自動控制原理

本書結合具體的控制系統介紹了自動控制的基本理論及工程應用。主要內容包括緒論、控制系統的數學模型、線性系統的時域分析、根軌跡法、線性系統的頻域分析、控制系統設計、非線性系統分析、線性離散系統、線性系統的狀態空間分析，以及自動控制系統綜合案例。本書融入了課程思政內容，從實際應用出發，突出物理概念，減少數學公式推導；強化工程應用中常用知識點的介紹，採用不同方法對一個工程實例進行分析和設計，闡明自動控制原理的應用。

李彥梅，安慶師範大學機電系教工機械自動化黨支部支部書記，教授，碩士生導師，主要從事智能控制與流量檢測方面研究，公開發表學術論文20餘篇，出版教材3部，主持（參與）省級以上教科研項目4項。
 

第1章緒論·····································1
1.1自動控制的基本概念·· ···············1
1.1.1自動控制的定義·····················1
1.1.2控制理論的發展過程················1
1.1.3自動控制系統的組成················2
1.1.4自動控制系統的基本控制
方式···································4
1.2自動控制系統的分類··· ··············6
1.3對自動控制系統的基本要求········7
1.4控制系統實例·············· ·············8
1.4.1電冰箱製冷控制系統················8
1.4.2函數記錄儀····· ······················9
1.4.3爐溫控制系統···················· ·.10
本章小結·····································.11
習題····· ······································.11

第2章控制系統的數學模型·· ··········.13
2.1微分方程的建立·····················.13
2.2傳遞函數······························.14
2.2.1傳遞函數的基本概念······· ······.14
2.2.2傳遞函數的性質··················.15
2.2.3典型環節及其傳遞函數······ ····.16
2.3結構圖·································.17
2.3.1結構圖的組成和繪製·············.17
2.3.2結構圖的等效變換················.18
2.4信號流圖· ·····························.23
2.4.1信號流圖的基本概念·········· ···.23
2.4.2信號流圖的繪製··················.24
2.4.3梅森增益公式及其應用········ ··.25
本章小結·····································.26
習題···· ·······································.27

第3章線性系統的時域分析············.29
3.1典型輸入信號·······················.29
3.2自動控制系統的時域性能
指標····································.31
3.3一階系統的時域分析··· ···········.32
3.3.1一階系統的數學模型·············.32
3.3.2一階系統的單位階躍響應及
性能分析··························.32
3.3.3一階系統的單位斜坡響應及
性能分析········ ··················.33
3.3.4一階系統的單位加速度響應及
性能分析················· ·········.33
3.3.5一階系統的單位脈衝響應及
性能分析·························· .34
3.4二階系統的時域分析··············.34
3.4.1二階系統的數學模型·············.34
3.4.2二階系統的單位階躍響應·······.35
3.4.3欠阻尼二階系統的動態性能
分析·················· ·············.37
3.4.4二階系統的單位斜坡響應·······.42
3.4.5二階系統性能的改善······· ······.44
3.5高階系統的時域分析··············.46
3.6穩定性分析···························.48
3.6.1系統穩定的充分必要條件·······. 49
3.6.2勞斯判據··························.50
3.6.3相對穩定性········ ···············.53
3.7穩態誤差····························· ·.54
3.7.1誤差的定義·······················.54
3.7.2輸入引起的穩態誤差······· ······.55
3.7.3靜態誤差係數·····················.56
3.7.4擾動作用下的穩態誤差··· ·······.59
3.7.5改善系統穩態精度的方法········.60
本章小結··················· ··················.62
習題····························· ··············.63

第4章根軌跡法···························· .67
4.1根軌蹟的基本概念··················.67
4.1.1根軌跡················· ············.67
4.1.2根軌跡方程························.68
4.2根軌跡圖的繪製法則··············.70
4.3參數根軌跡······················· ····.80
4.4利用根軌跡分析系統性能········.82
4.4.1已知根軌跡增益確定閉環極點
和傳遞函數············· ···········.82
4.4.2已知系統性能指標確定閉環
極點·························· ······.83
4.4.3增加開環零點對系統性能的
影響······························ ··.84
4.4.4增加開環極點對系統性能的
影響································.87
本章小結·····································.88
習題········ ···································.89

