Basics of Control Systems MCQ Quiz - Objective Question with Answer for Basics of Control Systems - Download Free PDF
Last updated on Apr 11, 2025
Latest Basics of Control Systems MCQ Objective Questions
Basics of Control Systems Question 1:
For a Linear Time Invariant (LTI) system, in the absence of the input, the output tends towards zero irrespective of initial conditions. This type of stability is called:
Answer (Detailed Solution Below)
Basics of Control Systems Question 1 Detailed Solution
Explanation:
Correct Option Analysis:
The correct option is:
Option 1: Asymptotic Stability
This option correctly describes a type of stability in Linear Time Invariant (LTI) systems where, in the absence of input, the output tends towards zero irrespective of initial conditions. To understand why this is the correct option, let’s delve deeper into the concept of asymptotic stability in LTI systems.
Asymptotic Stability:
In control theory, an LTI system is said to be asymptotically stable if, when the input to the system is zero, the output not only remains bounded but also approaches zero as time tends to infinity. This means that any initial perturbations or deviations will eventually die out, and the system will settle back to the equilibrium state. The system's response to any initial condition will decay to zero over time.
Mathematically, an LTI system is asymptotically stable if all the poles of its transfer function have negative real parts. Poles with negative real parts indicate that the system's natural response components will decay exponentially with time, leading to a zero output in the absence of an input.
To illustrate this, consider the following example:
Let the transfer function of an LTI system be given by:
The pole of this system is at \(s = -2\), which has a negative real part. This implies that the system is asymptotically stable. If the input to the system is zero, the output will decay to zero over time, regardless of the initial conditions.
Additional Information:
To further understand the analysis, let’s evaluate the other options:
Option 2: Selective Stability
This term is not a standard term used in control theory for describing the stability of LTI systems. Stability classifications in control theory typically include asymptotic stability, bounded-input bounded-output (BIBO) stability, marginal stability, and absolute stability, among others. "Selective stability" does not describe any recognized stability property of an LTI system.
Option 3: Notion Stability
This term also does not correspond to any well-defined concept in control theory related to the stability of LTI systems. Stability concepts are well-established and include terms like asymptotic stability, BIBO stability, and so on. "Notion stability" is not one of them and does not describe the behavior of LTI systems.
Option 4: Relative Stability
Relative stability refers to a measure of how stable a system is, not whether it is stable or not. It involves comparing the degrees of stability of different systems or the stability of a system under different conditions. While it is a useful concept in control theory, it does not directly describe the behavior of the output of an LTI system in the absence of input.
Conclusion:
Understanding asymptotic stability is crucial for analyzing the behavior of LTI systems. Asymptotic stability ensures that any initial disturbances will diminish over time, leading the system output to approach zero in the absence of input. This characteristic is essential for the reliable operation of control systems, ensuring that they return to equilibrium after disturbances. While other terms like selective stability, notion stability, and relative stability might appear relevant, they do not accurately describe the fundamental stability property of LTI systems that asymptotic stability does.
Basics of Control Systems Question 2:
Find the gain of a system with transfer function G(s) = (s + 2) / [(s + 1) (s + 3) (s + 4)] for a.d.c. (zero frequency) input.
Answer (Detailed Solution Below)
Basics of Control Systems Question 2 Detailed Solution
Concept
The gain of a system with a given transfer function can be determined by evaluating the transfer function at specific frequencies. In this case, we are asked to find the gain for a.d.c. (zero frequency) input.
The transfer function given is:
\(G(s) = \frac{s + 2}{(s + 1)(s + 3)(s + 4)}\)
For a.d.c. input, the frequency is zero. Therefore, we substitute
Calculation
Substitute s = 0 into the transfer function:
\(G(0) = \frac{0 + 2}{(0 + 1)(0 + 3)(0 + 4)} = \frac{2}{1 \cdot 3 \cdot 4} = \frac{2}{12} = \frac{1}{6}\)
The gain of the system for a.d.c. input is
Basics of Control Systems Question 3:
When reducing a block diagram, which of the following is NOT a basic configuration?
Answer (Detailed Solution Below)
Basics of Control Systems Question 3 Detailed Solution
Explanation:
Block Diagram Reduction in Control Systems
Introduction: Block diagrams are graphical representations of control systems, used to illustrate the flow of signals and the relationships between system components. The process of reducing block diagrams involves simplifying these diagrams to make the analysis of the system more straightforward. This reduction process often involves combining blocks, eliminating loops, and simplifying cascades.
Basic Configurations: In control systems, several basic configurations are commonly used to represent and simplify block diagrams. These include series configurations, feedback configurations, and parallel configurations. Each of these configurations has specific rules for simplification:
- Series Configuration: When two or more blocks are connected in series, the overall transfer function of the system is the product of the individual transfer functions.
