1 $In a block diagram, what is the function of a summing point?$

Block diagram representation and reduction techniques Easy

A.

To take a signal for feedback

B.

To represent the overall transfer function

C.

To add or subtract signals algebraically

D.

To multiply two signals

2 $If two blocks with transfer functions and are connected in cascade (series), what is their equivalent transfer function?$

Block diagram representation and reduction techniques Easy

A.

B.

C.

D.

3 $If two blocks with transfer functions and are connected in parallel, what is their equivalent transfer function?$

Block diagram representation and reduction techniques Easy

A.

B.

C.

D.

4 $What is the primary goal of block diagram reduction techniques?$

Block diagram representation and reduction techniques Easy

A.

To analyze the transient response

B.

To find the overall transfer function of the system

C.

To determine the stability of the system directly

D.

To increase the number of blocks in the diagram

5 $In a Signal Flow Graph (SFG), what does a node represent?$

Signal flow graphs Easy

A.

The direction of signal flow

B.

A system variable or signal

C.

A system component or block

D.

A feedback loop

6 $What is a 'forward path' in a Signal Flow Graph?$

Signal flow graphs Easy

A.

A path that only contains nodes with a gain of 1

B.

A path from the input node to the output node that does not traverse any node more than once

C.

A path that starts and ends at the same node

D.

Any path between two nodes in the graph

7 $A 'loop' in a Signal Flow Graph is a path that:$

Signal flow graphs Easy

A.

Has no gain associated with it

B.

Starts and ends at the same node

C.

Connects the input node to the output node

D.

Is always a self-loop on a single node

8 $In a Signal Flow Graph, the arrows on the branches indicate the:$

Signal flow graphs Easy

A.

Direction of signal flow

B.

Phase of the signal

C.

Stability of the system

D.

Magnitude of the signal

9 $Mason's Gain Formula is a method used to find the:$

Mason Gain Formula Easy

A.

Overall transfer function of a system from its Signal Flow Graph

B.

Poles and zeros of a system

C.

Steady-state error of a system

D.

Stability margin of a closed-loop system

10 $In Mason's Gain Formula, what are 'non-touching loops'?$

Mason Gain Formula Easy

A.

Loops that have the same starting node

B.

Loops that do not share any common nodes

C.

Loops that are adjacent to each other

D.

Loops that have gains of opposite signs

11 $What does the term represent in the standard Mason's Gain Formula?$

Mason Gain Formula Easy

A.

The pole at location

B.

The gain of the loop

C.

The product of all loop gains

D.

The gain of the forward path

12 $The 'poles' of a transfer function are the values of 's' for which the magnitude of becomes:$

Concept of Poles and Zeros Easy

A.

Unity (1)

B.

Infinite

C.

Zero

D.

A negative value

13 $The 'zeros' of a transfer function are the roots of which part of the function?$

Concept of Poles and Zeros Easy

A.

The denominator polynomial

B.

The characteristic equation

C.

The impulse response

D.

The numerator polynomial

14 $For the transfer function, which of the following is a pole of the system?$

Concept of Poles and Zeros Easy

A.

B.

C.

D.

15 $For the transfer function, what is the zero of the system?$

Concept of Poles and Zeros Easy

A.

B.

C.

D.

16 $What is a primary advantage of using negative feedback in a control system?$

Effect of feedback Easy

A.

It always increases the overall gain of the system.

B.

It removes the need for an input signal.

C.

It reduces the system's sensitivity to parameter variations.

D.

It simplifies the system's mathematical model.

17 $In general, how does adding negative feedback affect the overall gain of a system?$

Effect of feedback Easy

A.

It decreases the gain.

B.

It has no effect on the gain.

C.

It increases the gain.

D.

It makes the gain infinite.

18 $Negative feedback in a control system generally helps to:$

Effect of feedback Easy

A.

Decrease bandwidth

B.

Increase non-linearity

C.

Increase the time constant

D.

Increase stability

19 $The basic principle of a feedback control system is to measure the output and...$

Effect of feedback Easy

A.

Amplify it to get a larger output

B.

Feed it directly back to the input without comparison

C.

Use it to calculate the system's poles

D.

Compare it with the desired input to generate an error signal

20 $For a BIBO (Bounded-Input, Bounded-Output) stable system, where must all the poles of the transfer function lie in the s-plane?$

Concept of Poles and Zeros Easy

A.

