线性控制系统分析与设计期末考+答案解析试
更新时间:2024-03-18 09:00:01 阅读量: 综合文库 文档下载
- 线性控制系统的设计与校正推荐度:
- 相关推荐
湖南工业大学期末考试试卷
线性控制系统分析与设计期末考试(七题命中)
一. (a)求位置y(t)与力f(t)有关的微分方程;(b)画出机械网络图;(c)确定传递函数G(D)=y/f。
(b) Draw the mechanical network.
K2
f
K1 K3
B
(a) node xa
?K1?K2?M1D2?xa?K2xb?f
node xb
?K2?K3?BD?M2D2xb?K2xa?0
K2 4322D?BD?KD?BKa?KaKb?K2?(c) G?D??where Ka?K1?K2, Kb?K2?K3, K?Ka?Kb
二、Solve the following differential equations. Assume zero initial conditions. Sketch the solutions.
D2x?16x?1 (1)
?r=1, k=0, w=0 ? q=k-w=0
The steady state output is therefore:
xss=b0 湖南工业大学期末考试试卷
D2 xss =0.
Inserting these values into previous equation(1): 16 xss =16 b0=1 xss =b0=
1 (2) 16The homogeneous equation is formed by letting the right side of the differential equation equal zero:
D2xt?16xt?0 (3)
the transient response is the solution of the homogeneous equation, is obtained by assuming a solution of the form
xt=Amemt (4) where m is a constant yet to be determined
the characteristic equation of system:
m2?16m0?m2?16?0 (5)
m1=4j, m2=-4j values of m are complex, by using the Euler identity
e?j?dt?cos?dt?jsin?dt and then combining terms, transient solutions are
xt?A1e4jt?A2e?4jt?B1cos4t?B2sin4t?Asin(4t??) (6)
x= xt + xss=Asin(4t??)?1 (7) 16Assume zero initial conditions, i.e., t=0, x(0)=0, Dx(0)=0, inserting these values into previous equation(7):
x(0)?Asin??1?0, Dx(0)?4Acos??0 16???2, A??1 16x= xt + xss=?
1?1sin(4t?)? 16216三、Write the Laplace transforms of the following equations and solve foe x(t); the initial conditions are given to the right.
湖南工业大学期末考试试卷
D2x+2.8Dx+4x=10 x(0)=2, Dx(0)=3 The Laplace transforms of the equation
s2X(s)-sx(0)- Dx(0)+ 2.8(sX(s)- x(0))+4X(s)=10s-1 X(s)(s2+2.8s+4)-(2s+8.6)= 10s-1
2s2?8.6s?10X(s)(s+2.8s+4)=
s2
A12s2?8.6s?102s2?8.6s?10As?B X(s)????2222s(s?2.8s?4)s[(s?1.4)?(2.04))ss?2.8s?4The inverse Laplace transforms of the equation(p637, appendxA 36) x(t)?2.5?1.69e?1.4tsin(2.04t?17.25)
A1?[sX(s)]s?02s2?8.6s?10?2?2.5 s?2.8s?4s?02s2?8.6s?102.5?0.5s?1.6 Xx???22ss(s?2.8s?4)s?2.8s?42s2?8.6s?102.5?0.5s?1.62.51s?3.2 X(s)?????2222s(s?2.8s?4)ss?2.8s?4s2(s?1.4)?2.04??The inverse Laplace transforms of the equation(p637, appendxA 26)
(?3.2?1.4)2?2.04?1.4t2.04x(t)=2.5-0.5esin(2.04t?tan?1)
2.04?3.2?1.4x(t)?2.5?1.69e?1.4tsin(2.04t?17.25)
四、 For the following system,
湖南工业大学期末考试试卷
(a)Draw an equivalent singal flow graph. (b) Derive transfer functions for E(s)/R(s), X(s)/R(s), B(s)/R(s), C(s)/R(s), and Y(s)/R(s). (a)
(b) Σ L1 =-HG1 (1)
Σ L2 =Σ L3 = 0 (2) Δ=1-ΣL1+ΣL2-ΣL3+…=1+ HG1 (3) T1=G1 T2=G2 (4)
?1?1 ?2?1?HG1 (5)
T?