- Feedback Configuration: In a feedback loop, the output is fed back to the input, often to achieve desired system behavior. The transfer function of a system with a feedback loop is calculated using the feedback formula.
- Parallel Configuration: When blocks are connected in parallel, their transfer functions are added together to get the overall transfer function.
Correct Option Analysis:
The correct option is:
Option 3: Diagonal Configuration
The diagonal configuration is not considered a basic configuration in block diagram reduction. Basic configurations are usually defined by their specific arrangement, such as series, feedback, and parallel. Diagonal connections do not fit into these standard categories and do not have a straightforward method for simplification.
Additional Information
To further understand the analysis, let’s evaluate the other options:
Option 1: Series Configuration
A series configuration is one of the most common arrangements in block diagrams. In this setup, blocks are connected end-to-end, and the overall transfer function is the product of the individual transfer functions. For example, if two blocks with transfer functions G1(s) and G2(s) are connected in series, the combined transfer function is G1(s) × G2(s).
Option 2: Feedback Configuration
Feedback configurations are also fundamental in control systems. In a feedback loop, part of the output is fed back to the input to create a closed-loop system. This configuration is crucial for controlling system behavior and achieving stability. The transfer function of a feedback system is derived using the feedback formula: T(s) = G(s) / (1 + G(s)H(s)), where G(s) is the forward path transfer function, and H(s) is the feedback path transfer function.
Option 4: Parallel Configuration
In a parallel configuration, blocks are connected side-by-side, and their outputs are summed. The overall transfer function is the sum of the individual transfer functions. For instance, if two blocks with transfer functions G1(s) and G2(s) are connected in parallel, the combined transfer function is G1(s) + G2(s).
Conclusion:
Understanding the basic configurations of series, feedback, and parallel is essential for simplifying block diagrams in control systems. These configurations have specific rules for combining transfer functions, which help in the analysis and design of control systems. The diagonal configuration, however, does not fit into these standard categories and is not considered a basic configuration in block diagram reduction.
Basics of Control Systems Question 4:
Which technique involves combining blocks in series or parallel to simplify a block diagram?
Answer (Detailed Solution Below)
Basics of Control Systems Question 4 Detailed Solution
Explanation:
In control system engineering, simplifying complex block diagrams is an essential step in analyzing and designing systems. One effective technique for achieving this is Block Diagram Reduction. Let’s delve into a detailed explanation of this technique and its importance in control system analysis.
Correct Option: Block Diagram Reduction
Explanation:
Block Diagram Reduction is a technique used in control systems to simplify complex systems into simpler forms. This is done by systematically reducing the block diagram into a simpler equivalent form, making the analysis and design of control systems more manageable. The primary goal is to reduce the number of blocks and interconnections to a minimum while retaining the essential characteristics of the system.
Steps Involved in Block Diagram Reduction:
- Identify Series Blocks: Blocks that are connected in series can be combined into a single block. If the transfer functions of two blocks are
G 1 ( s ) " id="MathJax-Element-28-Frame" role="presentation" style="position: relative;" tabindex="0">G 1 ( s ) " id="MathJax-Element-150-Frame" role="presentation" style="position: relative;" tabindex="0">G 1 ( s ) " id="MathJax-Element-19-Frame" role="presentation" style="position: relative;" tabindex="0"> andG 2 ( s ) " id="MathJax-Element-29-Frame" role="presentation" style="position: relative;" tabindex="0">G 2 ( s ) " id="MathJax-Element-151-Frame" role="presentation" style="position: relative;" tabindex="0">G 2 ( s ) " id="MathJax-Element-20-Frame" role="presentation" style="position: relative;" tabindex="0"> , the combined transfer function isG ( s ) = G 1 ( s ) × G 2 ( s ) " id="MathJax-Element-30-Frame" role="presentation" style="position: relative;" tabindex="0">G ( s ) = G 1 ( s ) × G 2 ( s ) " id="MathJax-Element-152-Frame" role="presentation" style="position: relative;" tabindex="0">G ( s ) = G 1 ( s ) × G 2 ( s ) " id="MathJax-Element-21-Frame" role="presentation" style="position: relative;" tabindex="0"> . - Identify Parallel Blocks: Blocks that are connected in parallel can also be combined. If the transfer functions are
