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Dr. CAN学习笔记-动态系统建模与分析 Ch02-4 拉普拉斯变换（Laplace）传递函数、微分方程
1. Laplace Transform 拉式变换
f ( t ) → F ( s ) f\left( t \right) \rightarrow F\left( s \right) f(t)→F(s) ： 时域 - 频域 s = σ + j w s=\sigma +jw s=σ+jw
2. 收敛域（ROC）与逆变换（ILT）
微分方程——描述动态世界
状态变量 ： d x ⃗ d t \frac{\mathrm{d}\vec{x}}{\mathrm{d}t} dtdx-时间
位移： s s s , 速度： d x d t \frac{\mathrm{d}x}{\mathrm{d}t} dtdx ，加速度： d 2 x d t 2 \frac{\mathrm{d}^2x}{\mathrm{d}t^2} dt2d2x
- F = m d 2 x d t 2 F=m\frac{\mathrm{d}^2x}{\mathrm{d}t^2} F=mdt2d2x
- d T d t = − k ( T − C ) \frac{\mathrm{d}T}{\mathrm{d}t}=-k\left( T-C \right) dtdT=−k(T−C)
- d P d t = − r p ( 1 − p k ) \frac{\mathrm{d}P}{\mathrm{d}t}=-rp\left( 1-\frac{p}{k} \right) dtdP=−rp(1−kp) 人口增长
常系数线性 —— 线性时不变系统
- 求解 3Step
从 t t t— s s s L [ f ( t ) ] \mathcal{L} \left[ f\left( t \right) \right] L[f(t)]
运算求解
从 s s s— t t t L − 1 [ F ( s ) ] \mathcal{L} ^{-1}\left[ F\left( s \right) \right] L−1[F(s)]
非线性
- 线性化
- 非线性分析控制
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