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3-1,设温度计需要在一分钟内指示出响应值的,98%,，,并且假设温度计为一阶系统，求时间常数,T,。如果将温度计放在澡盆内，澡盆的温度以,10,o,C/min,的速度线性变化，求温度计的误差。,第三章习题课,(3-1),解,:,c(t,)=c(,)98%,t=4T=1 min,r(t,)=10t,e(t,)=,r(t)-c(t,),c(t,)=10(t-T+,e,),-t/T,=10(T-,e,),-t/T,e,ss,=,lim,t,e(t,),=10T,=2.5,T=0.25,3-2,电路如图，设系统初始状态为领,第三章习题课,(3-2),解,:,求系统的单位阶跃响应,及,u,c,(t,1,)=8,时的,t,1,值,R,1,Cs+1,R,1,/,R,0,G,(,s,)=,R,0,=20 k,R,1,=200,k,C=2.5,F,u,c,(t,)=K(1 e,t,T,-,),K,Ts,+,1,=,T=R,1,C=0.5,K=R,1,/R,0,=10,=10(1 e,-2t,),8=10(1 e,-2t,),0.8=1 e,-2t,e,-2t,=0.2,t=0.8,-,+,+,R,1,R,0,C,u,r,u,c,g(t,)=,e,-t/T,T,K,t,1,=0.8,=4,(2),求系统的单位脉冲响应，单位斜坡,响应,及单位抛物响应在,t,1,时刻的值,第三章习题课,(3-2),解,:,u,c,(t,)=,K(,t-,T+T,e,-t/T,),=4,R(s,)=,1,s,2,R(s,)=1,R(s,)=,1,s,3,T,2,=K(,s,s+1/T,+,T,s,2,-,1,s,3,-,T,2,),=1.2,1,s,3,K,Ts,+,1,U,c,(s,)=,-0.5t+0.25-0.25e,-2t,),1,2,t,2,u,c,(t,)=10(,3-3,已知单位负反馈系统的开环传递函数，求系统的单位阶跃响应。,4,s(s+5),G(s,)=,第三章习题课,(3-3),解,:,=,s,2,+5s+4,C(s,),R(s,),4,s(s+1)(s+4),C(s,)=,4,R(s,)=,s,1,1/3,s+4,1,s,+,=,4/3,s,+,1,-,1,3,c(t,)=1+,-4t,-t,4,3,-,e,e,3-4,已知单位负反馈系统的开环传递函数，求系统的上升时间,t,r,、峰值时间,t,p,、超调量,%,和调整时间,t,s,。,1,s(s+1),G(s,)=,第三章习题课,(3-4),解,:,=,s,2,+s+1,C(s,),R(s,),1,2,=,1,n,2,n,=1,=0.5,=,1,n,=0.866,d,=,n,2,1-,=60,o,-,1,=,tg,2,1-,t,r,=,d,-,=,3.14-3.14/3,0.866,=2.42,t,p,=,d,3.14,0.866,=,=3.63,%=,100%,e,-,1-,2,=16%,-1.8,e,t,s,=,3,n,=6,t,s,=,4,n,=8,3-6,已知系统的单位阶跃响应,:,c(t,)=1+0.2e,-60t,-10t,-1.2e,(1),求,系统的闭环传递函数。,(2),求,系统的阻尼比和无阻尼振荡频率。,第三章习题课,(3-6),解,:,0.2,s+60,1,s,+,C(s,)=,1.2,s,+,10,-,s(s+60)(s+10),=,600,=,s,2,+70s+600,C(s,),R(s,),600,R(s,)=,s,1,2,=,600,n,2,n,=70,=1.43,=,24.5,n,3-7,设二阶系统的单位阶跃响应曲线如图，系统的为单位反馈，求系统的传递函数。,t,c(t,),0,1,0.1,1.3,解,:,第三章习题课,(3-7),t,p,=,=0.1,2,1-,n,=0.3,e,-,1-,2,e,1-,2,=3.3,n,2,1-,3.14,0.1,=,=31.4,2,1-,/,=ln3.3,=1.19,2,1-,),2,/,(,=1.42,9.86,2,=1.42-1.42,2,=0.35,=,33.4,n,n,n,s(s+2,),G(s,)=,2,1115.6,s(s+22.7),=,3-8,已知单位负反馈系统的开环传递函数，求系统,K,、,T,值以满足动态指标：,%30%,，,t,s,0.3(5%),。,K,s(Ts+1),G(s,)=,第三章习题课,(3-8),解,:,=,Ts,2,+s+K,C(s,),R(s,),K,s,2,+,=,T,1,s+,T,K,T,K,T,1,2,n,=,t,s,=,3,n,0.3,n,10,T,0.05,0.3,e,-,1-,2,0.35,28.6,n,2,=,n,T,K,=817.96,K,40.9,3-11,已知闭环系统的特征方程式，试用劳斯判据判断系统的稳定性。,第三章习题课,(3-11),(1),s,3,+20s,2,+9s+100=0,解：,劳斯表如下：,s,1,s,0,s,3,s,2,1,9,20,100,4,100,系统稳定。