(电气)自动控制原理33(第六章作业解答)

Email:[e-mail](1)1.1.)11.0(200)(0+=sssGo45≥pmφ(1)(1),,,,GMGM00)(0ωjGH0cω0pmφ0gω)11.0(200)(0+=ωωωjjjGHKK=200=200dBK46lg20=::--20dB/dec20dB/decωj111=10rad/sec=10rad/sec::--20dB/dec20dB/dec1011ωj+(())10rad/sec(1rad/sec,46dB)(1rad/sec,46dB)--20dB/dec20dB/dec10rad/sec--40dB/dec40dB/dec)101(200)(01ωωωjjjGHK+=10tan90)(1ωωφ−−−=o//radrad/sec/sec015102043100(()/)/-90-96-117-135-153-167-174-180sec//radω2010010110210304046decdB/40−decdB/20−dB3040205090−o/)(ωφ170−150−50180−7043167−o130cω0110−5130−190−)(01ωjGKsec/430radc=ωo130=pmφ∞=0gω∞=0GMo45≥pmφo45≥pmφ(3)(3)mφ00φφφφ∆+−=pmpmmoooo47151345=+−=(4)(4)..α44.647sin147sin1sin1sin1=−+=−+=oommφφα(5)(5))(mcωωdBjGKc09.844.6lg10lg10)(lg2001−=−=−=αωsec//radω2010010110210304046decdB/40−decdB/20−dB3040205090−o/)(ωφ170−150−50180−7043167−o130cω0110−5130−190−1.8−68(5)(5))(mcωωdBjGKc09.844.6lg10lg10)(lg2001−=−=−=αωsec/68radmc==ωω(6)(6)τzpsec006.044.66811=×==αωτmsec/8.261radzm===αωατsec/6.1728.2644.61radzp=×===ατ6.17218.2611111)(ωωτωατωωjjjjjGc++=++=(7)(7))()()()(0ωωωωjGjGjGjGHc⋅==)6.1721)(101()8.26/1(200ωωωωjjjj+++=8.26tan6.172tan10tan90)(111ωωωωφ−−−+−−−=o//radrad/sec/sec0151026.868100172.6(()/)/-90-94-108-118-123-125-129-141sec//radω2010010110210304046decdB/40−decdB/20−dB3040205090−o/)(ωφ170−150−50180−7043167−o130cω0110−5130−190−1.8−6827173o55cωsec/68radc=ωo55=pmφ∞=gω∞=GM6.1721)8.261()(sssGc++=2.MatlabMatlab6.16.16.16.111KKvv20s20s--11pmpm5050GMGM10dB10dB)2(4+ssR(s)Y(s)-Gc(s)1012345600.20.40.60.811.21.4StepResponseTime(sec)Amplitude0246810121416182002468101214161820LinearSimulationResultsTime(sec)Amplitude(2)1.1.)15.0(1)(0+=sssGo45≥pmφ110−=sKv(1)(1)KK11)15.0(1)(0+=sssG10115.01lim)(lim0000=+==→→sssGKssvKKvv=10s=10s--11KKvv=10s=10s--11,,KK11)15.0()(101+=ssKsGK1015.0lim)(lim10010=+==→→sKsGsKKssv101=K(2)(2),,,,GMGM00)(01ωjGHK0cω0pmφ0gω)21(10)()(0101ωωωωjjjGKjGHK+==KK=10=10dBK20lg20=::--20dB/dec20dB/decωj111=2rad/s=2rad/s::--20dB/dec(20dB/dec(2rad/s)2rad/s)211ωj+2rad/sec(1rad/sec,20dB)(1rad/sec,20dB)--20dB/dec20dB/dec2rad/sec--40dB/dec40dB/dec)21(10)(01ωωωjjjGHK+=2tan90)(1ωωφ−−−=o//radrad/sec/sec00.010.1124.610(()/)/-90-90-93-135-117-157-169-180sec//radω010−210−110−0103decdB/40−decdB/20−dB1020290−o/)(ωφ110−150−30170−o23130−180−157−6.40cω)(01ωjGKsec/6.40radc=ωo230=pmφ∞=0gω∞=0GMo45≥pmφ(3)(3)cωφφωφ∆+−=o180)(0pmcoooo130518045−=+−=sec//radω010−210−110−0103decdB/40−decdB/20−dB1020290−o/)(ωφ110−150−30170−o23130−180−157−6.40cω7.1(3)(3)cωφφωφ∆+−=o180)(0pmcoooo130518045−=+−=sec/7.1radc=ω(4)(4)sec/17.0101radzc===ωτ(5)(5)ααωlg20)(lg