Topic
Describing function
About: Describing function is a research topic. Over the lifetime, 1742 publications have been published within this topic receiving 26702 citations.
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TL;DR: Two practical methods are presented for predicting the existence and the location of chaotic motions as a function of the system parameters, when the system structure is fixed by rather general input-output or state equation models.
411 citations
TL;DR: In this paper, the authors derived both static and dynamic models that include quantization effects and used them to explain the origins of limit-cycle oscillations in dc-dc converters with a single voltage feedback loop.
Abstract: In digitally controlled dc-dc converters with a single voltage feedback loop, the two quantizers, namely the analog-to-digital (A/D) converter and the digital pulse-width modulator (DPWM), can cause undesirable limit-cycle oscillations. In this paper, static and dynamic models that include the quantization effects are derived and used to explain the origins of limit-cycle oscillations. In the static model, existence of dc solution, which is a necessary no-limit-cycle condition, is examined using a graphical method. Based on the generalized describing function method, the amplitude and offset-dependent gain model of a quantizer is applied to derive the dynamic system model. From the static and dynamic models, no-limit-cycle conditions associated with A/D, DPWM and compensator design criteria are derived. The conclusions are illustrated by simulation and experimental examples
367 citations
TL;DR: A systematic approach to the chattering analysis in systems with second-order sliding modes is developed, finding sufficient conditions for the existence of orbitally stable periodic motions in terms of the properties of corresponding Poincare maps.
Abstract: A systematic approach to the chattering analysis in systems with second-order sliding modes is developed. The neglected actuator dynamics is considered to be the main cause of chattering in real systems. The magnitude of oscillations in nonlinear systems with unmodeled fast nonlinear actuators driven by second-order sliding-mode control generalized suboptimal (2-SMC G-SO) algorithms is evaluated. Sufficient conditions for the existence of orbitally stable periodic motions are found in terms of the properties of corresponding Poincare maps. For linear systems driven by 2-SMC G-SO algorithms, analysis tools based on the frequency-domain methods are developed. The first of these techniques is based on the describing function method and provides for a simple approximate approach to evaluate the frequency and the amplitude of possible periodic motions. The second technique represents a modified Tsypkin's method and provides for a relatively simple, theoretically exact, approach to evaluate the periodic motion parameters. Examples of analysis and simulation results are given throughout this paper.
363 citations
Book•
01 Jan 2000
TL;DR: In this paper, the authors present a model predictive control approach for nonlinear systems, based on MPC, GPC, and DMM, which is based on the phase plane phase plane.
Abstract: Preface. Introduction. 1. Representation of linear systems 2. Properties of linear systems 3. Sampled data systems 4. Disturbance models 5. The closed loop system 6. Limitations and conflicts 7. Controller structures and design 8. Minimization of quadratic criteria 9. Shaping the loop again 10. Descriptions of nonlinear systems 11. Stability of nonlinear systems 12. Qualitative beviour. Phase Plane 13. Oscillations and describing functions 14. Controller synthesis for nonlinear systems 15. Model predictive control : MPC, GPC, and DMM 16. To compensate exactly for nonlinearities 17. Optimal control 18. Conclusion. Literature. Index. Index of examples.
361 citations
TL;DR: In this paper, a nonlinear parametric model of a torque-controlled thruster is developed and experimentally confirmed, and three forms of compensation are tested, utilizing a hybrid simulation combining an instrumented thruster with a real-time mathematical vehicle model.
Abstract: A nonlinear parametric model of a torque-controlled thruster is developed and experimentally confirmed. The model shows that the thruster behaves like a sluggish nonlinear filter, where the speed of response depends on the commanded thrust level. A quasi-linear analysis which utilizes describing functions shows that the dynamics of the thruster produce a strong bandwidth constraint and a limit cycle, which are both commonly seen in practice. Three forms of compensation are tested, utilizing a hybrid simulation combining an instrumented thruster with a real-time mathematical vehicle model. The first compensator, a linear lead network, is easy to implement and greatly improves performance over the uncompensated system, but does not perform uniformly over the entire operating range. The second compensator, which attempts to cancel the nonlinear effect of the thruster, is effective over the entire operating range but depends on an accurate thruster model. The final compensator, an adaptive sliding controller, is effective over the entire operating range and can compensate for uncertainties or the degradation of the thruster. >
349 citations