How does Control Design Linear Analysis / LTI Viewer linearize trig functions

Question

Shawn 2017-9-6

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/355459-how-does-control-design-linear-analysis-lti-viewer-linearize-trig-functions

I'm getting questionable results using Simulink Control Design (R2008b) to linearize a model containing trig functions (a transformation matrix from aircraft body axes to earth axes). I've searched documentation but was unable to find any information on how the cosine and sine functions are linearized. I was expecting sine to use a small angle approximation, i.e. sin(x) = x for small angles and cos(x) = 1 for small x.

This isn't what Simulink Control Design appears to do. As an experiment, I built a very simple Simulink model consisting of a step input followed by a gain (5/57.3) followed by the sine block followed by a one second 1st order lag [1/(s+1)]. Running the model gives the expected 1st order lag response with the output settling at a final value of sin(5/57.3). Running Simulink Control Design with the input port ahead of the gain and the output port on the output of the 1st order lag yields the same result for a LTI Viewer step response.

But change the trig function to a cosine and the results are not the same. Running the nonlinear model results in the expected 1st order lag response with a final value of cosine (5/57.3). But running Simulink Control Design yields a zero output for the linear step response.

Obviously I'm missing something fundamental here, probably associated with operating points. The Control Design linearization option was set to "Block by block analytic. If I try to switch to "numerical perturbation" I get an error message "The linearization must have both an input and an output to be viewed in the LTI viewer."

Perhaps I should just replace the body to earth transformation matrix with small angle approximations, i.e. sin(x) = x; cos(x) = 1. My analysis will be using small angle perturbations anyway. The end objective is to get a Bode plot of lateral stick to cross-track response for a landing approach.