,(3)s,4,+8s,3,+18s,2,+16s+5=0,1,18 5,s,4,s,3,8,16,劳斯表如下：,s,2,16,5,s,1,216,16,s,0,5,系统稳定。,3-12,已知单位负反馈系统的开环传递函数，试确定系统稳定时,K,值范围。,第三章习题课,(3-12),G(s,)=,s(s+1)(0.5s,2,+s+1),K(0.5s+1),解,:,0.5s,4,+1.5s,3,+2s,2,+s+0.5Ks+K=0,0.5,2 K,s,4,s,3,1.5,1+0.5K,s,2,b,31,b,31,=,1.5,*2-0,5(1+0.5K),1.5,3-0,5-0.25K0,0.25K0,0,3-14,已知系统结构如图，试确定系统稳定时,值范围。,第三章习题课,(3-14),R(s,),-,s+1,s,10,s(s+1),C(s),解,:,G(s,)=,s,2,(s+1),10(,s+1),(s)=,s,3,+s,2,+10,s+10,10(,s+1),s,3,s,2,1 10,1,10,s,1,b,31,s,0,10,b,31,=,10,-10,1,0,1,r(t,)=I(t)+2t+t,2,3-16,已知单位反馈系统的开环传递函数，试求,K,p,、,K,v,和,K,a,并求稳态误差,e,ss,第三章习题课,(3-16),解：,(0.1s+1)(0.2s+),(1),G(s,)=,20,K,p,=20,=0,e,ss1,=,R,0,1+K,s,2,R(s,)=,1,s,2,+,s,3,2,+,=,1,21,K,=0,e,ss2,=,K,a,=0,e,ss3,=,e,ss,=,=1,K,=10,K,a,=0,e,ss3,=,e,ss,=,s(s+2)(s+10),(2),G(s,)=,200,s(0.5s+1)(0.1s+1),=,10,K,p,=,e,ss1,=,0,e,ss2,=,K,2,=,2,10,s,2,(s,2,+4s+10),(3),G(s,)=,10(2s+1),=2,K,p,=,e,ss1,=,0,s,2,(0.1s,2,+0.4s+1),=,(2s+1),K,=,e,ss2,=,0,K,a,=,1,e,ss3,=,2,e,ss,=,2,3-17,已知系统结构如图。,第三章习题课,(3-17),解,:,-,R(s,),-,K,1,s,s,2,C(s),单位阶跃输入,:,G(s,)=,s,2,+K,1,s,K,1,(s)=,s,2,+K,1,s+K,1,K,1,确定,K,1,和,值,。,%=20%,t,s,=1.8(5%),2,n,=K,1,2,=,K,1,n,=0.2,e,-,1-,2,t,s,=,3,n,=1.8,=0.45,n,3,1.8*0.45,=,=3.7,2,n,K,1,=,=13.7,=0.24,(2),求系统的稳态误差：,r(t,)=,I(t,),t,1,2,t,2,解,:,G(s,)=,s,2,+K,1,s,K,1,=,s(,s+1),K,1,1,1,=1,K,p,=,e,ss1,=,0,R(s,)=,1,s,R(s,)=,s,2,1,K,=K,e,ss2,=,=0.24,R(s,)=,s,3,1,K,a,=0,e,ss3,=,第三章习题课,(3-17),3-18,已知系统结构如图。为使,=0.7,时,单位斜坡输入的稳态误差,e,ss,=0.25,第三章习题课,(3-18),解,:,确定,K,和,值,。,-,s,-,K,s(s+2),R(s,),C(s),G(s,)=,s,2,+2s+K,s,K,=,s(,s+1),2+K,1,2+K,K,(s)=,s,2,+(2+K,),s+K,K,2,n,=2+K,2,=,K,n,=2*0.7,K,e,ss,=,2+K,K,=0.25,=,0.25K,-2,K,K,=31.6,=0.186,+,R(s,),G(s,),F(s,),C(s,),+,-,D,1,(s),D,2,(s),E(s,),3-19,系统结构如图。,第三章习题课,(3-19),解,:,r(t,)=d,1,(t)=d,2,(t)=,I(t,),求,r(t,),作下的稳态误差,e,ssr,=lim s,1+G(s)F(s),s,0,s,1,=,1+G(0)F(0),1,(2),求,d,1,(t),和,d,2,(t),同时作用下的稳态误差,e,ssd,=,lim,s,-,F(s,),1+G(s)F(s),s,0,-1,1+G(s)F(s),+,s,1,E,d,(s)=,-G,2,(s)H(s),1+G,1,(s)G,2,(s)H(s),D(s,),=,1+G(0)F(0),-1+F(s),(3),求,d,1,(t),作用下的稳态误差,G(s,)=,K,p,+,K,s,Js,1,F(s,)=,e,ssd,=,lim,s,-,F(s,),1+G(s)F(s),s,0,s,1,-,s,0,s,1,=,lim,s,1+(K,p,+,K,s,Js,1,),Js,1,=0,返回,
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