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Observation of chaotic behavior in automatic tuning loops for continuous-time filters

機(jī)譯：連續(xù)時(shí)間濾波器自動(dòng)調(diào)諧環(huán)中混沌行為的觀察

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摘要

he appropriate linear dynamic modeling of continuous-time filters (CTFs) with automatic tuning loops should be obtained to assure stability in case an improved design of the loop controllers is to be carried out. With this aim, starting from a general and systematic analysis in order to obtain an equivalent small-signal linearized incremental model, from which transfer functions between output variables and control voltages are derived, the subsequent design of compensated loops with enhanced stability and dynamic performance is required. This systematic procedure allows obtaining improved controllers for the two involved control loops. However, CTFs with automatic tuning loops are nonlinear feedback systems with potential instability. What is more, nonlinear phenomena, which cannot be predicted by a design-oriented small signal modeling approach, are observed in this kind of tuning systems. The purpose of this work is to highlight that when control parameters are varied, the system could present different kinds of dynamical nonlinear phenomena such as bifurcations and chaotic behavior, which cannot be predicted by the small signal design-oriented model.
機(jī)譯：如果要對(duì)回路控制器進(jìn)行改進(jìn)的設(shè)計(jì)，則應(yīng)獲得具有自動(dòng)調(diào)整回路的連續(xù)時(shí)間濾波器（CTF）的適當(dāng)線性動(dòng)態(tài)建模，以確保穩(wěn)定性。為此，從一般的系統(tǒng)分析開(kāi)始，以獲得等效的小信號(hào)線性化增量模型，從中導(dǎo)出輸出變量和控制電壓之間的傳遞函數(shù)，隨后設(shè)計(jì)了具有增強(qiáng)的穩(wěn)定性和動(dòng)態(tài)性能的補(bǔ)償回路。需要。這種系統(tǒng)的過(guò)程可以為兩個(gè)涉及的控制回路獲得改進(jìn)的控制器。但是，具有自動(dòng)調(diào)整環(huán)的CTF是具有潛在不穩(wěn)定性的非線性反饋系統(tǒng)。此外，在這種調(diào)諧系統(tǒng)中會(huì)觀察到非線性現(xiàn)象，而這種非線性現(xiàn)象是無(wú)法通過(guò)面向設(shè)計(jì)的小信號(hào)建模方法來(lái)預(yù)測(cè)的。這項(xiàng)工作的目的是要突出顯示，當(dāng)控制參數(shù)發(fā)生變化時(shí)，系統(tǒng)可能會(huì)呈現(xiàn)出不同的動(dòng)力學(xué)非線性現(xiàn)象，例如分叉和混沌行為，而這是面向小信號(hào)設(shè)計(jì)的模型無(wú)法預(yù)測(cè)的。

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