On the imaginary axis

B.

In the left-half of the s-plane

C.

At the origin

D.

In the right-half of the s-plane

21 $For the block diagram shown below, what is the equivalent transfer function ? The forward path has gain and the negative feedback path has gain .$

Block diagram representation and reduction techniques Medium

A.

B.

C.

D.

22 $A system's transfer function is given by . What are the locations of the poles of this system?$

Concept of Poles and Zeros Medium

A.

s = -1, s = -3

B.

s = -1, s = -2, s = -3, s = -4

C.

s = 1, s = 2, s = 3

D.

s = -1, s = -2, s = -3

23 $In a signal flow graph, what is the overall transmittance if there are two parallel forward paths with gains and ?$

Signal flow graphs Medium

A.

B.

C.

D.

24 $For a system with one forward path and two non-touching loops and, what is the determinant of the graph according to Mason's Gain Formula?$

Mason Gain Formula Medium

A.

B.

C.

D.

25 $A key benefit of introducing negative feedback in a control system is its effect on sensitivity to parameter variations of the plant. If the open-loop gain is large, the closed-loop system becomes:$

Effect of feedback Medium

A.

Insensitive to the input signal.

B.

Less sensitive to variations in the plant's parameters.

C.

More sensitive to variations in the plant's parameters.

D.

Unstable regardless of the plant's parameters.

26 $A system has a pole at . If the value of 'a' is increased, moving the pole further into the left-half s-plane, how does the speed of the system's transient response change?$

Concept of Poles and Zeros Medium

A.

The speed of the response does not change.

B.

The response becomes faster.

C.

The system becomes more oscillatory.

D.

The response becomes slower.

27 $When moving a take-off point from a position after a block to a position before the same block, what modification must be made to the signal path from the take-off point?$

Block diagram representation and reduction techniques Medium

A.

A block with transfer function must be added to the take-off path.

B.

A summing junction must be added.

C.

No modification is needed.

D.

A block with transfer function must be added to the take-off path.

28 $Consider a signal flow graph with forward path gain and a single loop with gain . The loop touches the forward path. What is the transfer function using Mason's Gain Formula?$

Mason Gain Formula Medium

A.

B.

C.

D.

29 $How does negative feedback generally affect the bandwidth of an amplifier or control system?$

Effect of feedback Medium

A.

It has no effect on the bandwidth.

B.

It makes the bandwidth infinite.

C.

It decreases the bandwidth.

D.

It increases the bandwidth.

30 $A system is described by the differential equation, where is the output and is the input. What is the pole of the system?$

Concept of Poles and Zeros Medium

A.

B.

C.

D.

31 $A system has two blocks, and, in cascade. An inner negative feedback loop with gain is applied around block . What is the transfer function of this combined inner block?$

Block diagram representation and reduction techniques Medium

A.

B.

C.

D.

32 $Which of the following elements of a block diagram is represented by a node with more than one incoming branch in a signal flow graph?$

Signal flow graphs Medium

A.

The final output

B.

Take-off point

C.

Summing point

D.

A single block

33 $The presence of a zero in the right-half of the s-plane for a system's transfer function indicates that the system is:$

Concept of Poles and Zeros Medium

A.

An all-pass system

B.

A minimum phase system

C.

An unstable system

D.

A non-minimum phase system

34 $A disturbance enters a system just before the plant . In a unity negative feedback configuration, what is the transfer function relating the output to the disturbance ?$

Effect of feedback Medium

A.

$1$

B.

C.

D.

35 $In Mason's Gain Formula, what does (the cofactor of the k-th forward path) represent?$

Mason Gain Formula Medium

A.

The sum of all loop gains touching the k-th forward path.

B.

The gain of the k-th forward path.

C.

The determinant of the entire graph divided by the path gain .

D.

The value of for the part of the graph not touching the k-th forward path.

36 $A system's transfer function has a pole-zero cancellation at . If the pole and zero are not perfectly matched, but very close, what is the effect on the system response?$

Concept of Poles and Zeros Medium

A.

The response will be identical to a perfect cancellation.

B.

The system will become unstable.

C.

The system order will be increased by one.

D.

A slow-moving transient term corresponding to the pole will be present with a small amplitude.

