Identified linear system contribution of input is zero

Question

Valeriy 2024-4-27

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2112276-identified-linear-system-contribution-of-input-is-zero

评论： Valeriy 2024-4-27

采纳的回答： Paul

在 MATLAB Online 中打开

Hello,

I identified a cont. 3rd order linear system using System Identification Toolbox:

y = Cx + Du + e
dx/dt = Ax + Bu + Ke

Upon inspecting the model (which looked decent to me) I see that the "D" value, which is the contribution of input to system output, is zero.

How can this be? The system describes a DC motor controlled by PWM commands (output is shaft position). Surely the commands sent to the motor should influence the position?

I get the following values:

% A weights (3x3 matrix)
A = [ ...
  0.0356,   -3.4131,  -14.9525;
  -1.0591,   85.8128,  334.3098;
  1.5729,  -95.1123, -175.5517;
];
% B weights (3x1 vector)
B = [ ...
  -0.0019;
  0.0403;
  -0.0225;
];
% C weights (1x3 vector)
C = [ -5316.9, 24.87, 105.92 ];
% D weight (scalar)
D = 0;
% K weights (3x1 vector)
K = [ ...
  -0.0025;
  -0.0582;
  0.0984;
];
% Initial state
x0 = [ ...
  -0.0458;
  0.0099;
  -0.0139;
];

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Paul 2024-4-27

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2112276-identified-linear-system-contribution-of-input-is-zero#answer_1448776

The commands do influence the position of the motor through the dynamics as described by the differential equation. The output of the motor is position, so the input to the motor can't have an instantaneous effect on the position, as would be the case if D were non-zero. For example, torque has to integrate to velocity, which in turn has to integrate to position. Hence, a physically realizable applied torque will not cause an instantaneous change in position.