# Lecture 14


* here system is stable but it can be oscillatory and therefore we add some damping.


* Kv is effecting zheta and Kp is affecting omega . we usually want critically dampend system and for critically damped system zheta = 1 , Now if Kp is high there is disturbance rejection but we cannot make Kp too high otherwise we will reach that frequency where everthing will start shaking, and we have to keep away from it.
* response is higher with higher gain
* if this is real robot , with much larger gain , the structure start to vibrate and if we hit the resonating frequency everything will blow up
* we set zheta and omega , usually zheta is one and we have to set omega
* gains are need to be changed with mass we scale with mass to the unit mass system. we can also scale it with mass matrix.


* we first derive for unit mass and then multiple by mass.
* now we are adding some non-linear friction. we can model gravity than we can compenstae for the gravity
* we don't "b" we only know estimate given the estimate of state.
* we assuming that we will have some errors.
* here in the bloack diagram we are taking estimate of b and also unit mass controler scaled by mass estimate of the system so overall system will look like an unit mass system.
* in future we will have V,G, friction in place of b.
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* now with goal position we also have desired velocity, acceleration so now we have to modify f'
* if we only do $\ddot{x}_d$ system will drift therefore we will control error in velocity , position , acceleration.
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* what is an steady state error ? : error at zero velocity and zero acceleration.
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