• $y_t$ = 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.

• 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.

• $a_t=K_P(y_t-x_t)+K_D*\frac{d(y_t-x_t)}{d_t}$
• 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?