Chapter 9, Problem 44P

A position control is to be designed with a 10% overshoot, a settling time of I second, and $K_v=1000$ . You have on hand an amplifier and a power amplifier whose cascaded transfer function is $K_1/\left(s+40\right)$ with which to drive the motor. Two 10-turn pots are available to convert shaft position into voltage. A voltage of $\pm 20\pi$ volts is placed across the pots. A dc motor whose transfer function is of the form

$\frac{{\theta }_0\left(s\right)}{E_a\left(s\right)}=\frac{K}{s\left(s+a\right)}$

is also available. The following data are observed from a dynamometer test at 50 V. At 25 N-m of torque, the motor turns at 1433 rpm. At 75 N-m of torque, the motor turns at 478 rpm. The speed measured at the load is 0.1 that of the motor. The equivalent inertia, including the load, at the motor armature is 100 kg-m², and the equivalent viscous damping, including the load, at the motor armature is 50 N-m-s/rad.

a. Draw a complete block diagram of the system, specifying the transfer function of each component.

b. Design a passive compensator to meet the requirements in the problem statement.

c. Draw the schematic of the compensator showing all component values. Use an operational amplifier for isolation where necessary.

d. Use MATIAB or any other computer program to simulate your system and show that all requirements have been met.

MATLAB
ML