37 $Consider a system where two transfer functions, and, are in parallel. Their outputs are summed together. This combination is then placed in a unity negative feedback loop. What is the overall closed-loop transfer function?$

Block diagram representation and reduction techniques Medium

A.

B.

C.

D.

38 $While negative feedback improves stability margins and reduces sensitivity, what is the primary trade-off?$

Effect of feedback Medium

A.

Reduction in system gain.

B.

Increase in system non-linearity.

C.

Increase in the effect of disturbances.

D.

Reduction in system bandwidth.

39 $A 'self-loop' in a signal flow graph is a loop that consists of:$

Signal flow graphs Medium

A.

A path that passes through all nodes.

B.

Two forward paths with the same gain.

C.

A path from the output node back to the input node.

D.

A single branch that starts and ends at the same node.

40 $For a standard second-order system, what happens to the locations of the complex conjugate poles as the damping ratio () is increased from 0 towards 1?$

Concept of Poles and Zeros Medium

A.

They move away from the origin along the real axis.

B.

They move parallel to the imaginary axis.

C.

They remain in a fixed position.

D.

They move from the imaginary axis towards the real axis along a circular arc.

41 $For a unity feedback system with a forward path transfer function, a disturbance is injected at the summing junction between blocks and . What is the transfer function relating the output to the disturbance, assuming the reference input is zero?$

Block diagram representation and reduction techniques Hard

A.

B.

C.

D.

42 $A system's signal flow graph has forward paths and individual loops . The only non-touching loop pairs are and . Path touches all loops. Path is non-touching with loop only. Path is non-touching with loops and . According to Mason's Gain Formula, what is the numerator of the overall transfer function ?$

Mason Gain Formula Hard

A.

B.

C.

D.

43 $A stable second-order system with transfer function () is modified by adding a zero at, where . The new transfer function is, with chosen to keep the DC gain unchanged. How does this right-half plane (non-minimum phase) zero affect the system's step response?$

Concept of Poles and Zeros Hard

A.

It only adds a time delay to the response without changing its shape.

B.

It introduces an initial undershoot and may increase the percentage overshoot.

C.

It significantly reduces the rise time and eliminates overshoot.

D.

It makes the system unstable.

44 $The sensitivity of a closed-loop transfer function with respect to variations in the forward path is defined as . If the loop gain over a frequency range, what is the approximate magnitude of the sensitivity in that range?$

Effect of feedback Hard

A.

Approximately 0.

B.

Approximately .

C.

Approximately 1.

D.

Approximately, which is very small.

45 $A control system's block diagram consists of a forward path with blocks and in cascade. A negative feedback loop with gain is placed around block . This entire structure is then enclosed in an outer negative feedback loop with gain . What is the overall transfer function ?$

Block diagram representation and reduction techniques Hard

A.

B.

C.

D.

46 $A signal flow graph is defined by the following path gains between nodes (input),,, and (output): is, is, is . Feedback path gains are: is, is, and is . Assuming is the input node, what is the transfer function ?$

Signal flow graphs Hard

A.

B.

C.

D.

47 $A controller is used with a plant to achieve pole-zero cancellation. If there is a slight mismatch such that the controller zero is actually at, where is a small value, what is the most significant consequence for the closed-loop system response?$

Concept of Poles and Zeros Hard

A.

The mismatch has a negligible effect on the system response because is small.

B.

The system becomes unstable for any positive gain K.

C.

The steady-state error to a step input becomes infinite.

D.

A slow pole-zero dipole is formed, introducing a long-settling tail in the transient response.

48 $In a unity negative feedback system, the output due to a disturbance added at the plant output is given by . To achieve high rejection of low-frequency disturbances, what characteristic should the open-loop transfer function exhibit?$

Effect of feedback Hard

A.

Very low gain at low frequencies (i.e., as).

B.

A constant gain of 1 across all frequencies.

C.

A phase angle of exactly -180 degrees at low frequencies.

D.

Very high gain at low frequencies (i.e., as).

49 $A signal flow graph has three individual loops with gains . The only pair of non-touching loops is . There is also a pair of non-touching loops of the second order, consisting of three non-touching loops where is another loop in the system. Which expression correctly represents the graph determinant ?$

Mason Gain Formula Hard

A.

B.

C.

D.

50 $A unity feedback system has an open-loop transfer function with all poles and zeros being positive real numbers (). If the poles and zero are ordered such that, where on the real axis of the s-plane will the root locus exist?$

Concept of Poles and Zeros Hard

A.

