Chp. 2 Review Questions

Question 1

What are the two forms of Newton’s law?

Answer 1

Translational motion is described by F = ma. Rotational motion is
described by M = Iα.

Question 2

For a structural process to be controlled, such as a robot arm, what is the meaning of “collocated control”?
“Noncollocated control”?

Answer 2

When the actuator and the sensor are located on the same rigid body, the control is said to be “collocated.” When
they are on different bodies that are connected by springs, the control is “noncollocated.”

Question 3

State Kirchhoff’s current law.

Answer 3

The algebraic sum of all currents entering a junction or circuit is zero.

Question 4

State Kirchhoff’s voltage law.

Answer 4

The algebraic sum of voltages around a closed path in an electric circuit is zero.

Question 5

When, why, and by whom was the device named an “operational amplifier”?

Answer 5

In a paper in 1947, Ragazzini,
Randall, and Russell named the high-gain, wide-bandwidth amplifier used in feedback to realize operational
calculus “operations” the operational amplifier.

Question 6

What is the major benefit of having zero input current to an operational amplifier?

Answer 6

With zero input current the
amplifier does not load the input circuit; thus, the transfer function of the device is not dependent of the amplifier
characteristics. Also, the analysis of the circuit is simplified in this case.

Question 7

Why is it important to have a small value for the armature resistance Ra of an electric motor?

Answer 7

The armature resistance causes power loss when the armature current flows and thus reduces the efficiency of the
motor.

Question 8

What are the definition and units of the electric constant of a motor?

Answer 8

A rotating motor produces a voltage (called the back emf) in its armature proportional to the rotational speed.
The electric constant Ke is the ratio of this voltage to the speed, so that e = Ke*tetha dot . The units are volt-sec/radians.

Question 9

What are the definition and units of the torque constant of an electric motor?

Answer 9

When current ia flows in the
armature of an electrical motor, a torque τ is produced that is proportional to the current. The torque constant Kt
is the constant of proportionality, so that τ = Ktia. The units are Newton-meters/amp.

Question 10

Why do we approximate a physical model of the plant (which is always nonlinear) with a linear model?

Answer 10

Analysis and design of linear models is vastly simpler than with nonlinear models. Furthermore, it has been
shown (by Lyapunov) that, if the linear approximation is stable, then there is at least some region of stability for
the nonlinear model.