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Some time I found that some robot controller uses a critically damped reference control signal such as in Autonomous Surface Vehicle (ASV) heading controller. My question is how do we implement this reference signal in the actual robot implementation?

See figure heading example.

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  • $\begingroup$ Welcome to Robotics, Mei. As it stands, it's not clear what you're asking. Are you asking how you implement the Laplace transfer function on a microcontroller? Are you asking where the reference signal comes from? What work have you done so far while trying to solve your problem? Please edit your question to include what you want to happen, what you tried, what you expected to see, and what you saw. Showing details of the work you've done already really helps everyone understand what you're trying to do and where any conceptual or implementation errors may exist. $\endgroup$ – Chuck Jan 23 '18 at 14:43
  • $\begingroup$ Hi Chuck. Thank you for your response. I actually try to implement the reference signal given in the Figure. From my understanding, i have to discretize the transfer function at a specific sampling time and form a difference equation for implementation on the micro controller. But actually I also wonder why we need this low pass filter in the actual implementation? Or is it really just for simulation purpose? $\endgroup$ – Mei Jan 24 '18 at 7:45
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I think you misunderstood the Simulink. The transfer function is the system and the reference signal in the picture you've posted is the step function. The input for the system in the Simulink is a constant value of 20 magnitude. You can see that from the figure. The curve goes to 20 in 18 unit time and stays for the future which indicates the system is stable.

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  • $\begingroup$ Thank you Croco. Not really, the system model is not given in the model above. I understand your point but in some application such as ASV heading control, this kind of low pass filter for reference signal is implemented. $\endgroup$ – Mei Jan 26 '18 at 16:52
  • $\begingroup$ Well the low-pass filter is a system. $\endgroup$ – CroCo Jan 26 '18 at 16:58
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The transfer function in the simulink sketch serves as a pre-filter. In general, pre-filters are used to smooth the input since step reference signals are’nt logical for tracking (tracking step command will require infinite accelerations). Most of the time these filter are chosen as the close loop desired transfer function. Working this way creates a reference model for tracking and prevents integrator windup and derivative induced saturations in PID controllers. If you want to implement one in Matlab/Simulink you can design a continues reference model and then use the c2d command in Matlab which transforms continues systems into discrete systems given some sampling frequency.

Good luck!

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