第5章線性系統的頻域分析···· ········.92
5.1頻率特性的基本概念··············.92
5.1.1頻率特性的定義··········· ·······.92
5.1.2頻率特性的表示方法·············.93
5.2典型環節及系統頻率特性········.94
5.2.1典型環節的頻率特性·············.95
5.2.2開環系統的頻率特性·············103
5.3頻域特性法的穩定性分析········109
5.3.1奈奎斯特穩定判據················109
5.3.2穩定裕度··· ·······················114
5.3.3開環對數幅頻特性曲線與
系統性能之間的關係········ ·····117
本章小結·····································126
習題··· ········································127

第6章控制系統設計··· ···················131
6.1概述···························· ········131
6.2 PID控制器··························.131
6.2.1 PID控制器概述·· ···············.131
6.2.2比例控制器······················.131
6.2.3比例微分控制器·················.132
6.2.4積分控制器····················· ·.133
6.2.5比例積分控制器·················.133
6.2.6比例積分微分控制器············.134
6.3基於頻域法的控制系統
設計···································.135
6.3.1相位超前補償····················.135
6.3.2相位滯後補償····················.137
6.3.3相位滯後?超前補償·············.138
6.3.4串聯補償網絡的期望幅頻
特性設計方法·············· ······.139
6.3.5反饋補償·························.146
本章小結········ ····························.148
習題··················· ·······················.148

第7章非線性系統分析·················. 150
7.1非線性系統概述···················.150
7.1.1為什麼研究非線性系統·········.150
7.1.2非線性系統的特性··············.150
7.1.3非線性系統的特點··············.153
7.1.4非線性系統的分析方法·········.154
7.2相平面法·························· ···.155
7.2.1相平面的基本概念··············.155
7.2.2相軌蹟的繪製·············· ······.156
7.2.3奇點······························.158
7.2.4非線性系統的相平面分析······.160
7.3描述函數法··························.162
7.3.1描述函數的基本概念············.162
7.3.2典型非線性環節的描述函數····.166
7.3.3非線性系統的描述函數法
分析······ ························.170
本章小結······················ ··············.176
習題································· ·········.177

第8章線性離散系統····················.179
8.1計算機控制系統概述······ ·······.179
8.1.1計算機控制系統簡圖·············179
8.1.2計算機控制系統的組成··········180
8.1.3計算機控制系統的特點··········180
8.1.4信號的採樣與恢復················181
8.2計算機控制系統分析· ·············181
8.2.1離散系統的穩定性分析··········181
8.2.2線性採樣系統穩定的充要
條件····· ···························183
8.2.3離散系統的過渡響應分析········184
本章小結·· ···································186
習題············· ······························186

第9章線性系統的狀態空間分析······187
9.1概述· ···································187
9.2基本概念··········· ···················187
9.2.1系統·························· ······187
9.2.2系統狀態空間描述················188
9.2.3動態系統狀態空間表達式的
一般形式······· ···················190
9.3線性多變量系統的運動
分析····································191
9.3.1線性系統狀態方程的解··· ·······192
9.3.2狀態轉移矩陣的性質·············192
9.4 Lyapunov穩定性分析··············194
9.4.1概述································194
9.4.2 Lyapunov意義下的穩定性
問題··· ···························.194
9.5 Lyapunov穩定性理論············.195
9.5. 1 Lyapunov **法················.195
9.5.2 Lyapunov第二法················.196
本章小結····································.198
習題··········· ·······························.198

第10章自動控制系統綜合案例······.200
10.1水位控制系統建模···············.200
10.1.1單容水箱······················ ··.200
10.1.2雙容水箱和三容水箱··········.201
10.2系統性能分析·····················.202
10.2.1時域分析法的水位控制
系統分析··········· ·············.202
10.2.2根軌跡分析法和頻域分析法的
水位控制系統分析·············.205
10.3系統的校正和綜合設計········.206
10.3.1超前校正························.206
10.3.2 PID控制器·····················.207
本章小結························ ············.208

附錄A拉普拉斯變換與反變換·········.209
附錄B常用函數的拉普拉斯
變換錶···· ··························.214
參考文獻···················· ···················.215