目 錄
第1 章 緒論 ················································································································.1
1.1 控制與反饋控制 ···································································································.1
1.2 開環(huán)控制和閉環(huán)控制 ·····························································································.4
1.2.1 開環(huán)控制 ···································································································.4
1.2.2 閉環(huán)控制 ···································································································.4
1.3 控制系統(tǒng)的分類 ···································································································.5
1.4 控制理論的發(fā)展歷程 ·····························································································.7
1.5 控制系統(tǒng)性能的基本要求和設(shè)計(jì) ··············································································.9
1.5.1 控制系統(tǒng)性能的基本要求 ··············································································.9
1.5.2 控制系統(tǒng)的設(shè)計(jì) ·························································································.10
習(xí)題 ························································································································.11
第2 章 控制系統(tǒng)的數(shù)學(xué)模型 ·······················································································.12
2.1 數(shù)學(xué)模型概述 ·····································································································.12
2.2 控制系統(tǒng)的微分方程 ····························································································.13
2.2.1 控制系統(tǒng)微分方程的建立 ·············································································.13
2.2.2 非線性微分方程的線性化 ·············································································.17
2.3 控制系統(tǒng)的狀態(tài)方程 ····························································································.20
2.3.1 基本概念 ··································································································.20
2.3.2 線性系統(tǒng)狀態(tài)空間表達(dá)式的建立 ····································································.23
2.4 控制系統(tǒng)的傳遞函數(shù) ····························································································.26
2.4.1 傳遞函數(shù)的定義和特性 ················································································.26
2.4.2 傳遞函數(shù)的計(jì)算 ·························································································.28
2.4.3 傳遞函數(shù)的基本形式 ···················································································.29
2.4.4 典型環(huán)節(jié)的傳遞函數(shù) ···················································································.30
2.5 控制系統(tǒng)的框圖 ··································································································.35
2.5.1 框圖的組成及建立步驟 ················································································.35
2.5.2 框圖的等效變換 ·························································································.36
2.5.3 梅遜公式 ··································································································.43
2.6 控制系統(tǒng)的傳遞函數(shù) ····························································································.47
2.6.1 閉環(huán)控制系統(tǒng)的開環(huán)傳遞函數(shù) ·······································································.47
2.6.2 閉環(huán)控制系統(tǒng)的閉環(huán)傳遞函數(shù) ·······································································.48
2.7 應(yīng)用MATLAB 建立系統(tǒng)數(shù)學(xué)模型 ···········································································.51
2.7.1 傳遞函數(shù)的MATLAB 模型 ···········································································.51
2.7.2 狀態(tài)空間表達(dá)式的MATLAB 模型 ··································································.55
習(xí)題 ························································································································.58
第3 章 控制系統(tǒng)的時(shí)域分析 ·······················································································.66
3.1 概述 ·················································································································.66
3.2 控制系統(tǒng)的典型輸入信號(hào) ······················································································.67
3.3 控制系統(tǒng)時(shí)域響應(yīng)的求解 ······················································································.70
3.3.1 基于微分方程求解時(shí)域響應(yīng) ··········································································.70
3.3.2 基于狀態(tài)方程求解時(shí)域響應(yīng) ··········································································.72
3.3.3 基于傳遞函數(shù)求解時(shí)域響應(yīng) ··········································································.76
3.4 控制系統(tǒng)的時(shí)域性能指標(biāo) ······················································································.77
3.4.1 系統(tǒng)時(shí)域響應(yīng)的時(shí)間歷程 ·············································································.77
3.4.2 系統(tǒng)的動(dòng)態(tài)性能指標(biāo) ···················································································.78
3.4.3 系統(tǒng)的穩(wěn)態(tài)性能指標(biāo) ···················································································.79
3.5 控制系統(tǒng)的時(shí)域分析與性能指標(biāo)計(jì)算 ·······································································.79
3.5.1 一階系統(tǒng)的時(shí)域分析與性能指標(biāo)計(jì)算 ······························································.80
3.5.2 二階系統(tǒng)的時(shí)域分析與性能指標(biāo)計(jì)算 ······························································.82
