使用有限區間二次倒回最佳化控制

Abstract

本論文以Finite Receding Horizon Quadratic Optimal Control為基礎設計D類音頻放大器。D類音頻放大器，相對於A類或AB類放大器，有效率高、功率級設計較易的優勢。在數位訊號處理上有一個重要的量化誤差問題，所以在本論文中以量化誤差為目標，訂定出其成本函數，然後使用有限區間二次倒回最佳化控制的方法去最小化量化失真。以回授迴圈的方式實現一個Multi-Step Optimal Converter，它以更一般的方法來嵌入Sigma-Delta Modulation並且提供更好的效能。D類放大器常以Pulse-Width Modulator產生切換式控制訊號，但產生的諧波問題較為嚴重。相對的，Multi-Step Optimal Converter回授量化誤差，經過迴圈轉移函數，改變量化誤差能量分佈，得到更高的訊號雜訊比。本論文將設計與實現穩定數位的Multi-Step Optimal Converter、USB介面與切換式功率放大器，完成一全數位式音頻放大器。

The objective of this thesis is to design a Class D audio amplifier based on Finite Receding Horizon Quadratic Optimal Control. Comparing to the traditional Class A or Class AB amplifiers, audio amplifiers based on Class D topology are more efficient in terms of energy conversion and have low cost. An important aspect of digital signal processing is the impact of quantization errors. In this thesis, we focus on the topic about quantization errors and define a cost function, which is utilized to minimize a measure of the quantization distortion by using finite receding horizon quadratic optimal control. We propose a Multi-Step Optimal Converter, which can be implemented as a feedback loop. It embeds Sigma-Delta Modulation in a more general setting and typically provides better performance. Class D amplifiers commonly rely on Pulse-Width Modulation to generate the output switching waveforms which gives rise to more serious problems in unwanted harmonics . On the other hand, using Multi-Step Optimal Converter, it is possible to design the loop filter so that the harmonic distortion is reduced. This thesis will analyze and implement a stable digital Multi-Step Optimal Converter, USB interfaces, and a switching power stage to complete a full digital audio amplifier.