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cs-470:pd-controllers [2015/01/06 21:44] (current)
ryancha created
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 +==P Controller==
  
 +* $y_t$ = where I want to be at time t.
 +* $x_t$ = where I am at time t.
 +* $(y_t - x_t)$ = error 
 +
 +* P controller (P for proportional)
 +* $a_t = K_P (y_t - x_t)$
 +* Is the spring law.
 +
 +==STABILITY==
 +
 +* Stable = small perturbations lead to a bounded error between the robot and the reference signal.
 +* Strictly Stable= it is able to return to its reference path upon such perturbations ​
 +* P controller is stable, but not strictly stable. ​
 +
 +==PD controller==
 +
 +* $a_t=K_P(y_t-x_t)+K_D*\frac{d(y_t-x_t)}{d_t}$
 +* Notice that in discrete land, you can't compute the derivative directly, instead approximate:​
 +** $ d(y_t-x_t) = (y_t-x_t) - (y_{t-1}-x_{t-1})$
 +* Dampens the perturbations. ​
 +
 +[[pd code]]
 +
 +Other links: [[http://​students.cs.byu.edu/​~cs470ta/​goodrich/​fall2008/​MATLAB/​PDControl.m Original code]]
 +
 +I like to:
 +
 +*Change N=200 see it act like a spring
 +*kd=4.5 dampens
 +*kp=.01
 +*kd=0.5
 +*Add the random term in
 +*Add the cos term
 +*Take out the random term
 +*Play with kp and kd
 +*Can you over do kd?
cs-470/pd-controllers.txt ยท Last modified: 2015/01/06 21:44 by ryancha
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