3.5.3 高階系統(tǒng)的時(shí)域分析與性能指標(biāo)計(jì)算 ······························································.90
3.6 控制系統(tǒng)的穩(wěn)態(tài)誤差 ····························································································.93
3.6.1 穩(wěn)態(tài)誤差的概念 ·························································································.93
3.6.2 系統(tǒng)的型次 ·······························································································.94
3.6.3 系統(tǒng)穩(wěn)態(tài)誤差的計(jì)算 ···················································································.95
3.6.4 提高系統(tǒng)穩(wěn)態(tài)精度的方法 ···········································································.100
3.7 控制系統(tǒng)的穩(wěn)定性分析 ·······················································································.102
3.7.1 穩(wěn)定性的概念 ··························································································.102
3.7.2 系統(tǒng)穩(wěn)定的條件 ·······················································································.103
3.7.3 系統(tǒng)穩(wěn)定性的勞斯判據(jù) ··············································································.107
3.7.4 勞斯判據(jù)的應(yīng)用 ·······················································································.110
3.8 控制系統(tǒng)的可控性和可觀測(cè)性 ··············································································.112
3.8.1 可控性及其判斷 ·······················································································.112
3.8.2 可觀測(cè)性及其判斷 ····················································································.116
3.8.3 系統(tǒng)傳遞函數(shù)與可控性和可觀測(cè)性的關(guān)系 ······················································.118
3.9 基于MATLAB 的系統(tǒng)時(shí)域響應(yīng)計(jì)算和時(shí)域性能分析 ·················································.119
3.9.1 系統(tǒng)的時(shí)域響應(yīng)計(jì)算 ·················································································.119
3.9.2 系統(tǒng)的動(dòng)態(tài)響應(yīng)特性分析 ···········································································.122
3.9.3 系統(tǒng)穩(wěn)定性分析 ·······················································································.123
3.9.4 可控性和可觀測(cè)性分析 ··············································································.127
習(xí)題 ······················································································································.129
第4 章 控制系統(tǒng)的根軌跡分析 ··················································································.134
4.1 根軌跡的概念 ···································································································.134
4.2 根軌跡的基本條件與繪制規(guī)則 ··············································································.136
4.2.1 根軌跡的基本條件 ····················································································.137
4.2.2 根軌跡的繪制規(guī)則 ····················································································.138
4.3 控制系統(tǒng)根軌跡的繪制 ·······················································································.148
4.3.1 最小相位系統(tǒng)的根軌跡繪制 ········································································.148
4.3.2 零度根軌跡的繪制 ····················································································.149
4.3.3 系統(tǒng)的參量根軌跡繪制 ··············································································.153
4.4 控制系統(tǒng)的根軌跡分析 ·······················································································.155
4.4.1 增加開環(huán)零點(diǎn)和開環(huán)極點(diǎn)對(duì)根軌跡的影響 ······················································.155
4.4.2 系統(tǒng)性能的根軌跡分析 ··············································································.158
4.5 基于MATLAB 的系統(tǒng)根軌跡分析 ·········································································.162
習(xí)題 ······················································································································.164
第5 章 控制系統(tǒng)的頻域分析 ·····················································································.166
5.1 控制系統(tǒng)的頻率響應(yīng)與頻率特性函數(shù) ·····································································.166
5.1.1 系統(tǒng)的頻率響應(yīng) ·······················································································.166
5.1.2 系統(tǒng)的頻率特性函數(shù) ·················································································.168
5.2 控制系統(tǒng)的頻率特性圖 ·······················································································.170
5.2.1 系統(tǒng)的極坐標(biāo)圖 ·······················································································.170
5.2.2 系統(tǒng)的對(duì)數(shù)頻率特性圖 ··············································································.179
5.3 奈奎斯特穩(wěn)定判據(jù) ·····························································································.192
5.3.1 系統(tǒng)的奈奎斯特穩(wěn)定條件 ···········································································.192
5.3.2 基于對(duì)數(shù)頻率特性圖的系統(tǒng)穩(wěn)定性判據(jù) ·························································.199
5.4 控制系統(tǒng)的相對(duì)穩(wěn)定性 ·······················································································.201
5.5 控制系統(tǒng)的頻域性能指標(biāo) ····················································································.205
5.5.1 系統(tǒng)的閉環(huán)頻率特性 ·················································································.205
5.5.2 系統(tǒng)閉環(huán)頻率特性與開環(huán)頻率特性的關(guān)系 ······················································.208
5.6 基于MATLAB 的系統(tǒng)頻域性能分析 ······································································.210
