【正文】 Chapter 3 System Identification and Parameter Estimation 第三章 系統(tǒng)辨識與參數(shù)估計 Introduction 概述 What is the Model of Dynamic System? 什么是模型？ ? Theory model and experiment model 理論模型與實驗模型 ? Modeling from Theory and Analysis: educe system model according to physical, chemical or other natural rules. 理論（分析）建模：根據(jù)已知的物理、化學規(guī)律推導 ? In practice, Theory Modeling is not easy. 現(xiàn)實中理論建模存在困難 ? Experiment Modeling: Fit the model to experimental data according to an optimized criterion. 實驗建模：按一定準則的數(shù)據(jù)擬和 ? Experiment model: holistic approach, plemented by theory model 實驗建模的特點：整體性、可用機理模型彌補（互補） Chapter 3 System Identification and Parameter Estimation 第三章 系統(tǒng)辨識與參數(shù)估計 2 System Identification and Parameter Estimation 系統(tǒng)辨識與參數(shù)估計 ? System Identification: is the experimental approach to process modeling, and the modeling method for identification of dynamical systems from input/output data, which confirm a model in a set of models that presents the dynamic characteristics of the system under an optimized criterion. 系統(tǒng)辨識 ：根據(jù)系統(tǒng)的輸入、輸出數(shù)據(jù)，從一類模型中確定出一個在某中意義下最能代表該系統(tǒng)的數(shù)學模型。 ? Three essentials: an input/output dada, a set of models, and an optimized criterion 三個要素 ：輸入 /輸出數(shù)據(jù)、模型集、最優(yōu)準則 ? Parameter Estimation: a simplified system identification problem when the model structure is known, only its parameters is unknown. 參數(shù)估計 ：結(jié)構(gòu)已知。參數(shù)未知時，系統(tǒng)辨識問題的簡化 Chapter 3 System Identification and Parameter Estimation 第三章 系統(tǒng)辨識與參數(shù)估計 3 Development of System Identification 系統(tǒng)辨識 的發(fā)展 ? Modern Control Theory is based on known a mathematic model of dynamic process. 現(xiàn)代控制理論建立在數(shù)學模型已知的前提下 ? The obstacle using Modern Control Theory in practice : It is not easy to obtain a mathematic model of dynamic process, thus the theory deviates from the practice. 實際應用中的障礙：數(shù)學模型并不容易獲得，造成理論與實際脫節(jié) ? System Identification and Parameter Estimation just fill up this gap between the theory and the practice. 系統(tǒng)辨識 /參數(shù)估計正是為了彌合這一差距 Chapter 3 System Identification and Parameter Estimation 第三章 系統(tǒng)辨識與參數(shù)估計 4 System identification includes the following steps 系統(tǒng)辨識 的步驟 ? Experiment design: Its purpose is to obtain good experimental data, it includes the choice of the measured variables and of the character of the input signals. 實驗設計 ：如何獲取盡可能多的信息，包括檢測信號和輸入信號的選取。 ? Selection of model structure: A suitable model structure is chosen using prior knowledge and trial and error. 模型結(jié)構(gòu) ：根據(jù)先驗知識和試湊確定模型的結(jié)構(gòu)。 ? Choice of the criterion to fit: A suitable cost function is chosen, which reflects how well the model fits the experimental data. 最優(yōu)準則 ：選擇能反應模型對實驗數(shù)據(jù)擬合程度的目標函數(shù)。 ? Parameter estimation: An optimization problem is solved to obtain the numerical values of the model parameters. 參數(shù)估計 ：得到模型參數(shù)數(shù)值解的優(yōu)化問題。 ? Model validation: The model is tested in order to reveal any inadequacies. 校驗與確認 ：測試模型以發(fā)現(xiàn)存在的問題。 Chapter 3 System Identification and Parameter Estimation 第三章 系統(tǒng)辨識與參數(shù)估計 5 System identification methods 系統(tǒng)辨識 的方法 ? Method: There are many system identification methods, but the least squares estimation is used most frequently. 方法 ：有多種方法，其中最小二乘法最常用。 ? Offline identification: plete estimation one time based on the data set in a long period. 離線辨識 ：將一定時間內(nèi)積累的采樣數(shù)據(jù)集中進行一次辨識計算 . ? Online identification : plete recursive estimation one time based on new data in every sampling interval. It is able to decrease calculating time spending and memory occupancy, and easy to find out system actuality. 在線辨識 ：每個采樣周期都根據(jù)新的采樣數(shù)據(jù)進行一次遞推辨識計算，節(jié)省計算時間和內(nèi)存空間，便于及時掌握系統(tǒng)現(xiàn)狀。 Chapter 3 System Identification and Parameter Estimation 第三章 系統(tǒng)辨識與參數(shù)估計 6 Linear Difference Equation Model 線性差分方程模型 Difference equation model of linear constant SISO system 線性定常單輸入單輸出系統(tǒng)的差分方程模型 () Here 其中 () () The model of noise 噪聲模型 (1) Random variable 隨機變量 x Mathematic description: probability density function 數(shù)學描述 ：概率密度函數(shù) )()()()( 11 kuqBkyqA ?? ?aa nn qaqaA ?? ???? ?111bb nn qbqbbB ?? ???? ?110Chapter 3 System Identification and Parameter Estimation 第三章 系統(tǒng)辨識與參數(shù)估計 7 ? Mathematical expectation of random variable 數(shù)學期望（均值） E(x) ? Variance of random variable 方差（二階中心距） D(x) () （ 2） Steady random sequence: Statistical character is independent of time 平穩(wěn)隨機序列 ：各個時刻隨