控制系统设计与校正
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课程设计报告
题 目 控制系统设计与校正
课 程 名 称 自动控制原理课程设计
院 部 名 称 机电工程学院
专 业 电气工程及其自动化
班 级
学 生 姓 名
学 号
课程设计地点
课程设计学时 1周
指 导 教 师
2 目 录
一、 课程设计目的及任务······································01
1.1课程设计目的··············································01
1.2课程设计任务··············································01
二、 系统性能分析················································02
2.1校正前系统分析············································02
2.1.1确定0K···············································02
2.2利用MATLAB绘画未校正系统的bode图·························02
2.2.1校正前Bode图··········································02
2.2.2第一次超前校正后的Bode图·····························03
2.2.3第二次超前校正后的Bode图·····························04
三、 三种响应曲线···············································06
3.1单位脉冲响应··············································06
3.1.1校正前的单位脉冲响应··································06
3.1.2校正后的单位脉冲响应··································06
3.2单位阶跃响应··············································07
3.2.1校正前的单位阶跃响应··································07
3.2.2校正前的单位阶跃响应··································08
3.3单位斜坡响应··············································08
3.3.1校正前的单位斜坡响应··································08
3.3.2校正前的单位斜坡响应··································09
四、特征根······················································10
4.1系统校正前的特征根·········································10
4.2系统校正后的特征根········································10
五、系统的动态性能指标·······································11
5.1校正前的动态性能指标······································11
5.2校正后的动态性能指标······································12
5.3系统的稳态误差············································13
3 六、根轨迹·····················································13
6.1校正前的根轨迹············································13
6.2校正后的根轨迹············································15
七、系统的Nyquist图··········································16
7.1系统校正前的Nyquist图····································16
7.2系统校正后的Nyquist图····································16
八、心得体会····················································18
参考文献························································18
4 一、课程设计目的及任务
1.1 课程设计目的
1.掌握自动控制原理的时域分析法，根轨迹法，频域分析法，以及各种补偿（校正）装置的作用及用法，能够利用不同的分析法对给定系统进行性能分析，能根据不同的系统性能指标要求进行合理的系统设计，并调试满足系统的指标。
2.学会使用MATLAB语言及Simulink动态仿真工具进行系统仿真与调试。
1.2 课程设计任务
设计题目：设原系统的开环传递函数为 0()(0.51)(0.21)KGSSSS试选用串联滞后或串联超前校正装置，要求校正后系统的相角裕度 ,
幅值裕度 K g =6 分贝，静态速度误差系数1vK10s。
要求：根据给定的性能指标选择合适的校正方式对原系统进行校正（须 写清楚校正过程），使其满足工作要求。然后利用MATLAB对未校正系统和校正后系统的性能进行比较分析，针对每一问题分析时应写出程序，输出结果图和结论。最后还应写出心得体会与参考文献等。具体要求如下：
1.首先， 根据给定的性能指标选择合适的校正方式对原系统进行校正，使其满足工作要求。要求程序执行的结果中有校正装置传递函数和校正后系统开环传递函数，校正装置的参数T，等的值。
2.利用MATLAB函数求出校正前与校正后系统的特征根，并判断其系统是否稳定，为什么?
3.利用MATLAB作出系统校正前与校正后的单位脉冲响应曲线，单位阶跃响应曲线，单位斜坡响应曲线，分析这三种曲线的关系？求出系统校正前与校正后的动态性能指标σ%、tr、tp、ts以及稳态误差的值，并分析 其
5 有何变化？
4.绘制系统校正前与校正后的根轨迹图，并求其分离点、汇合点及与虚轴交点的坐标和相应点的增益K值，得出系统稳定时增益K的变化范围。绘制系统校正前与校正后的Nyquist图，判断系统的稳定性，并说明理由？
5.绘制系统校正前与校正后的Bode图，计算系统的幅值裕量，相位裕量，幅值穿越频率和相位穿越频率。判断系统的稳定性，并说明理由？
二、系统性能分析
2.1 确定校正传递函数
2.1.1 确定0K
VK=0lim()()ssGsHs=)12.0)(1(0.5slim00sssks=)12.0)(1(0.5lim00ssks=0k
-s10 )12.0)(1(0.510)(0sssSG
2.2 利用MATLAB绘画未校正系统的bode图
2.2.1 校正前Bode图
利用matlab进行编程，用程序：
num=[0 0 0 10];
den=[0.1 0.7 1 0];
sys=tf(num,den);
bode(num,den);
[gm1,pm1,wcg1,wcp1]=margin(sys0)
可得到Bode图
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图1、校正前系统Bode图
2.2.2第一次超前校正后的Bode图：
利用matlab进行编程，用程序：
phy=65;
phy1=phy+10;
phy2=phy1*pi/180;
a1=(1+sin(phy2))/(1-sin(phy2)
M1=1/sqrt(a1);
[m1,p1,w1]=bode(G);
wc1=spline(m1,w1,M1);
T1=1/(wc1*sqrt(a1))
gc1=tf([a1*T1 1],[T1 1])
sys1=G*gc1;
[gm1,pm1,wcg1,wcp1]=margin(sys1)
输出校正装置传递函数及其参数：
a1 = 57.6955
T1 = 0.0153
7 Transfer function:
0.8821 s + 1
-------------
0.01529 s + 1
输出经一次超前网络校正后系统的幅值裕度、相角裕度、穿越频率、剪切频率
gm1 = 4.7519
pm1 = 28.1721
wcg1 = 19.6895
wcp1 = 8.6214
>> margin(sys1) 【输出一次校正后 的bode图】
2.2.3、第二次超前校正后的Bode图：
利用matlab进行编程，用程序：
>> wc2=18.5;
[m2,p2,w2]=bode(sys1);
M2=spline(w2,m2,wc2);
a2=M2^(-2)
T2=1/(wc2*sqrt(a2))
