vault backup: 2025-06-27 16:08:57

书籍/力学书籍/BladedTheoryManual/Model Linearisation/auto/Model Linearisation.md

@@ -31,7 +31,7 @@ It is important to note that in order to enable proper linearised wind turbine d
 矩阵 $\mathbf{A}$、$\mathbf{B}$、$\mathbf{C}$ 和 $\mathbf{D}$ 代表这些向量之间的线性化关系。这代表对完整（Bladed）模型的一个简化，该模型使用一组完全非线性方程来计算状态导数和输出。
 
 $$
-\begin{array}{r}{\dot{\mathbf{x}}=f(t,\mathbf{x},\mathbf{u})}\\ {\mathbf{y}=h(t,\mathbf{x},\mathbf{u}).}\end{array}
+\begin{array}{r}{\dot{\mathbf{x}}=f(t,\mathbf{x},\mathbf{u})}\\ {\mathbf{y}=h(t,\mathbf{x},\mathbf{u})}\end{array}
 $$
 
 需要注意的是，为了能够建立适当的线性化风轮动力学系统，需要考虑以下模型准备原则：

工作OKRs/25.6-8 OKR.canvas

@@ -1,12 +1,12 @@
 {
 	"nodes":[
 		{"id":"8359617e1edc48ba","type":"text","text":"状态指标：\n推进OKR的时候也要关注这些事情，它们是完成OKR的保障。\n\n\n效率状态  green","x":-76,"y":-306,"width":456,"height":347},
-		{"id":"a4eaccbbfadaaf17","type":"text","text":"# 目标：多体动力学模块完善\n### 每周盘点一下它们\n\n\n关键结果：建模原理、建模方法掌握    （9/10）\n\n关键结果：风机多体动力学文献调研情况完成 （5.5/10）\n关键结果：风机模型线性化原理、方法掌握  （5.5/10）","x":-76,"y":-693,"width":456,"height":347},
+		{"id":"a4eaccbbfadaaf17","type":"text","text":"# 目标：多体动力学模块完善\n### 每周盘点一下它们\n\n\n关键结果：建模原理、建模方法掌握    （9.2/10）\n\n关键结果：风机多体动力学文献调研情况完成 （5.5/10）\n关键结果：风机模型线性化原理、方法掌握  （7/10）","x":-76,"y":-693,"width":456,"height":347},
 		{"id":"d2c5e076ba6cf7d7","type":"text","text":"# 推进计划\n未来四周计划推进的重要事情\n\n文献调研启动\n\n建模重新推导\n\n\n","x":-600,"y":-306,"width":456,"height":347},
 		{"id":"82708a439812fdc7","type":"text","text":"# 7月已完成\n\n","x":-220,"y":134,"width":440,"height":560},
-		{"id":"505acb3e6b119076","type":"text","text":"# 6月已完成\n\n\nP1 结果对比\n- Herowind 带3.5气动与fast3.5对比 相同\n- Herowind 带4.0气动与fast4.0对比 相同\n- Herowind 带hrl气动与fast对比 需气动支持15MW\n\nP1 Bladed交流问题汇总\n\nP1 模型线性化原理 done\n- Bladed 线性化理论手册 仔细阅读\n- multibody blade transform\n- fast线性化理论\n- 梳理Bladed线性化方法框架","x":-700,"y":134,"width":440,"height":560},
