目 录
第1 章 绪论 ················································································································.1
1.1 控制与反馈控制 ···································································································.1
1.2 开环控制和闭环控制 ·····························································································.4
1.2.1 开环控制 ···································································································.4
1.2.2 闭环控制 ···································································································.4
1.3 控制系统的分类 ···································································································.5
1.4 控制理论的发展历程 ·····························································································.7
1.5 控制系统性能的基本要求和设计 ··············································································.9
1.5.1 控制系统性能的基本要求 ··············································································.9
1.5.2 控制系统的设计 ·························································································.10
习题 ························································································································.11
第2 章 控制系统的数学模型 ·······················································································.12
2.1 数学模型概述 ·····································································································.12
2.2 控制系统的微分方程 ····························································································.13
2.2.1 控制系统微分方程的建立 ·············································································.13
2.2.2 非线性微分方程的线性化 ·············································································.17
2.3 控制系统的状态方程 ····························································································.20
2.3.1 基本概念 ··································································································.20
2.3.2 线性系统状态空间表达式的建立 ····································································.23
2.4 控制系统的传递函数 ····························································································.26
2.4.1 传递函数的定义和特性 ················································································.26
2.4.2 传递函数的计算 ·························································································.28
2.4.3 传递函数的基本形式 ···················································································.29
2.4.4 典型环节的传递函数 ···················································································.30
2.5 控制系统的框图 ··································································································.35
2.5.1 框图的组成及建立步骤 ················································································.35
2.5.2 框图的等效变换 ·························································································.36
2.5.3 梅逊公式 ··································································································.43
2.6 控制系统的传递函数 ····························································································.47
2.6.1 闭环控制系统的开环传递函数 ·······································································.47
2.6.2 闭环控制系统的闭环传递函数 ·······································································.48
2.7 应用MATLAB 建立系统数学模型 ···········································································.51
2.7.1 传递函数的MATLAB 模型 ···········································································.51
2.7.2 状态空间表达式的MATLAB 模型 ··································································.55
习题 ························································································································.58
第3 章 控制系统的时域分析 ·······················································································.66
3.1 概述 ·················································································································.66
3.2 控制系统的典型输入信号 ······················································································.67
3.3 控制系统时域响应的求解 ······················································································.70
3.3.1 基于微分方程求解时域响应 ··········································································.70
3.3.2 基于状态方程求解时域响应 ··········································································.72
3.3.3 基于传递函数求解时域响应 ··········································································.76
3.4 控制系统的时域性能指标 ······················································································.77
3.4.1 系统时域响应的时间历程 ·············································································.77
3.4.2 系统的动态性能指标 ···················································································.78
3.4.3 系统的稳态性能指标 ···················································································.79
3.5 控制系统的时域分析与性能指标计算 ·······································································.79
3.5.1 一阶系统的时域分析与性能指标计算 ······························································.80
3.5.2 二阶系统的时域分析与性能指标计算 ······························································.82
3.5.3 高阶系统的时域分析与性能指标计算 ······························································.90
3.6 控制系统的稳态误差 ····························································································.93
3.6.1 稳态误差的概念 ·························································································.93
3.6.2 系统的型次 ·······························································································.94
3.6.3 系统稳态误差的计算 ···················································································.95
3.6.4 提高系统稳态精度的方法 ···········································································.100
3.7 控制系统的稳定性分析 ·······················································································.102
3.7.1 稳定性的概念 ··························································································.102
3.7.2 系统稳定的条件 ·······················································································.103
3.7.3 系统稳定性的劳斯判据 ··············································································.107
3.7.4 劳斯判据的应用 ·······················································································.110
3.8 控制系统的可控性和可观测性 ··············································································.112
3.8.1 可控性及其判断 ·······················································································.112
3.8.2 可观测性及其判断 ····················································································.116
3.8.3 系统传递函数与可控性和可观测性的关系 ······················································.118
3.9 基于MATLAB 的系统时域响应计算和时域性能分析 ·················································.119
3.9.1 系统的时域响应计算 ·················································································.119
3.9.2 系统的动态响应特性分析 ···········································································.122
3.9.3 系统稳定性分析 ·······················································································.123
3.9.4 可控性和可观测性分析 ··············································································.127
习题 ······················································································································.129
第4 章 控制系统的根轨迹分析 ··················································································.134
4.1 根轨迹的概念 ···································································································.134
4.2 根轨迹的基本条件与绘制规则 ··············································································.136
4.2.1 根轨迹的基本条件 ····················································································.137