5.6.1 系統(tǒng)的頻域特性函數(shù) ·················································································.210
5.6.2 利用MATLAB 繪制頻率特性圖 ···································································.212
習(xí)題 ······················································································································.216
第6 章 控制系統(tǒng)的設(shè)計(jì) ····························································································.221
6.1 控制系統(tǒng)設(shè)計(jì)的基本問題 ····················································································.221
6.1.1 系統(tǒng)的校正 ·····························································································.221
6.1.2 串聯(lián)校正裝置的一般結(jié)構(gòu) ···········································································.223
6.2 串聯(lián)校正裝置的設(shè)計(jì) ··························································································.226
6.2.1 串聯(lián)超前校正裝置的設(shè)計(jì) ···········································································.226
6.2.2 串聯(lián)滯后校正裝置的設(shè)計(jì) ···········································································.233
6.2.3 串聯(lián)滯后-超前校正裝置的設(shè)計(jì) ···································································.237
6.3 PID 控制系統(tǒng)的設(shè)計(jì) ··························································································.243
6.3.1 PID 控制器的設(shè)計(jì) ····················································································.243
6.3.2 設(shè)計(jì)PID 控制器的Z-N 法 ··········································································.250
6.4 狀態(tài)反饋與極點(diǎn)配置設(shè)計(jì) ····················································································.255
6.4.1 狀態(tài)反饋 ································································································.256
6.4.2 極點(diǎn)配置設(shè)計(jì)法 ·······················································································.256
6.5 應(yīng)用MATLAB 進(jìn)行控制系統(tǒng)設(shè)計(jì) ·········································································.259
習(xí)題 ······················································································································.265
第7 章 離散控制系統(tǒng)的基礎(chǔ)理論 ··············································································.270
7.1 概述 ···············································································································.270
7.1.1 采樣控制系統(tǒng) ··························································································.271
7.1.2 數(shù)字控制系統(tǒng) ··························································································.271
7.2 離散信號(hào)與Z 變換 ·····························································································.272
7.2.1 信號(hào)采樣與離散信號(hào) ·················································································.272
7.2.2 離散信號(hào)的Z 變換 ····················································································.278
7.3 離散控制系統(tǒng)的數(shù)學(xué)模型 ····················································································.284
7.3.1 差分方程 ································································································.284
7.3.2 離散控制系統(tǒng)的狀態(tài)空間表達(dá)式 ··································································.287
7.3.3 脈沖傳遞函數(shù) ··························································································.289
7.4 離散控制系統(tǒng)的性能分析 ····················································································.295
7.4.1 離散控制系統(tǒng)的時(shí)域分析 ···········································································.295
7.4.2 離散控制系統(tǒng)的穩(wěn)定性分析 ········································································.299
7.4.3 離散控制系統(tǒng)的穩(wěn)態(tài)誤差 ···········································································.304
7.4.4 離散控制系統(tǒng)的根軌跡分析 ········································································.308
7.4.5 離散控制系統(tǒng)的頻域分析 ···········································································.309
7.5 離散控制系統(tǒng)的設(shè)計(jì) ··························································································.312
7.5.1 離散PID 控制器的模擬化設(shè)計(jì) ····································································.312
7.5.2 離散控制系統(tǒng)的離散化設(shè)計(jì) ········································································.316
7.6 應(yīng)用MATLAB 分析與設(shè)計(jì)離散控制系統(tǒng) ································································.316
7.6.1 連續(xù)控制系統(tǒng)的離散化 ··············································································.317
7.6.2 離散控制系統(tǒng)的數(shù)學(xué)模型 ···········································································.318
7.6.3 離散控制系統(tǒng)的分析 ·················································································.319
7.6.4 基于MATLAB 離散控制系統(tǒng)設(shè)計(jì) ································································.324
習(xí)題 ······················································································································.325
參考文獻(xiàn) ·····················································································································.330
附錄A 拉氏變換 ·······································································································.331
附錄B 常用函數(shù)的拉氏變換與Z 變換表 ····································································.336
附錄C 部分習(xí)題參考答案 ·························································································.337