title: How to smooth rectangular signal with high order rate-limiter in Simulink?
body: <p>Imagine I have a rectangular reference value for the position/displacement <code>x</code> and I need to smooth it. </p>
  
  <p>The math for translatoric movements is quite simple:</p>
  
  <pre><code>speed: v = x'
  acceleration: a = v' = x''
  jerk. j = a' = v'' = x'''
  </code></pre>
  
  <p>I need to limit all these values. So I thought about using rate limiters in Simulink:
  <img src="https://i.stack.imgur.com/OYuva.jpg" alt="enter image description here">
  This approach works perfect for ramp signals, as you can see in the following output:
  <img src="https://i.stack.imgur.com/CDBrF.jpg" alt="enter image description here"></p>
  
  <p>BUT, my reference signals for <code>x</code> are no ramps, they are rectangles/steps. Hence the rate limiters are not working, because the derivatives they get to limit are already infinite and Simulink throws an error. How can I resolve this problem? Is there actually a more elegant way to implement the high order rate-limiters? I guess this approach could be unstable in some cases.</p>
  
  <hr>
  
  <p>continue reading: <a href="https://stackoverflow.com/questions/20240450/3rd-order-rate-limiter-in-simulink-how-to-generate-smooth-triggered-signals">related question</a></p>