ME369-系统模型、分析与控剂 2.3模型形式 School of Mechanical Engineering ME369-lecture 2.3 Shanghai Jiao Tong University Fall 2015 [引例]状态空间模型(State Space Form) School of Mechanical Engineering ME369-lecture 2.3 Shanghai Jiao Tong 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)
状态空间模型 u={4,4,4.,un} 状态变量 y={4,,.…,yp 输入量 X={化1,x2,3,Xn} 输出量 元=f(X,2,x3.,Xn,41,4,,4m) 状态方程 文=Ak+Bu 元2=f(x,x2,x3.,xn,4,42,43,m) 一阶常微分方程组 n=fn(x1,x2,x3.,xn,4,42,43,24m) 输出方程 y=Cx+Du 片=81(X1,x2,X3,,xn,41,42,43,4m) 2=82(X1,X2,X3,,xn,41,42,43,4m) 代数方程组 yp=8p(X1,2,x3.,Xn41,42,43,4nm) School of Mechanical Engineering ME369-lecture 2.3 Shanghai Jiao Tong University Fall 2015 输入/输出模型 输入量 输出量 u(t) 线性定常系统 yt) (Linear time invariant,LTI) n阶常徽分方程 a,y0+anya-+…+a2ji+a少+ay =bn侧+bn-1m-+…+b,i+bi+b,u y(m)(dldt)"y School of Mechanical Engineering ME369-lecture 2.3 Shanghai Jiao Tong University Fall 2015
2 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 f xx 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 uuu u x xu A B 状态变量 输入量 1 2 3, { , , ..., }p y yyy y 输出量 y C D x u 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 状态空间模型 一给出了系统的内部状态 一易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输出(multi-input multi-output,MIMO)、 非线性系统 输入输出模型 一表达明确 一时域求解困难 -可转化为频域,传递函数(transfer functions,TF)工程应用广泛 School of Mechanical Engineering ME369-lecture 2.3 Shanghai Jiao Tong University Fall 2015 [例1-1]矢量形式 10x+8x+40x-25x2=(t) 5x2-25x+25x2-5x=3(t1) School of Mechanical Engineering ME369-lecture 2.3 Shanghai Jiao Tong University Fall 2015
3 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
[例1-2]状态空间模型 10元+8元+40x1-25x2=u(t) 5求2-25x1+25x2-5x=3u(t) School of Mechanical Engineering ME369-lecture 2.3 Shanghai Jiao Tong University Fall 2015 [例1-3]输入输出模型 10x+8x+40x-25x2=(t) 5求2-25x1+25x2-5x=3u(t) School of Mechanical Engineering ME369-lecture 2.3 Shanghai Jiao Tong University Fall 2015 4
4 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