1E369-系航模显、分桥幅控制 引例状态空间模型(State Space Form) 2.3模型形式 School of Mechanical Engineering 睡E369-4 ecture23 School of Mechanical Engineering ME369-ecture 2.3 Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University Fall 2015 状态空间模型 输入/输出模型 u={4,h,.,4nm} 状态变量 y={4,2,,yp 输入量 轴出量 输入量 X={,3,x} 雏出最 u1) 线性定常系统 (t) (Linear time invariant,LTI) 年=fx,叫品叫山) 状态方程 i=A+B阳 克=(化高,4马,4) n阶常徽分方程 一阶常撒分方程组 a y)+dy+.+a+ay+doy =,,44,44) =b)+bii+hi+bou 输出方程了=C+Du =8(,,4,44) =8(,高X,4,马马山) yo±(dldi)'y 代数方叠姐 p=8p(,4,,马…) Schoel of Mechanical Engineering ME369-leeture 2.3 School of Mechanical Engineering ME369-ecture 2.3 Shanshai lias Tong Unbrsraity Fall 2015 Shanghai Fsg Tora University Fall 2015 1
1 BE315-Lecture 2.3 Fall 2011 ME369-lecture 2.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University ME369-系统模型、分析与控制 2.3 模型形式 BE315-Lecture 2.3 Fall 2011 ME369-lecture 2.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [引例]状态空间模型(State Space Form) BE315-Lecture 2.3 Fall 2011 ME369-lecture 2.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 状态空间模型 1 1 1 2 3, 1 2 3 2 2 1 2 3, 1 2 3 1 2 3, 1 2 3 ( , , ..., , , , ,... ) ( , , ..., , , , ,... ) ... ( , , ..., , , , ,... ) n m n m nn n m x fxx x xuu u u x f xx x xuu u u x f xx x xuu u u 状态方程 一阶常微分方程组 1 2 3, { , , ..., }n x x xx x 1 2 3, { , , ..., }m u uu u u x xu A B 状态变量 输入量 1 2 3, { , , ..., }p y yyy y 输出量 yxu C D 1 1 1 2 3, 1 2 3 2 2 1 2 3, 1 2 3 1 2 3, 1 2 3 ( , , ..., , , , ,... ) ( , , ..., , , , ,... ) ... ( , , ..., , , , ,... ) n m n m pp n m y gxx x xuu u u y g xx x xuu u u y g xx x xuu u u 输出方程 代数方程组 BE315-Lecture 2.3 Fall 2011 ME369-lecture 2.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 输入/输出模型 n阶常微分方程 u t( ) y( )t 输入量 输出量 线性定常系统 (Linear time invariant, LTI) 1 1 210 1 1 210 ... ... n n n n m m m m a y a y ay ay ay b u b u b u bu b u (/ ) n n y d dt y
对比 【例11]矢量形式 状态空间模型 10元+8元+40x1-25x3=0) 给出了系统的内部状态 5元2-25x1+25x2-5元=3u(0) 一马于分解复杂构成的输出 一易于计算机仿真 一可用于表达多输入多轴出(ulti-input multi-output,0)、 非线性系统 输入输出模型 衰达明确 一时城求解困难 一可转化为颜域,传递函数(t缸ansfer functions,.TF)工程应用广泛 Schoel of Mechanical Engineering 睡E369-4 eeture23 School of Mechanical Engineering ME369-ecture 2.3 Shanghai Jiao Tong University Fall 2015 Shanghai Jiao Tong University Fall 2015 [例1-2]状态空间模型 [例1-3引输入输出模型 10元+8元+40x-25x2=(t) 10元+8元+40x-25x2=4() 5元-25x1+25x3-5元=3u(t) 5元2-25x1+25x2-5元=3u(t) School of Mechanical Engineering ME369-leeture 2.3 School of Mechanical Engineering ME369-ecture 2.3 Shanshai Jias Tena Unbrsraity Fall 2015 Shanghai Fss Toma University Fall 2015 2
2 BE315-Lecture 2.3 Fall 2011 ME369-lecture 2.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 对比 状态空间模型 输入输出模型 --表达明确 --时域求解困难 --可转化为频域,传递函数(transfer functions,TF)工程应用广泛 --给出了系统的内部状态 --易于分解复杂构成的输出 --易于计算机仿真 --可用于表达多输入多输出(multi-input multi-output ,MIMO)、 非线性系统 BE315-Lecture 2.3 Fall 2011 ME369-lecture 2.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例1-1] 矢量形式 11 1 2 2 1 21 10 8 40 25 ( ) 5 25 25 5 3 ( ) x x x x ut x x x x ut BE315-Lecture 2.3 Fall 2011 ME369-lecture 2.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 11 1 2 2 1 21 10 8 40 25 ( ) 5 25 25 5 3 ( ) x x x x ut x x x x ut [例1-2] 状态空间模型 BE315-Lecture 2.3 Fall 2011 ME369-lecture 2.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 11 1 2 2 1 21 10 8 40 25 ( ) 5 25 25 5 3 ( ) x x x x ut x x x x ut [例1-3] 输入输出模型