Lab 4 - Virtual Dampers

Two kinds of virtual dampers were experimented with in this lab. A digital damper was implemented by use of a memory variable that would store the previous location of the armature and compare it against the current location. The difference would then be multiplied by a damping gain, b, and added to the total force equation as follows:

Force = (Neutral Position - Current Position)*KSpring + (Previous Position - Current Position)*KDamper

Again the sign was taken to map to the direction of the PWM and the absolute value because the magnitude of the PWM.

The range of damping coefficients (aka gain b) was somewhat narrow before the system would grow unstable. We do not believe this was due to the mathematical dynamics of the system, because the system became unstable with high damping, which is the opposite as one would think. Instead, like we saw in the previous lab with the spring constant, since the signal and PWM are sampled and sent out in discrete packets of time, they are simply not fast enough to change to compensate for large forces. Therefore each successive PWM would grow unboundedly if any PWM was enough to push the armature fast enough that the discrete system could not catch up.

Regardless, some damping was implemented and its effects can be seen below.



Then, after the digital implementation was proven a success, an analog analog was created using a capacitor in series with Ri and in parallel with Rf. Because of the time needed to charge the capacitors, there was induced a lag between full conveyance of signal from the input and the output of op-amp. Therefore, if the voltage changed too quickly (velocity), the charge would not catch up and the action would be weakened. This can be observed in the form of damping. Below is a video of the effect of the capacitor in parallel with Rf and then the undamped system after the capacitor has been removed.



Since the gains were easier to modify in the digital implementation, the other virtual environments such as the virtual wall, etc. were performed through purely digital computations. They were no more elaborate than in the previous lab (adjusting spring gains very high for walls, etc.), and the effects were comparably improved as they were with the simply virtual spring.