状态控制表达中-状态变量的转换
Transformation: State Space ↔ State Space
系统的状态变量表示不是唯一的。事实上，有无穷多的表现形式。下面将讨论从一组状态变量转换到另一组状态变量的方法，并给出一个示例。
1 Use MatLab to convert from state space to state space (symbolic) 2 This script requires the MatLab's symbolic toolbox 3 4 % Start by clearing everything 5 clear all 6 clc 7 format compact 8 Declare all symbolic variables 9 10 syms k1 k2 b m 11 Define state space system 12 13 A=[0 1 0; -(k1+k2)/m 0 k1/m; k1/b 0 -k1/b]; 14 B=[0; 1/m; 0]; 15 C=[0 0 1]; 16 D=0; 17 18 Define state transformation matrix and find its inverse 19 20 T=[1/2 0 1/2; -1 0 1; 0 1 0;]; 21 Tinv=inv(T) 22 Tinv = 23 1.0000 -0.5000 0 24 0 0 1.0000 25 1.0000 0.5000 0 26 27 Find new state space system 28 29 % Ahat 30 Ahat = simplify(T*A*Tinv) 31 32 % Bhat 33 Bhat = T*B 34 35 % Chat 36 Chat = C*Tinv 37 38 % Dhat 39 Dhat = D 40 Ahat = 41 [ 0, -k1/(2*b), 1/2] 42 [ 0, -k1/b, -1] 43 [ -k2/m, (2*k1 + k2)/(2*m), 0] 44 Bhat = 45 0 46 0 47 1/m 48 Chat = 49 1.0000 0.5000 0 50 Dhat = 51 0