+		{"id":"505acb3e6b119076","type":"text","text":"# 6月已完成\n\n\nP1 结果对比\n- Herowind 带3.5气动与fast3.5对比 相同\n- Herowind 带4.0气动与fast4.0对比 相同\n- Herowind 带hrl气动与fast对比 需气动支持15MW\n- 叶根坐标系转换 \n\t- 叶尖变形量 - 变形向量 dot product 叶根坐标系方向\n\t- 叶片载荷输入量呢 载荷传递在blade mesh.force moment，mesh.orientation = coord_sys.n\n\nP1 Bladed交流问题汇总\n\nP1 模型线性化原理 done\n- Bladed 线性化理论手册 仔细阅读\n- multibody blade transform\n- fast线性化理论\n- 梳理Bladed线性化方法框架\n\n\nP1 编写线性化理论手册 done\nP1 上手Bladed \\ fast 线性化功能，研究OpenFAST线性化实现原理 done","x":-700,"y":134,"width":440,"height":560},
-		{"id":"c18d25521d773705","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\n\nP1 柔性部件 叶片、塔架主动力惯性力算法 主线\n- 变形体动力学 简略看看ing\n- 柔性梁弯曲变形振动学习，主线 \n\t- 广义质量 刚度矩阵及含义\n- 如何静力学求解 \n\t- 基于本构方程 读孟的论文\n\t- normal mode shape 能否使用？\n\t- F = kx 外载与弹性势能相等\n\t\n- 梳理bladed动力学框架 this week\n\t- 子结构文献阅读\n\t- 叶片模型建模 done\n\n\nP1 结果对比\n- Bladed与FAST之间的对比 去掉角度 不能直接比较\n- 叶根坐标系转换 \n\t- 叶尖变形量 - 变形向量 dot product 叶根坐标系方向\n\t- 叶片载荷输入量呢 载荷传递在blade mesh.force moment，mesh.orientation = coord_sys.n\n\nP1 编写线性化理论手册\nP1 上手Bladed \\ fast 线性化功能\n\nP2 如何优雅的存储、输出结果。\nP2 yaw 自由度再bug确认 已知原理了\n","x":-594,"y":-693,"width":450,"height":347},
+		{"id":"30cb7486dc4e224c","type":"text","text":"# 8月已完成\n\n","x":260,"y":134,"width":440,"height":560},
-		{"id":"30cb7486dc4e224c","type":"text","text":"# 8月已完成\n\n","x":260,"y":134,"width":440,"height":560}
+		{"id":"c18d25521d773705","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\n\nP1 柔性部件 叶片、塔架主动力惯性力算法 主线\n- 变形体动力学 简略看看ing\n- 柔性梁弯曲变形振动学习，主线 \n\t- 广义质量 刚度矩阵及含义\n- 如何静力学求解 \n\t- 基于本构方程 读孟的论文\n\t- normal mode shape 能否使用？\n\t- F = kx 外载与弹性势能相等\n\t\n- 梳理bladed动力学框架 this week\n\t- 子结构文献阅读\n\t- 叶片模型建模 done\n\nP1 工况点稳态载荷求解，F=kx\nP1 数值扰动+回归的线性化方法原理探究\n\nP2 如何优雅的存储、输出结果。\nP2 yaw 自由度再bug确认 已知原理了\n","x":-594,"y":-693,"width":450,"height":347}
 	],
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 }

