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 · Last modified: 2015/01/06 21:44 by ryancha
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