连续系统离散化方法

5.2.11()1()()UsDsEss==5.1()()dutetdt=()()(1)()dutukukekdtT−−≈=5.25.2Z1(1)()()zUzTEz−−=1()1()1()UzDzzEzT−==−5.35.15.35.1s11zsT−−=5.411()()zsTDzDs−−==5.51z−2211...2TsTszeTs−−==−+−5.611z−Ts≈−21811zsT−−=5.7s5.45.4zs0)Re(sz01Re1Re1⎟⎠⎞⎜⎝⎛−=⎟⎟⎠⎞⎜⎜⎝⎛−−TzzTzTzωσjz+=01Re⎟⎟⎠⎞⎜⎜⎝⎛+−+ωσωσjj()()()()222222221ReRe0jjjjjσωσωσσωωσσωσωσωσωσω⎡⎤+−−⎡⎤−++−+==⎢⎥⎢⎥+−++⎣⎦⎣⎦2222121⎟⎠⎞⎜⎝⎛+⎟⎠⎞⎜⎝⎛−ωσsz2/1=σ0=ω5-32/1jωσIm0ω=1z=Re5-3sz5-3sz219()sD()zDT2()1()()UsDsEss==5.8()()dutetdt=()(1)()()dutukukekdtT+−≈=Z(1)()(zUzTEz−=)()1()1()UzDzzEzT==−5.95.85.9s()Ds1zsT−=5.101()()zsTDzDs−==(5.11z221...2TsTszeTs==+++2201zTs≈+1zsT−=s5.10zs0)Re(sz1Re0zT−⎛⎞⎜⎟⎝⎠ωσjz+=01Re⎟⎠⎞⎜⎝⎛−+Tjωσ0T01−σ1σ5-4jωσIm0ω=1z=Re5-4szsz3TustinZTsze=Tse22122TsTsTseee−=5.121212TszTs+=−5.13s11211zsTz−−−=+5.145-5()[(1)][[(1)]()]2TykTykTxkTxkT=−+−+5.15kT5.15Z()ykT11()1()21YzTzXzz−−+=−5.165-55.1611211()()zsTzDzDs−−−=+=5.175.14sz222()Dz5.14s[Re()0]sz112121ReRe011zzTzTz−−⎛⎞−−⎛⎞=⎜⎟⎜⎟++⎝⎠⎝⎠T00)1(21Re11Re11Re2222⎟⎟⎠⎞⎜⎜⎝⎛++++−=⎟⎟⎠⎞⎜⎜⎝⎛++−+=⎟⎠⎞⎜⎝⎛+−ωσωωσωσωσjjjzz2221+ωσz5-6szzTsez=jωσIm0ω=1z=ReBωω=Bωω=∞5-6szD(s)D(z)D(s)D(z)D(z)D(s)D(s)5.1ssEsUsD1)()()(==5.142231111112(1)2(1)(1)(1)()1(1)()()()2(1)zszTzsTzUzTzDzDsEzsz−−−−−−−=−+=++====−)()1(2)()1(11zEzTzUz−−+=−{}])1[()(2])1[()(TkekTeTTkukTu−++−=kTD(z))()(kTekTu1()Dss=MATLABT=1snum=1;den=[1,0];[dnum,dden]=c2dm(num,den,1,'tustin');printsys(dnum,dden,'z')num/den=0.5z+0.5-----------z–1numdenc2dmMATLABtustindnumddensZΩωsj=ΩjTzeω=11211zsTz−−−=+2112tan2jTjTejTeTjTωωω−−−Ω=+=5.182242tan2TTωΩ=5.19ΩωTω0~πΩ0~∞0Tωπ]()Ds()Dz()Ds()Ds()Dz1SZ()Ds()Dz()Dz()Ds4()Ds()Dz1()[()DgkTZDz−=1()[()]gtLDs−=kTtDtgkTg==)()(()[()]DzZDs=5.20()Ds()Dz225()DszZZ()Dz()Ds()Ds()Dz()Dz()Ds()Ds()Dz()Ds5()Ds()Dz()Dz11111()()1tkTZDzLDszs−−−=⎡⎤⎡=⎢⎥⎢−⎣⎦⎣⎤⎥⎦111()1ZDzz−−⎡⎤⎢⎥−⎣⎦()Dz11()LDss−⎡⎤⎢⎥⎣⎦Z()Ds1111()()1DsDzZLDsZzs−−⎧⎫⎡⎤⎡⎤⎡==⎨⎬⎢⎥⎢⎥⎢−⎣⎦⎣⎦⎣⎩⎭()s⎤⎥⎦1()()(1)DsDzzZs−⎡⎤=−⎢⎥⎣⎦2261()()TseDzZDss−⎡⎤−=⎢⎥⎣⎦5.21--5-7()Ds()Ds()Ys()Xs1Tses−−5-7()DsZ()Ds()Dz()Dz()Ds6ZZZ()Gs()Dz()Gs()Dz()Gsnm()mn≤()Gsm()nm−s=∞112()()()(szGsspspsp3)+=+++1sz=−s=∞Z2271()GssTze=()2222()()2cosaTajbTaTaTsazesajbzesabzzebTe−−±−−+⇒−+±⇒−++⇒−+M5.222()Gss=∞1z=−31()Dz()Dz410lim()lim()zsDzGs→→=5.231lim()lim()zsDzGs→−→∞=5.242n2()Gs()Dzm−()Dz5.2()1/()Gssa=+Z21()aTzDzKze−+=−5.2310lim()lim()211zsaTDzGsKe→→−==−12aTeK−−=22811()2aTaTezDzze−−−+=−31()1aTaTDzKzeKe−−=−=−1()aTaTeDzze−−−=−1()Dssa=+ZMATLABT=1=1anum=1;den=[1,1];ts=1;[dnum,dden]=c2dm(num,den,ts,'matched');printsys(dnum,dden,'z')num/den=0.63212-----------z-0.36788c2dmZ5.3()/()Gsssa=+Z01()TaTaTzezDzKKzeze−⋅−−−−==−−1lim()lim()1111zsaTDzGsKe→−→∞−=−−=−−22912aTeK−+=11()2aTaTezDzze−−+−=⋅−7:5.1()/()Gsasa=+5.1()/()Gsasa=+()Dz()Dz11zsT−−=1()1aDzzaT−=−+111zsTz−−−=11()1aDzzaTz−−=−+11211zsTz−−−=+11()211aDzzaTz−−=−++()[()]DzZGs=()aTazDzze−=−1()()TseDzZGss−⎡⎤−=⎢⎥⎣⎦1()aTaTeDzze−−−=−Z11()2aTaTezDzze−−−+=−2306