线性化求解器/状态、状态空间概念.md

@@ -11,7 +11,7 @@
 
 系统的状态：能够完全表征系统时间域行为的最小内部变量组
 $$
-x(t) = 
+x(t) = {[x_1(t), x_2(t), ..., x_n(t)]}^T
 $$
 
 状态变量：构成系统状态的每一个变量。状态变量构成的列向量为状态向量
@@ -52,7 +52,7 @@ $$
 2、输出方程：描述系统**输出变量**与**状态变量**和**输入变量**之间函数关系的代数方程组。
 ![[Pasted image 20250626160850.png]]
 
-状态空间表达式：状态方程与输出方程的组合成为状态空间表达式，又称为状态方程或状态空间描述
+3、状态空间表达式：状态方程与输出方程的组合成为状态空间表达式，又称为状态方程或状态空间描述
 
 对于一个n个状态变量，p个输入变量，q个输出变量的系统
 

线性化求解器/线性化理论手册.md

@@ -1,3 +1,76 @@
+
+# 状态空间方程基础
+## 状态空间描述
+状态空间描述（内部描述）：通过建立系统内部状态和系统的输入以及输出之间的数学关系，来描述系统的行为。
+
+系统输入引起系统状态的变化，输入及系统状态共同导致系统输出的变化
+
+状态空间描述是对系统完全的描述，能表征系统的一切动力学
+
+## 状态
+
+系统的状态：能够完全表征系统时间域行为的最小内部变量组
+
+$$
+x(t) = {[x_1(t), x_2(t), ..., x_n(t)]}^T
+$$
+
+状态变量：构成系统状态的每一个变量。状态变量构成的列向量为状态向量
+
+## 状态空间
+
+状态向量的取值空间称为状态空间
+
+状态空间：以n个线性无关的状态向量作为基底所组成的n维空间称为状态空间$R^n$。
+系统在任意时刻的状态在状态空间中都可以用一点表示。
+状态轨线：随着时间的推移，系统状态$x(t)$在状态空间所留下的轨迹称为状态轨线或状态轨迹
+
+## 状态空间描述的形式
+
+1、状态方程：描述系统**状态变量**与**输入变量**之间关系的一阶微分方程组（连续时间系统）或一阶差分方程组（离散时间系统）
+
+**表征系统中输入所引起的内部状态变化的过程。**
+连续时间系统：
+$$
+\dot{x}(t) = f[x(t), u(t), t]
+$$
+离散时间系统
+$$
+{x}(t_{k+1}) = f[x(t_k), u(t_k), t_k]
+$$
+
+2、输出方程：描述系统**输出变量**与**状态变量**和**输入变量**之间函数关系的代数方程组。
+连续时间系统：
+$$
+{y}(t) = g[x(t), u(t), t]
+$$
+离散时间系统
+$$
+{y}(t_{k}) = g[x(t_k), u(t_k), t_k]
+$$
+
+3、状态空间表达式：状态方程与输出方程的组合成为状态空间表达式，又称为状态方程或状态空间描述
+
+对于一个n个状态变量，p个输入变量，q个输出变量的连续时间系统：
+$$
+\begin{array}{r}
+{\dot{x}(t) = f[x(t), u(t), t] }\\
+{{y}(t) = g[x(t), u(t), t]}
+\end{array}
+$$
+连续线性系统：
+$$
+\begin{array}{r}
+{\dot{x}(t) = A(t)x(t) + B(t)u(t) }\\
+{{y}(t) = C(t)x(t)+ D(t)u(t)}
+\end{array}
+$$
+
+其中：
+- $A(t)$系统矩阵
+- $B(t)$控制矩阵
+- $C(t)$观测矩阵
+- $D(t)$前馈矩阵
 # 1. 线性化分析背景
 
   

线性化求解器/计算流程框架.canvas

@@ -5,13 +5,22 @@
 		{"id":"82e0fa4b70baffed","type":"text","text":"每个工况点求稳态解","x":-200,"y":-140,"width":250,"height":60},
 		{"id":"d3aa69200118cea0","type":"text","text":"小扰动求A, B, C, D","x":-200,"y":0,"width":250,"height":60},
 		{"id":"f8e0af85235be889","type":"text","text":"A上做特征值、模态","x":-200,"y":140,"width":250,"height":60},
-		{"id":"5818e7212360b063","type":"text","text":"可选是否MBC转换","x":160,"y":-140,"width":250,"height":60}
+		{"id":"5818e7212360b063","type":"text","text":"可选是否MBC转换","x":160,"y":-140,"width":250,"height":60},
+		{"id":"03f26deb8603c7c3","x":-200,"y":280,"width":250,"height":60,"type":"text","text":"输出哪些量"},
+		{"id":"226774e95f4236f0","x":160,"y":140,"width":250,"height":60,"type":"text","text":"问题2 非线性，如何线性化"},
+		{"id":"65a392a60c82cf13","x":135,"y":-15,"width":300,"height":90,"type":"text","text":"问题1 动力学方程是二阶线性还是二阶非线性"},
+		{"id":"8c2eadcabf51301e","x":540,"y":-37,"width":250,"height":135,"type":"text","text":"非线性\n$$\n\\begin{array}{r}{\\dot{\\mathbf{x}}=f(t,\\mathbf{x},\\mathbf{u})}\\\\ {\\mathbf{y}=h(t,\\mathbf{x},\\mathbf{u})}\\end{array}\n$$"},
+		{"id":"e3f81d5e91896a13","x":540,"y":140,"width":250,"height":60,"type":"text","text":"小扰动+回归"}
 	],
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