{"id":60,"date":"2009-07-14T20:24:02","date_gmt":"2009-07-14T20:24:02","guid":{"rendered":"https:\/\/blogs.mathworks.com\/seth\/2009\/07\/14\/refining-the-output-of-a-simulation\/"},"modified":"2009-07-14T20:25:29","modified_gmt":"2009-07-14T20:25:29","slug":"refining-the-output-of-a-simulation","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/simulink\/2009\/07\/14\/refining-the-output-of-a-simulation\/","title":{"rendered":"Refining the Output of a Simulation"},"content":{"rendered":"

Today I am pleased to share a post from regular guest\r\nblogger, Guy\r\nRouleau<\/a>.\u00a0 Enjoy!<\/p>\r\n\r\n

\"Guy<\/p>\r\n\r\n

I often use Simulink to model the dynamics of simple\r\nsystems. In most cases, the Simulink default settings provide a good tradeoff\r\nbetween accuracy and simulation speed. These settings usually allow me to\r\nobserve the signals I am interested in.<\/p>\r\n\r\n\r\n\r\n

I recently ran into situations where I needed to change\r\nthe default Simulink settings to observe the signals I was expecting.<\/p>\r\n\r\n\r\n\r\n

Let\u2019s begin by a very simple case: Simulating a 100Hz\r\nsine wave of amplitude 1 for 10 seconds<\/p>\r\n\r\n\r\n\r\n

\"The<\/p>\r\n\r\n\r\n\r\n

With the default Simulink settings, the Sine wave observed\r\non the scope is the following:<\/p>\r\n\r\n\r\n\r\n

\"The<\/p>\r\n\r\n\r\n\r\n

Before screaming \u201cSimulink is broken!\u201d, let\u2019s look at the\r\nwarning displayed at the MATLAB command prompt when playing this model. <\/p>\r\n\r\n\r\n\r\n

\"Warnings<\/p>\r\n\r\n\r\n\r\n

The first warning mentions that the selected solver\r\n\"ode45\" is replaced by the Variable-Step Discrete solver. The second warning\r\nsays that Simulink will use a default step size of 0.2 sec. <\/p>\r\n\r\n\r\n\r\n

The combination of these two warnings results in Simulink\r\nevaluating the Sine wave at time [ 0 \u00a00.2 \u00a00.4 \u00a0\u2026\u00a0 9.8 \u00a010 ] where it\u2019s value\r\nis always zero. To observe the Sine wave properly, a very useful option is to\r\nrefine the output:<\/p>\r\n\r\n\r\n\r\n

\"Configuration<\/p>\r\n\r\n\r\n\r\n

By setting an appropriate value for the refine factor, it\r\nis possible to observe the expected Sine wave. This is the result with a refine\r\nfactor of 250:<\/p>\r\n\r\n\r\n\r\n

\"Sine<\/p>\r\n\r\n\r\n\r\n

Now you might think, \"Interesting, but I never create\r\nmodels with only a Sine Wave.\" I agree, so let\u2019s look at a more realistic\r\nsimulation and model a servo motor commanded by a discrete controller. Our\r\nSimulink model looks like:<\/p>\r\n\r\n

\"Servo<\/p>\r\n\r\n

Using the default settings, the Scope block displays the\r\nposition, velocity and acceleration as:<\/p>\r\n\r\n\r\n\r\n

\"Servo<\/p>\r\n\r\n

Attentive eyes probably noticed that after 0.2 second,\r\nthe acceleration signal seems constant around a value of 14, while the velocity\r\nsignal is also constant at 1. Since the slope of the input ramp is 1, we can conclude\r\nthat Simulink computes the velocity value accurately, but why isn\u2019t the acceleration\r\nzero as one could expect?<\/p>\r\n\r\n\r\n\r\n

Maybe we should refine the output. Setting the refine\r\nfactor to 4 provides a better resolution in time and shows the real behavior of\r\nthe system.<\/p>\r\n\r\n

\"Servo<\/p>\r\n\r\n

In that case, it shows that the servo motor acceleration\r\nsignal oscillates when submitted to the 100Hz discrete steps of the command\r\ncoming from the computer.<\/p>\r\n\r\n\r\n\r\n

What else should we know about the refine factor?<\/strong><\/p>\r\n\r\n

\r\n