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 — cs-470:pd-controllers [2015/01/06 14:44] (current)ryancha created 2015/01/06 14:44 ryancha created 2015/01/06 14:44 ryancha created Line 1: Line 1: + ==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? 