4.2.2 根轨迹的绘制规则 ····················································································.138
4.3 控制系统根轨迹的绘制 ·······················································································.148
4.3.1 最小相位系统的根轨迹绘制 ········································································.148
4.3.2 零度根轨迹的绘制 ····················································································.149
4.3.3 系统的参量根轨迹绘制 ··············································································.153
4.4 控制系统的根轨迹分析 ·······················································································.155
4.4.1 增加开环零点和开环极点对根轨迹的影响 ······················································.155
4.4.2 系统性能的根轨迹分析 ··············································································.158
4.5 基于MATLAB 的系统根轨迹分析 ·········································································.162
习题 ······················································································································.164
第5 章 控制系统的频域分析 ·····················································································.166
5.1 控制系统的频率响应与频率特性函数 ·····································································.166
5.1.1 系统的频率响应 ·······················································································.166
5.1.2 系统的频率特性函数 ·················································································.168
5.2 控制系统的频率特性图 ·······················································································.170
5.2.1 系统的极坐标图 ·······················································································.170
5.2.2 系统的对数频率特性图 ··············································································.179
5.3 奈奎斯特稳定判据 ·····························································································.192
5.3.1 系统的奈奎斯特稳定条件 ···········································································.192
5.3.2 基于对数频率特性图的系统稳定性判据 ·························································.199
5.4 控制系统的相对稳定性 ·······················································································.201
5.5 控制系统的频域性能指标 ····················································································.205
5.5.1 系统的闭环频率特性 ·················································································.205
5.5.2 系统闭环频率特性与开环频率特性的关系 ······················································.208
5.6 基于MATLAB 的系统频域性能分析 ······································································.210
5.6.1 系统的频域特性函数 ·················································································.210
5.6.2 利用MATLAB 绘制频率特性图 ···································································.212
习题 ······················································································································.216
第6 章 控制系统的设计 ····························································································.221
6.1 控制系统设计的基本问题 ····················································································.221
6.1.1 系统的校正 ·····························································································.221
6.1.2 串联校正装置的一般结构 ···········································································.223
6.2 串联校正装置的设计 ··························································································.226
6.2.1 串联超前校正装置的设计 ···········································································.226
6.2.2 串联滞后校正装置的设计 ···········································································.233
6.2.3 串联滞后-超前校正装置的设计 ···································································.237
6.3 PID 控制系统的设计 ··························································································.243
6.3.1 PID 控制器的设计 ····················································································.243
6.3.2 设计PID 控制器的Z-N 法 ··········································································.250
6.4 状态反馈与极点配置设计 ····················································································.255
6.4.1 状态反馈 ································································································.256
6.4.2 极点配置设计法 ·······················································································.256
6.5 应用MATLAB 进行控制系统设计 ·········································································.259
习题 ······················································································································.265
第7 章 离散控制系统的基础理论 ··············································································.270
7.1 概述 ···············································································································.270
7.1.1 采样控制系统 ··························································································.271
7.1.2 数字控制系统 ··························································································.271
7.2 离散信号与Z 变换 ·····························································································.272
7.2.1 信号采样与离散信号 ·················································································.272
7.2.2 离散信号的Z 变换 ····················································································.278
7.3 离散控制系统的数学模型 ····················································································.284
7.3.1 差分方程 ································································································.284
7.3.2 离散控制系统的状态空间表达式 ··································································.287
7.3.3 脉冲传递函数 ··························································································.289
7.4 离散控制系统的性能分析 ····················································································.295
7.4.1 离散控制系统的时域分析 ···········································································.295
7.4.2 离散控制系统的稳定性分析 ········································································.299
7.4.3 离散控制系统的稳态误差 ···········································································.304
7.4.4 离散控制系统的根轨迹分析 ········································································.308
7.4.5 离散控制系统的频域分析 ···········································································.309
7.5 离散控制系统的设计 ··························································································.312
7.5.1 离散PID 控制器的模拟化设计 ····································································.312
7.5.2 离散控制系统的离散化设计 ········································································.316
7.6 应用MATLAB 分析与设计离散控制系统 ································································.316
7.6.1 连续控制系统的离散化 ··············································································.317
7.6.2 离散控制系统的数学模型 ···········································································.318
7.6.3 离散控制系统的分析 ·················································································.319
7.6.4 基于MATLAB 离散控制系统设计 ································································.324
习题 ······················································································································.325
参考文献 ·····················································································································.330
附录A 拉氏变换 ·······································································································.331
附录B 常用函数的拉氏变换与Z 变换表 ····································································.336
附录C 部分习题参考答案 ·························································································.337
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