Engineers at HewlettPackard have contracted your time to con

Engineers at Hewlett-Packard have contracted your time to consult in the preliminary design of a new industrial laser printer. Laser printers such as those manufactured by HP use a laser beam to rapidly print copy pages. The engineers currently envision using a pivoting scanning mirror mounted to a servo motor to position the laser beam. The motor’s position will be controlled via a RC circuit consisting of a variable 0-28 VDC source in series with a resistor and a 180 micro?F capacitor.

The engineers at HP have decided that the laser beam pointing control system must have a settling time of Ts = 293 milliseconds to provide sufficient time for the toner to deposit onto the paper as it transits across the drum. However, the engineers are not sure what resistor (or combination of resistors) to use in the RC circuit to provide the required Ts, since the voltage source is variable between 0 and 28 V.   

As the controls engineer hired to consult on the project, what is your recommendation?

Laser Pivotating mirror Drum onisator Drum Toner Paper ionisator

Solution

the settiling time is given us = 293ms

so the settling of the system is equal to 5 times of the time constant if we consider 2% steady state tolarence. so we will consider the settling time is about 6 time constans. so 6*T = 293ms

where T time costant of the system. here we cosider first oder RC series circuit whose expression for time constant is given by T = RC = 293/6 ms = 48.8333ms

C = 180 micro farads

so R = ( 48.8333ms) /(180micro farads) = 271 ohms

so if want more delay in the responce we need to use more than this resistance. or else if we need to seetle less than this time we will go with less than this 271 ohm resistance