On the segments and

B.

On the segments and

C.

Only on the segment

D.

On the segments and

51 $A system contains an inner positive feedback loop with forward gain and feedback gain . This inner loop is part of the forward path of an outer negative feedback loop. A critical condition that makes the overall closed-loop system very likely to be unstable is:$

Block diagram representation and reduction techniques Hard

A.

The poles of the outer loop feedback path are in the right-half plane.

B.

The inner loop gain is negative.

C.

The characteristic equation of the inner loop,, has a root in the right-half s-plane.

D.

The DC gain of the outer loop is greater than 1.

52 $In a signal flow graph, four loops L1, L2, L3, and L4 are identified. The nodes involved in each loop are L1:{2,3,4}, L2:{2,4}, L3:{1,2,3}, L4:{5,6,7}. What is the term in the graph's determinant,, that represents the sum of the products of the gains of all pairs of non-touching loops?$

Mason Gain Formula Hard

A.

B.

C.

$0$ (There are no non-touching loops)

D.

53 $A third-order system has a transfer function, with . Under what condition can the system's transient response be accurately approximated by a standard second-order response of the form ?$

Concept of Poles and Zeros Hard

A.

When the damping ratio of the complex poles is equal to 1.

B.

When the real pole at is located very close to the origin, i.e., .

C.

When the real pole at has the same real part as the complex poles, i.e., .

D.

When the real pole at is located much farther from the origin than the complex poles, i.e., .

54 $A plant with a first-order open-loop transfer function is placed in a unity negative feedback configuration. How is the bandwidth of the closed-loop system related to the open-loop bandwidth?$

Effect of feedback Hard

A.

The bandwidth is unchanged by feedback.

B.

The closed-loop bandwidth is times the open-loop bandwidth.

C.

The closed-loop bandwidth is times the open-loop bandwidth.

D.

The closed-loop bandwidth is times the open-loop bandwidth.

55 $A linear system has two inputs, and, and one output . Its Signal Flow Graph has a determinant . The sum of forward path gains from to multiplied by their cofactors is, and from to is . What is the correct expression for the total output ?$

Signal flow graphs Hard

A.

B.

C.

D.

56 $To simplify a block diagram, a summing junction located after a block with transfer function is moved to be before the block. If one of the external inputs to the summing junction was, what modification must be made to this input path?$

Block diagram representation and reduction techniques Hard

A.

No modification is needed for the input path of .

B.

The sign of the input at the summing junction must be inverted.

C.

The input signal must now pass through a block with transfer function before reaching the junction.

D.

The input signal must now pass through a block with transfer function before reaching the junction.

57 $For a system represented by a simple SFG with one forward path and one negative feedback loop, the transfer function is . If a parameter affects ONLY the loop gain such that (where is constant), what is the sensitivity of the closed-loop transfer function with respect to, ?$

Mason Gain Formula Hard

A.

B.

C.

D.

58 $The pole-zero plot of a system's transfer function shows a zero at and a pair of complex conjugate poles at . What is the impulse response of this system?$

Concept of Poles and Zeros Hard

A.

A pure exponential decay, .

B.

A purely damped cosine function, .

C.

A purely damped sine function, .

D.

A combination of damped sine and cosine waves.

59 $In a unity feedback system with an open-loop transfer function, what is the primary performance trade-off when increasing the controller gain ?$

Effect of feedback Hard

A.

The response becomes slower (rise time increases), and the relative stability worsens (overshoot increases).

B.

The response becomes faster (rise time decreases), but the relative stability worsens (overshoot increases).

C.

The steady-state error to a step input increases, and the response becomes more sluggish.

D.

The response becomes faster (rise time decreases), and the relative stability improves (overshoot decreases).

60 $When constructing a system model from a set of linear differential equations, what is the crucial first step required to create a Signal Flow Graph that is less explicit in Block Diagram modeling?$

Signal flow graphs Hard

A.

All initial conditions must be proven to be zero.

B.

The number of non-touching loops must be determined before any nodes are drawn.

C.

Each variable (in the Laplace domain) must be explicitly isolated on the left-hand side of an equation, representing a node as a sum of other weighted variables.

D.

The system must first be converted to its state-space representation.

Unit 2 - Practice Quiz