2001=cjGHKsec//radω016210−110−0103decdB/40−decdB/20−dB1020290−o/)(ωφ110−150−30170−o23130−180−157−6.40cω7.1cω(5)(5)ααωlg20)(lg2001=cjGHKdBjGHKc16)(lg20lg2001≈=ωα3.6=α7=α(6)(6)psec/024.0717.01radzp====αατ024.0117.0111)(1ωωατωτωωjjjjjGc++=++=::024.01)17.01(10)()(11ωωωωjjjGKjGcc++==(7)(7))()()()(0ωωωωjGjGjGjGHc⋅==)21)(024.01()17.01(10ωωωωjjjj+++=17.02024.090)(111ωωωωφ−−−+−−−=tgtgtgo//radrad/sec/sec00.010.10.17-139-13211.7210(()/)/-90-110-125-135-139-170-180sec//radω015210−110−0103decdB/40−decdB/20−dB1020290−o/)(ωφ110−150−30170−o23130−180−157−6.40cω7.1cωo45)(ωjGsec/7.1radc=ωo45=pmφ∞=gω∞=GM024.01)17.01(10)(sssGc++=2.MatlabMatlab6.26.26.26.222KKvv5s5s--11pmpm4040GMGM10dB10dB)2)(1(05.1++sssR(s)Y(s)-Gc(s)2010203040506000.20.40.60.811.21.4StepResponseTime(sec)Amplitude0246810121416182002468101214161820LinearSimulationResultsTime(sec)Amplitude(3)1.1.————)1501)(1101(20)(0++=ssssGo45≈pmφ01.0≤ssesradc/25≥ω(1)(1)KK11)1501)(1101(20)(10++=sssKsG1100020)102.0)(11.0(20lim)(limKssKssGKssv=++==→→01.020111≤==KKevss51≥K51=K)501)(101(100)()(0101ωωωωωjjjjGKjGHK++==(2)(2),,,,GMGM00)(01ωjGHK0cω0pmφKK=100=100dB40lg20=K::--20dB/dec20dB/decωj111=10rad/s=10rad/s::--20dB/dec(20dB/dec(10rad/s)10rad/s)1011ωj+22=50rad/s=50rad/s::--20dB/dec(20dB/dec(50rad/s)50rad/s)5011ωj+(())10rad/sec(1rad/sec,40dB)(1rad/sec,40dB)--20dB/dec20dB/dec10rad/sec50rad/sec--40dB/dec40dB/dec50tan10tan90)(11ωωωφ−−−−−=o50rad/sec--60dB/dec60dB/dec)501)(101(100)(01ωωωωjjjjGHK++=//radrad/sec/sec00.115103450100(()/)/-90-91-146-97-122-198-214-238-270sec//radω0110−010decdB/40−decdB/20−dB10202090−o/)(ωφ130−210−30250−340cωdecdB/60−170−270−180−220gω6050179−dB81102104050o18−,,)(01ωjGKsec/340radc=ωo45≥pmφsec/25radc≥ωo180−=pmφsec/220radg=ωdBGM80−=)(01ωjGK(3)(3)cωsec/25radc≥ωsec/30radc=ωsec/301radcm==ωω(4)(4)mφφωφφφ∆+−−=)(1800cpmmosec//radω0110−010decdB/40−decdB/20−dB10202090−o/)(ωφ130−210−30250−340cωdecdB/60−170−270−180−220gω6050179−dB81102104050o18−194−30(4)(4)mφφωφφφ∆+−−=)(1800cpmmoooooo645)194(18045=+−−−=(5)(5)γ8.1864sin164sin1sin1sin1=−+=−+=oommφφγ(6)(6)1z1psec/9.68.1830111radzc====γωτsec/130111radzp===γτγ(7)(7)2z2psec/3103010122radzc====ωτsec/16.08.1831222radzp====γγτ(8)(8)2K0lg10lg20)(lg202=+=γωcKjGH)(lg2001−ωcjGKsec//radω0110−010decdB/40−decdB/20−dB10202090−o/)(ωφ130−210−30250−340cωdecdB/60−170−270−180−220gω6050179−dB81102104050o18−194−303(8)(8)2K0lg10lg20)(lg202=+=γωcKjGH)(lg2001−ωcjGK08.18lg103lg202=−+K1.32=K(9)(9)BodeBode⎟⎟⎠⎞⎜⎜⎝⎛++⎟⎟⎠⎞⎜⎜⎝⎛++=γωτωτωγτωτω1122211111)(jjjjKKjGc⎟⎟⎠⎞⎜⎜⎝⎛++⎟⎟⎠⎞⎜⎜⎝⎛++××=112211111.35pjzjpjzjωωωω⎟⎟