HW #6

Due Thursday, February 4

An armature-controlled D.C. motor (similar to the one we have in the controls lab), has the following functional schematic

Where Va is the input voltage, q _m is the output motor shaft angular position, E_b is the back emf, T_m is the motor torque, F is the coefficient of friction, J is inertia, R_a is the armature resistance, and L_a is the armature inductance. The physical equations relating these variables are:

where K_T is the motor torque constant and K_b is the back emf constant.

1a) Use the above equations and your circuit analysis skills to find the following sub-system transfer functions:

b) Use your answers to part a) to help you to draw a block diagram for the D.C. motor with Va as the input and q _m as the output.

c) Now reduce this block diagram to find the overall transfer function, q _m(s)/V_a(s)

d) In EE571, we actually measure the values for the D.C. motor parameters. Suppose we have done this and we obtain the transfer function,. Find the unit step response.

e) In EE571, it is our goal to make the output follow our reference input (in this case 1). Notice that your answer to part d) has a ramp which tends to infinity (which is not 1). In EE571, we employ FEEDBACK as a mechanism to stabilize systems (i.e., we feed the output back to the input). Find the step response for the following system with simple negative unity feedback:

e) Does y(t) now follow the reference input (i.e., is the final value of y(t)=1)?

2a) Reduce the following block diagrams to obtain the transfer function shown:

1)

2)