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控制工程基础(第2版) 读者对象:本书是高等学校仪器仪表、机械工程等机电大类专业本科学生的教材,也可供相关专业师生和从事自动化方面的工程技术人员参考。
本书主要介绍机械工程、电气工程等工程系统分析与控制的基础理论,主要内容包括工程系统(简称系统)的数学模型、时域分析、根轨迹分析、频域分析,以及工程系统控制设计等。本书的特点是以"工程控制系统—建模—分析—设计”为主线,重点突出工程系统控制性能的分析及设计,不强调严格的数学推演,在继续保持第1 版内容的系统性和完整性的基础上,侧重基本概念、思想方法的理解和应用,适应传授理论知识和培养创新能力并重的需要。
谭跃刚,工学博士,现为武汉理工大学机电工程学院教授、博士生导师。研究方向为机器人及其控制、控制理论与应用、机械装备动态监测技术与应用。
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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