(电气)自动控制原理31(非线性系统)(含第七章作业)

Email:[e-mail]6677661212447.17.27.37.17.27.211rc-Gxy1Nrc-GxyNtXtxωsin)(=)()sin())(()(tntXntxntyωω===∑∞=++=10)sincos(2)(nnntnBtnAAtyωω∑∞=++=10)sin(nnntnYYϕω∫=πωωπ20)(cos)(1ttdntyAn∫=πωωπ20)(sin)(1ttdntyBnnnnBA1tan−=ϕ22nnnBAY+=00=Y∑∞=+=1)sin()(nnntnYtyϕω∑∞=+++=211)sin()sin(nnntnYtYϕωϕω)sin()(11ϕω+=tYtytBtAωωsincos11+=c-GxyNr∫=πωωπ201)(cos)(1ttdtyA∫=πωωπ201)(sin)(1ttdtyB21211BAY+=1111tanBA−=ϕ)(XN),(ωXNXjABeXBAXeYNBAjj11tan212111111+=+==−ϕbb−XkxyxtωytωtXtxωsin)(=⎩⎨⎧=kbtkXtyωsin)(btXbtX≤ωωsinsintBtAtyωωsincos)(11+=0,01=A)(sin)(1201tdttyBωωππ∫=⎥⎦⎤⎢⎣⎡+=∫∫)(sin)(sin4202tdtkbtdtkXωωωωππψψytωπ2πψψ−X2π0tkXωsinkb.sin1tByω=⎥⎦⎤⎢⎣⎡+=∫∫)(sin)(sin4202tdtXbtdtkXωωωωππψψ⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛−+=21arcsin2XbXbXbkXπ)(bXbb−kyxXBXjABXN111)(=+=⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛−+=211arcsin2XbXbXbkXBπ)(bXbb−kyxXBXjABXN111)(=+=⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛−+=21arcsin2XbXbXbkπ)(bXψψπ−ψsinX=∆2ππyykxxXtωtωπtXtxωsin)(=⎩⎨⎧∆−=)sin(0)(tXktyω∆∆≤tXtXωωsinsin,01=A.sin1tByω=)(sin)(1201tdttyBωωππ∫=)(sin)(420tdttyωωππ∫=)(sin)sin(42ttdtXkωωωππψ∫∆−=⎥⎦⎤⎢⎣⎡∆−=∫∫)(sin)(sin4222tdtXtdtkXωωωωππψπψ⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛∆−∆−∆−=211arcsin22XXXkXBππ)(∆X⎥⎥⎦⎤⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛∆−∆−∆−==211arcsin22)(XXXkXBXNππ)(∆X∆kyxbkyxXjABXN11)(+=)1(4)1()21(2)21arcsin(2−+⎥⎦⎤⎢⎣⎡−−+−+=XbXkbjXbXbXbXbkπππ)(bXMyxM−XMXNπ4)(=MyxM−h2)(14)(XhXMXN−=π)(hX≥7.3c-GxyNr(1)(1)(2)(2)c-GxyNr(3)(3)(4)(4)7.222Y-GN(X)2R()()()ωωωωjGXNjGXNjRjY)(1)()(+=()0)(1=+ωjGXN())(1XNjG−=ωY(s)G(s)-R(s)()()()ωωωωjGjGjRjY+=1)(()01=+ωjG()1−=ωjG()ωjG)(1XN−(1)(1)()ωjG)(1XN−(2)(2)()ωjG)(1XN−(3)(3)()ωjG)(1XN−()ωjGReImAABBtXωsin00)(1XN−()ωjGReImAABB00)(1XN−AA:::)(1XN−↑XAAAABB:::)(1XN−BBBBBB()ωjGReImAABB00)(1XN−↑X()ωjGReImAABB00)(1XN−AA::AAAAAABBBBCC)(AA′→↑X↑XBA→′)(AA′′→↓X↓XCA→′′AABB::()ωjGReImAABB00)(1XN−AAAAAABBBBBBBB)(BB′→↑X↓XBB→′)(B′′→B↓X↑XBB→′′7.17.133-2)10025.0)(101.0(460++sss33XMXNπ4)(=(())(1)(1)XMXNπ4)(=2=MXXNπ8)(=(2)(2)XXNπ8)(=8)(1XXNπ−=−0≥X-N-1(X)∞010∞−393.0−X-N-1(X)∞01ImRe0)(1XN−−393.0−0∞−393.0−(3)(3))10025.0)(101.0(460)(++=ssssG)10025.0)(101.0(460)(++=ωωωωjjjjG22)0025.0(1)01.0(1460)(ωωωω++=jG()ωωωϕ0025.0tan01.0tan9011−−−−−=oω)(ωjG15059.1)(ωϕo167−18013.1o175−20092.0o180−25058.0o190−40020.0o211−∞0o270−ImRe0)(1XN−−393.0−)(ωjG(4)(4))105.21(0125.0460)(252ωωωω−×−+−=jjG[]0)(Im=ωjGsradA/200=ωAImRe0)(1XN−−393.0−)(ωjG)(ωjG[]92.0)(Re200−==ωωjG92.08)(1−=−=−−XXNπ34.2=AXAImRe0)(1XN−−393.0−)(ωjG92.0−ttyA200sin34.2)(=(5)(5))(1XN−−)(tyAAAAAImRe0)(1XN−−393.0−)(ωjGA7.27.244-0.71.7)10025.0)(101.0(460++sss44(())2)(14)(XhXMXN−=π)(hX≥(1)(1),14)(2⎟⎠⎞⎜⎝⎛−=XhXMXNπhX≥7.1=M7.0=h,7.018.6)(2⎟⎠⎞⎜⎝⎛−=XXXNπ7.0≥X(2)(2)27.0118.6)(1⎟⎠⎞⎜⎝⎛−−=−XXXNπ)7.0(≥XX-N-1(X)∞77.025.3−∞−∞−0))((1=−−dXXNd0)7.0118.6(2=⎟⎠⎞⎜⎝⎛−−XXdXdπ99.0=X647.0)99.0(1−=−−NX-N-1(X)99.0∞7.0647.0−∞−∞−ImRe0)(1XN−−647.0−(3)(3))10025.0)(101.0(460)(++=ssssG)10025.0)(101.0(460)(++=ωωωωjjjjG)105.21(0125.0460252ωωω−×−+−=j22)0025.0(1)01.0(1460)(ωωωω++=jG()ωωωϕ0025.0tan01.0tan9011−−−−−=oω)(ωjG15059.1)(ωϕo167−18013.1o175−20092.0o180−25058.0o190−40020.0o211−∞0o270−ImRe)(1XN−−647.0−0)(ωjG??(4)(4))105.21(0125.0460)(252ωωωω−×−+−=jjGImRe)(1XN−−647.0−0)(ωjGAB[]0)(Im=ωjGsradBA/200==ωω)(ωjG[]92.0)(Re200−==ωωjG92.07.0118.6)(21−=⎟⎠⎞⎜⎝⎛−−=−−XXXNπ757.0=AX843.1=BXttyA200sin757.0)(=ttyB200sin843.1)(=(5)(5)ImRe)(1XN−−647.0−0)(ωjGAB)(tyA)(1XN−−AAAABBBB)(tyB)(1XN−−11)(1XN−−114yx114−XMXNπ4)(=22)(1XN−−3313=Myx221=h224)(14)(XMhjXhXMXNππ−⎥⎦⎤⎢⎣⎡−=)hX(≥1.-10010702++ss11)(XN224)1(14)(XjXXMXNππ−−=)1,1(=≥MX2.-42)1(10+ss22XMXNπ4)(=(())