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cs-470:pd-controllers [2015/01/06 14:44] (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? |