一、PID控制核心公式解析
1. 数学模型
PID控制器的原始理论模型基于微分方程： \[
u(t) = K_p \cdot e(t) + K_i \int_{0}^{t} e(\tau) \,d\tau + K_d
\frac{de(t)}{dt}
\] - 比例项 \(K_p
e(t)\)：当前误差的直接响应，控制速度与误差成正比 -
积分项 \(K_i \int
e(τ)\,dτ\)：累计历史误差，用于消除稳态偏差 -
微分项 \(K_d
de/dt\)：通过预测误差变化趋势抑制超调
[WARNING] 参数失衡的代价
过大的Ki：可能导致积分饱和，系统振荡加剧
过大的Kd：对高频噪声敏感，放大控制噪声
二、离散化实现：从连续到数字
实际编程中，计算机以周期性采样的方式处理信号，离散化后的PID公式为：
\[
u[n] = K_p e[n] + K_i \Delta t \sum_{k=0}^n e[k] + K_d
\frac{e[n]-e[n-1]}{\Delta t}
\] -
积分离散化：通过累加误差与采 ...
1. Processor Architectures
CISC
Complex Instrcuction Set Computer
Uses many instruction formats
Uses variable length instructions
Makes use of different addressing modes
Uses few registers
Has a large instruction set
Requires complex circuits
Frequently uses cache
Instructions (converted to sub-instructions that) may require many
clock cycles
Programmable CU
RISC
Reduced Instruction Set Computer
Uses simple instructions
Uses fixed length instructions
Instructions only requ ...
Networking devices
Interconnected devices that enable fast data transmission within a
network.
Networking benefits
File sharing: Easily share data between different
interconnected devices.
Resource sharing: Use network-connected output
devices like printers or share software within the network.
Higher storage: Files can be stored in
network-connected storage mediums.
LAN
WAN
A network that connects devices within a small geographical area,
often within the ...
8.1. File Based System
Data stored in discrete files, stored on computer,
and can be accessed, altered or removed by the user.
Disadvantages of
File Based System
No enforcing control on organization/structure of
files
Data repeated in different files; manually change
each
Sorting must be done manually or must write a
program
Data may be in different formats; difficult to find
and use
Impossible for it to be multi-user; chaotic
Security not sophisticated; users can access
eve ...
常规
Ctrl+Shift+P, F1：显示命令面板
Ctrl+P：快速打开...
Ctrl+Shift+N：新窗口/实例
Ctrl+W：关闭窗口/实例
Ctrl+,：用户设置
Ctrl+K Ctrl+S：键盘快捷键
基本编辑
Ctrl+X：剪切（空选时剪切整行）
Ctrl+C：复制（空选时复制整行）
Alt+↑ / ↓：向上/向下移动行
Shift+Alt+↑ / ↓：复制向上/向下的行
Ctrl+Shift+K：删除行
Ctrl+Enter：在下面插入行
Ctrl+Shift+Enter：在上面插入行
Ctrl+Shift+\：跳转到匹配的括号
Ctrl+/：注释/取消注释行
Shift+Alt+A：块注释
Alt+Z：切换自动换行
导航
Ctrl+T：显示所有符号
Ctrl+P：快速打开文件
Ctrl+Shift+O：跳转到符号
Ctrl+G：跳转到行
F8：跳转到下一个错误或警告
Ctrl+Shift+Tab：导航活动组历史记录
...
1. Information Representation
1.1. Data Representation
The two fundamental characteristics of any number system are:
Base: The number of different digits that a system
can use to represent numbers.
Place value: The specific value of a digit based on
its position within a number.
Denary - Base 10
Binary Systems - Base 2: Possible bits (binary
digits): 0 and 1. All data and characters are represented in
binary.
Example1
65 in binary is 0100001.
Denary vs. Binary prefixes
...
学习笔记
未读Define problem
明确分析物理量, 化简题目给的方程式 \(f(x) =
kx + b\)
Dependent variable \(f(x)\):
Independent variable \(x\):
Control varable(s):
画草图
Data collection
列举所有变量的测量方法
重复测量保证精确
Method of analysis
"Plot the graph of (dependent variable) against (independent
variable)."
"If the given function is true:" 分析是否过原点, 斜率和y轴交点的意义
The gradient of the best-ft line is _____ ,thus \(Gradient\) = _____.
The \(y_{intercept}\) of the
best-ft line is _____ ,thus \(y_{intercept}\) = _____. ...
学习笔记
未读12. Motion in circle
\(\omega = \frac{2\pi}{T}\)
\(v_c = \omega r\)
\(a_c = \omega^2 r\)
\(F_c = ma_c = m\omega^2 r =
\frac{mv^2}{r}\)
13. Gravitational
fields
\(F_g=\frac{Gm_1m_2}{r^2}\)
For satellites: \(F_c = F_g\)
\(g=\frac{GM}{r^2}\)
\(\phi = -\frac{GM}{r}\)
\(E_p = -\frac{GmM}{r}\)
Example Problems from Chapter
13
State Newton's law of
gravitation:
(把 \(F_g=\frac{Gm_1m_2}{r^2}\)
解释一遍)
#
Ans
Mark
1
Gravitational force is directl ...
Part1: Central
Processor Unit
1.\(\star\) Von Neumann &
Stored-program concept
Von Neumann
architecture
Singal processor
Program consists of a sequence of instructions
Instructions & data are identical in memory
Stored in contiguous blocks of main menory
Instructions are fetched & executed in sequence
Stored-program
concept
(笔记有误)
2.Register
2.1 General pupose
Hold data that frequently used by CPU
Used by the programmer when addressing CPU
Accumalator
...
学习笔记
未读1. Eembbedded
System(嵌入式系统)
Bulit into the device
Combination to hard ware & sotf ware for
specific functions
Must contain Processor,Memory &
input/output
Hard to upgrade
2. \(\clubsuit\) Hardwares
2.1 Laser Printer
Revolving drum(OPC drum) is initially given
charge (-)
Laser beam reflects by
mirrors
Scans back & front across the drum
Discharging certain parts of the
drum
The drum is coated with oppositely
charged toner
The drum rolls over electro-statically
...