C?s??R?s??T?nn??G1?G2(1?HG1) (6)
1?HG1五、 For each of the following cases, determine the range of values of K for which the response c(t) is stable, where the driving function is a step function. Determine the roots on the imaginary axis that yied sustained oscilations. (a) C?s??K 2s[s(s?2)(s?4s?20)?K]Solution:
r(t)?u?1(t)?1, R?s??L[r(t)]?L[u?1(t)]?1 sKC?s?s[s(s?2)(s2?4s?20)?K]KG(s)??? 21R?s?s(s?2)(s?4s?20)?KsThe characteristic equation of the system is:
湖南工业大学期末考试试卷
Q(s)?s(s?2)(s2?4s?20)?K?s4?6s3?28s2?40s?K
The Routhian array:
s4s3s2s1s016643?6K?25603K28K40K
Based Routh’s stability criterion, for stable operation of the system, the range of K:
K?0? ??6K?2560/3?0?the range of values of K
0?K?1280 9
六、 A unity-feedback control system has (1) G?s??20K
s[(s?1)(s?5)?20]where r(t)=2t. (a) If K=1.5, determine e(t)ss; (b) It is desired that for a ramp input e (t)ss≤1.5, what minimum value K1 have for this condition to be satisfied? (1) Solution:
(a) determining e(t)ss r(t)?2t, R?s??L[r(t)]?E(s)?R(s)2?2?1?H(s)G(s)s2 2s112(s?1)(s?5)?40??
20Kss[(s?1)(s?5)?20]?20K1?s[(s?1)(s?5)?20]湖南工业大学期末考试试卷
12(s?1)(s?5)?40e(t)ss?e(?)?limsE(s)?lims?s?0s?0ss[(s?1)(s?5)?20]?20K
2(s?1)(s?5)?402(0?1)(0?5)?4055?lim???s?0s[(s?1)(s?5)?20]?20K20K2K3 (b) finding the minimum value K1 If e (t)ss≤1.5 is desired, then K?
七、 For each of the transfer functions
G(s)?4(1?0.5) 2s(1?0.2s)(1?0.05s)55?K1?Kmin? 335?1.5, so 2K(a) draw the log magnitude (exact and asymptotic) and phase diarams; (b) draw the polar plot
湖南工业大学期末考试试卷
12(s?1)(s?5)?40e(t)ss?e(?)?limsE(s)?lims?s?0s?0ss[(s?1)(s?5)?20]?20K
2(s?1)(s?5)?402(0?1)(0?5)?4055?lim???s?0s[(s?1)(s?5)?20]?20K20K2K3 (b) finding the minimum value K1 If e (t)ss≤1.5 is desired, then K?
七、 For each of the transfer functions
G(s)?4(1?0.5) 2s(1?0.2s)(1?0.05s)55?K1?Kmin? 335?1.5, so 2K(a) draw the log magnitude (exact and asymptotic) and phase diarams; (b) draw the polar plot
正在阅读:
线性控制系统分析与设计期末考+答案解析试03-18
2019《秋声赋》导学案语文11-12
澳大利亚中学留学如何做到不耽误高考06-16
暑期实践心得体会(移动公司)文档2篇05-09
云南民族大学考试试卷(套题库8)09-17
职业与人生 作业答案20170405-16
Moudle1,2单元教案06-21
试验设计与分析论文09-16
- 多层物业服务方案
- (审判实务)习惯法与少数民族地区民间纠纷解决问题(孙 潋)
- 人教版新课标六年级下册语文全册教案
- 词语打卡
- photoshop实习报告
- 钢结构设计原理综合测试2
- 2014年期末练习题
- 高中数学中的逆向思维解题方法探讨
- 名师原创 全国通用2014-2015学年高二寒假作业 政治(一)Word版
- 北航《建筑结构检测鉴定与加固》在线作业三
- XX县卫生监督所工程建设项目可行性研究报告
- 小学四年级观察作文经典评语
- 浅谈110KV变电站电气一次设计-程泉焱(1)
- 安全员考试题库
- 国家电网公司变电运维管理规定(试行)
- 义务教育课程标准稿征求意见提纲
- 教学秘书面试技巧
- 钢结构工程施工组织设计
- 水利工程概论论文
- 09届九年级数学第四次模拟试卷
- 线性
- 控制系统
- 期末
- 解析
- 答案
- 分析
- 设计
- 模糊修辞与对外汉语教学
- 班主任每日常规工作
- 创新科研实践,培育教育特色,促进内涵发展
- 浅谈隧道盾构始发技术
- 高考句型翻译(全)
- (辽师大版)四年级品德与社会期末复习题(下学期)
- 渠道衬砌(0203) Microsoft Office Word 文档
- 北师大版六年级语文上册《语文天地6》教学设计
- (人教B版,理科)课时作业35
- 《广州市中田汽车城可行性研究报告》
- 六年级数学下册《节约用水》教学设计
- 永续债
- 2015年一级建造师《建设工程法规及相关知识》
- 微蜂窝课程开题报告
- 小学生心理咨询案例报告
- 小初高学习2018年九年级政治全册 第二单元 五星红旗我为你骄傲测
- 高大烟囱新建
- 全国出版社青年编校技能竞赛试题答案及讲评
- 幼儿园大班社会活动:祖国之最
- 普通化学(第六版)课后习题答案