Ch. 5 Block Diagram Reduction

Front 1

Name the four components of a block diagram for a linear, time-invariant system.

Back 1

Signals, systems, summing junctions, pickoff points

Front 2

Name three basic forms for interconnecting subsystems.

Back 2

Cascade, parallel, feedback

Front 3

For each of the forms in Question 2, state (respectively) how the equivalent transfer function is found.

Back 3

Product of individual transfer functions, sum of individual transfer functions, forward gain divided by
one plus the product of the forward gain times the feedback gain

Front 4

Besides knowing the basic forms as discussed in Questions 2 and 3, what other equivalents must you know in order to perform block diagram reduction?

Back 4

Equivalent forms for moving blocks across summing junctions and pickoff points

Front 5

For a simple, second-order feedback control system of the type shown in Figure 5-14, describe the effect that variations of forward-path gain, K, have on the transient response.

Back 5

As K is varied from 0 to ∞, the system goes from over damped to critically damped to under damped.
When the system is under damped, the settling time remains constant.

Front 6

For a simple, second-order feedback control system of the type shown in Figure 5-14, describe the changes in damping ratio as the gain, K, is increased over the underdamped region.

Back 6

Since the real part remains constant and the imaginary part increases, the radial distance from the origin
is increasing. Thus the angle θ is increasing. Since ζ= cos θ the damping ratio is decreasing.

Front 7

Name the two components of a signal-flow graph.

Back 7

Nodes (signals), branches (systems)

Front 8

How are summing junctions shown on a signal-flow graph?

Back 8

Signals flowing into a node are added together. Signals flowing out of a node are the sum of signals
flowing into a node.

Front 9

If a forward path touched all closed loops, what would be the value of ?

Back 9

One

Front 10

Name five representations of systems in state space.

Back 10

Phase-variable form, cascaded form, parallel form, Jordan canonical form, observer canonical form

Front 11

Which two forms of the state-space representation are found using the same method?

Back 11

The Jordan canonical form and the parallel form result from a partial fraction expansion.

Front 12

Which form of the state-space representation leads to a diagonal matrix?

Back 12

Parallel form

Front 13

When the system matrix is diagonal, what quantities lie along the diagonal?

Back 13

The system poles, or eigenvalues

Front 14

What terms lie along the diagonal for a system represented in Jordan canonical form?

Back 14

The system poles including all repetitions of the repeated roots

Front 15

What is the advantage of having a system represented in a form that has a diagonal system matrix?

Back 15

Solution of the state variables are achieved through decoupled equations. i.e. the equations are solvable
Individually and not simultaneously.

Front 16

Give two reasons for wanting to represent a system by alternative forms.

Back 16

State variables can be identified with physical parameters; ease of solution of some representations

Front 17

For what kind of system would you use the observer canonical form?

Back 17

Systems with zeros

Front 18

Describe state-vector transformations from the perspective of different bases.

Back 18

State-vector transformations are the transformation of the state vector from one basis system to another.
i.e. the same vector represented in another basis.

Front 19

What is the definition of an eigenvector?

Back 19

A vector which under a matrix transformation is collinear with the original. In other words, the length
of the vector has changed, but not its angle.

Front 20

Based upon your definition of an eigenvector, what is an eigenvalue?

Back 20

An eigenvalue is that multiple of the original vector that is the transformed vector.