上海交通大学：《系统模型、分析与控制 Modeling、Analysis and Control》课程教学资源[07]Lecture51-electrical system 电气系统建模

ME369-系统模型、分析与控制 5.1电气系统建模 School of Mechanical Engineering ME369-lecture 5.1 Shanghai Jiao Tong University Fall 2015 变量 q:电荷 [C,Coulomb] i:电流 [A] 9=i e:电压[V] p:功率[] 96)=g,)+d w:功[J] p=ei w()=w)+pdi=w)+(e.)di School of Mechanical Engineering ME369-lecture 5.1 Shanghai Jiao Tong University Fall 2015 1

1 ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 5.1 电气系统建模 ME369-系统模型、分析 与控制 ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 变量 q i  1 0 1 0 ( ) ( )    t t q t q t idt 1 1 0 0 1 0 0 ( ) ( ) ( ) ( )        t t t t w t w t pdt w t e i dt q: 电荷 [C，Coulomb] i: 电流 [A] e: 电压 [V] p: 功率[W] w: 功 [J] p ei 

理想元件 电阻(Resistor)R eg=Ri R “发热耗能” q=Ce。 电容(Capacitor)C i=C dec dt "e-clue “电场蓄能” School of Mechanical Engineering ME369-lecture 5.1 Shanghai Jiao Tong University Fall 2015 理想元件 电感 (Inductor)L di e -000- e.=L dt “磁场蓄能” 理想电压源 (Ideal Voltage source 理想电流源 (Ideal Current source) -e(0+ O一 0 School of Mechanical Engineering ME369-lecture 5.1 Shanghal Jiao Tong University Fall 2015 2

2 ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 理想元件 电阻（Resistor） R 电容（Capacitor） C R e Ri  c q Ce  1 R i e R  “发热耗能” 2 2 1 p Ri e R   C de i C dt        “电场蓄能” 1 2 2 w Cq  1 C e idt C   ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 理想元件 电感（Inductor） L 理想电压源 (Ideal Voltage source ) L di e L dt        1 2 2 w Li  理想电流源 (Ideal Current source) “磁场蓄能

相关定律 基尔霍夫电压定律 (Kirchhoff's Voltage Law) 基尔霍夫电流定律 (Kirchhoff's Current Law) 回路压降为零 节点电流和为零 ∑4=0 i=LOO 4，=0 i-NET School of Mechanical Engineering ME369-lecture 5.1 Shanghal Jiao Tong University Fal12015 建模步骤 [1]理解功能，分析系统，确定输入、输入变量 [2]采用基本元件画出简化图 [3]推导数字模型，如微分方程(dif.Eq.) 一标记元件及对应压降 标记节点及对应电流 一应用相关定律 一-检查未知变量及方程的个数 [4]取消中间变量，化简方程形式 [5]化成标准形式，得到运动方程(Equation of Motion,EOM) School of Mechanical Engineering ME369-lecture 5.1 Shanghai Jiao Tong University Fall 2015 3

3 ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 相关定律 基尔霍夫电压定律 （Kirchhoff’s Voltage Law） 回路压降为零 基尔霍夫电流定律 （Kirchhoff’s Current Law） 节点电流和为零 1 u 2 u 3 u 4 u        i=LOOP 0 i  u  j=NET 0 j  i  ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University Modeling Steps 建模步骤 [1]理解功能，分析系统，确定输入、输入变量 [2] 采用基本元件画出简化图 [3]推导数字模型，如微分方程（diff. Eq.） --标记元件及对应压降 --标记节点及对应电流 --应用相关定律 --检查未知变量及方程的个数 [4]取消中间变量， 化简方程形式 [5] 化成标准形式， 得到 运动方程（Equation of Motion, EOM)

例1-1-回路法 输入e(),输出i(t) et) School of Mechanical Engineering ME369-lecture 5.1 Shanghal Jiao Tong University Fall 2015 例1-2]-节点法 输入e(),输出i(①) 000 R R School of Mechanical Engineering ME369-lecture 5.1 Shanghal Jiao Tong University Fall 2015 4

4 ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例1-1]- 回路法 输入ei (t) ，输出i(t) ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例1-2]- 节点法 输入ei (t) ，输出i(t)

阻抗(Complex Impedance) 电阻(Resistor) W eg=Ri Z= R(s)=R R I(s) 电容(Capacitor) e-efud Zc= Ee(s）_1 I(s)Cs 电感(Inductor) di -0 e.=L Z, E,(s) =Ls I(s) School of Mechanical Engineering ME369-lecture 5.1 Shanghai Jiao Tong University Fal12015 例1-3]-阻抗法 输入e(),输出i(①) School of Mechanical Engineering ME369-lecture 5.1 Shanghal Jiao Tong University Fall 2015 5

5 ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 阻抗（Complex Impedance） 电感（Inductor） 电阻（Resistor） 电容（Capacitor） L di e L dt        1 C e idt C   R e Ri  ( ) ( ) R R E s Z R I s   ( ) 1 ( ) C C E s Z I s Cs   ( ) ( ) L L E s Z Ls I s   ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例1-3]- 阻抗法 输入ei (t) ，输出i(t)

阻抗(Complex Impedance) 并联 1 1 1 Z(s)Z(s)Z(s) Zy(s) I(s) Is) I(s)=I,(s)+I(s)+…+Iv(s) Vs+++ V(s) Z(s)Z(s) Zy(s) 串联 Z(s)=Z(s)+Z2(s)+...+Zx(s) V(s)=(s)+V(s)+.+Vx(s） =Z(s)I(s)+Z(s)I(s)+...+Zy(s)I(s) V:(s) V: VN(s) V(s) School of Mechanical Engineering ME369-lecture 5.1 Shanghai Jiao Tong University Fal12015 运放建模 (OP-amps) e=K(e2-e)=-K(e-e2) 差动放大器 School of Mechanical Engineering ME369-lecture 5.1 Shanghal Jiao Tong University Fall 2015 6

6 ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 2 1 2 ( ) ( ) ( ) ... ( ) ( ) ( ) ( ) ( ) ... ( ) ( ) N N V s V s V s V s Z s I s Z s I s Z s I s         1 2 ( ) ( ) ( ) ... ( ) Z s Z s Z s Z s p N     1 2 1 2 ( ) ( ) ( ) ... ( ) ( ) ( ) ( ) ... ( ) ( ) ( )         N N I s I s I s I s V s V s V s Z s Z s Z s 1 2 1 1 1 1 ... ( ) ( ) ( ) ( ) Z s Z s Z s Z s p N 并联     串联 阻抗（Complex Impedance） ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 0 2 1 1 2 e K e e K e e      ( ) ( ) 运放建模 (OP-amps) 差动放大器

反相运放电路 School of Mechanical Engineering ME369-lecture 5.1 Shanghal Jiao Tong University Fall 2015 同相运放电路 R2 w R M 0 0 等效电路 School of Mechanical Engineering ME369-lecture 5.1 Shanghal Jiao Tong University Fall 2015 7

7 ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 反相运放电路 ME369-lecture 5.1 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 等效电路 i e  同相运放电路