant by replacing the uncertain nonlinear plant with an ,equivalent' family of linear plants. The problem is then finding a linear QFT controller for this family of linear plants. While this approach is clearly limited, it follows in a long tradition of linearization approaches to nonlinear control (describing functions, extended linearization, etc.) which have been found to be quite effective in a wide range of applications. In recent work, the authors have developed an alternative function space method for the derivation and validation of nonlinear QFT that has clarified and simplified several important features of this approach. In particular, single validation conditions are identified for evaluating the linear equivalent family, and as a result, the nonlinear QFT problem is reduced to a linear equivalent problem decoupled from the linear QFT formalism. In this paper, we review this earlier work and use it in the development of (1) new results on the existence of nonlinear QFT solutions to robust control problems, and (2) new techniques for the circumvention of problems encountered in the application of this approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] Analysis of optical and terahertz multilayer systems using microwave and feedback thoeryMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 5 2009Dong-Joon Lee Abstract The principles of microwave and feedback theory are independently applied to the analysis of both optical and terahertz-regime multilayer systems. An analogy between the two approaches is drawn, and useful recursion relations, along with a signal-flow approach, are presented for both reflection and transmission cases. These relations, in terms of S-parameters, allow an exact analytical solution for even arbitrary, active, stratified structures, not only for any wavelength in the radio-frequency spectrum, but also for optical wavelengths. This approach also provides a bridge between the microwave and optical bands and leads to beneficial design solutions for intermediate bands such as the THz regime. Comparisons with conventional methodologies are provided using practical multilayer simulations. In addition, graphical design techniques from microwave theory are used along with examples for efficient design and understanding. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1308,1312, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24301 [source] Direction-of-change forecasting using a volatility-based recurrent neural networkJOURNAL OF FORECASTING, Issue 5 2008S. D. Bekiros Abstract This paper investigates the profitability of a trading strategy, based on recurrent neural networks, that attempts to predict the direction-of-change of the market in the case of the NASDAQ composite index. The sample extends over the period 8 February 1971 to 7 April 1998, while the sub-period 8 April 1998 to 5 February 2002 has been reserved for out-of-sample testing purposes. We demonstrate that the incorporation in the trading rule of estimates of the conditional volatility changes strongly enhances its profitability, after the inclusion of transaction costs, during bear market periods. This improvement is being measured with respect to a nested model that does not include the volatility variable as well as to a buy-and-hold strategy. We suggest that our findings can be justified by invoking either the ,volatility feedback' theory or the existence of portfolio insurance schemes in the equity markets. Our results are also consistent with the view that volatility dependence produces sign dependence. Copyright © 2008 John Wiley & Sons, Ltd. [source] | ||||||||||