$(20$ pts$)$ a$)$ Find the wheel count per revolution if the system uses an encoder with

a rating of $500$ cpr $($counts per revolution$)$ and the gear ration is $50$:$1.$ Assume

that the system employs quadrature decoding. Also, find the wheel angular

resolution $[$deg$/$count$].$

b$.$ Based on the figure below, an error occurs if the code execution time is greater

than the control time step. Discuss possible solutions to avoid the control error.