G 1 ( s ) " id="MathJax-Element-31-Frame" role="presentation" style="position: relative;" tabindex="0">G 1 ( s ) " id="MathJax-Element-153-Frame" role="presentation" style="position: relative;" tabindex="0">G 1 ( s ) " id="MathJax-Element-22-Frame" role="presentation" style="position: relative;" tabindex="0"> andG 2 ( s ) " id="MathJax-Element-32-Frame" role="presentation" style="position: relative;" tabindex="0">G 2 ( s ) " id="MathJax-Element-154-Frame" role="presentation" style="position: relative;" tabindex="0">G 2 ( s ) " id="MathJax-Element-23-Frame" role="presentation" style="position: relative;" tabindex="0"> , the combined transfer function isG ( s ) = G 1 ( s ) + G 2 ( s ) " id="MathJax-Element-33-Frame" role="presentation" style="position: relative;" tabindex="0">G ( s ) = G 1 ( s ) + G 2 ( s ) " id="MathJax-Element-155-Frame" role="presentation" style="position: relative;" tabindex="0">G ( s ) = G 1 ( s ) + G 2 ( s ) " id="MathJax-Element-24-Frame" role="presentation" style="position: relative;" tabindex="0"> . - Eliminate Feedback Loops: Feedback loops can be simplified using the formula for a negative feedback loop. If
G ( s ) " id="MathJax-Element-34-Frame" role="presentation" style="position: relative;" tabindex="0">G ( s ) " id="MathJax-Element-156-Frame" role="presentation" style="position: relative;" tabindex="0">G ( s ) " id="MathJax-Element-25-Frame" role="presentation" style="position: relative;" tabindex="0"> is the forward path transfer function andH ( s ) " id="MathJax-Element-35-Frame" role="presentation" style="position: relative;" tabindex="0">H ( s ) " id="MathJax-Element-157-Frame" role="presentation" style="position: relative;" tabindex="0">H ( s ) " id="MathJax-Element-26-Frame" role="presentation" style="position: relative;" tabindex="0"> is the feedback path transfer function, the equivalent transfer function isG ( s ) 1 + G ( s ) H ( s ) G ( s ) 1 + G ( s ) H ( s ) G ( s ) 1 + G ( s ) H ( s ) - Move Summing Points and Pickoff Points: Summing points and pickoff points can be relocated within the block diagram to facilitate simplification. This involves algebraically manipulating the equations to reflect the new configuration.
- Simplify Block Combinations: Continue combining blocks until the block diagram is reduced to a single transfer function representing the entire system.
Example:
Consider a block diagram with three blocks in series:
The steps to reduce this block diagram are:
- Combine the series blocks:
G ( s ) = G 1 ( s ) × G 2 ( s ) × G 3 ( s ) " id="MathJax-Element-41-Frame" role="presentation" style="position: relative;" tabindex="0">G ( s ) = G 1 ( s ) × G 2 ( s ) × G 3 ( s ) " id="MathJax-Element-163-Frame" role="presentation" style="position: relative;" tabindex="0">G(s)=G1(s)×G2(s)×G3(s) - Apply the feedback loop formula:
T ( s ) = G ( s ) 1 + G ( s ) H ( s ) T ( s ) = G ( s ) 1 + G ( s ) H ( s ) T(s)=G(s)1+G(s)H(s)
The resulting transfer function
Importance of Block Diagram Reduction:
- Simplifies Analysis: Reducing complex block diagrams simplifies the analysis of control systems, making it easier to understand system behavior and performance.
- Facilitates Design: Simplified block diagrams aid in the design and tuning of control systems by providing a clearer view of the system's dynamics.
- Improves Accuracy: Accurate reduction of block diagrams ensures that the essential characteristics of the system are retained, leading to more precise analysis and design.
- Reduces Computational Complexity: Simplified block diagrams reduce the computational complexity involved in analyzing and simulating control systems.
Analysis of Other Options:
Option 1: Mason's Gain Formula
Mason's Gain Formula is a method used to find the overall transfer function of a system represented by a signal flow graph. It involves identifying forward paths, loops, and their gains, and applying a specific formula to compute the transfer function. While it is useful for signal flow graphs, it is not the same as block diagram reduction.
Option 3: Nyquist Stability Criterion
The Nyquist Stability Criterion is a graphical method used in control systems to determine the stability of a closed-loop system. It involves plotting the Nyquist plot of the open-loop transfer function and analyzing its encirclements around the critical point. This technique is related to stability analysis, not block diagram simplification.
Option 4: Routh-Hurwitz Criterion
The Routh-Hurwitz Criterion is an algebraic method used to determine the stability of a linear time-invariant system. It involves constructing the Routh array from the characteristic equation of the system and checking the sign changes in the first column. Like the Nyquist Criterion, this method is focused on stability analysis rather than block diagram reduction.
Conclusion:
Block Diagram Reduction is a crucial technique in control system engineering, enabling the simplification of complex systems into more manageable forms. By systematically combining series and parallel blocks, eliminating feedback loops, and relocating summing and pickoff points, the block diagram is reduced to a single transfer function representing the entire system. This simplification facilitates easier analysis and design, improves accuracy, and reduces computational complexity. Understanding this technique is essential for control system engineers to effectively analyze and design control systems.
Basics of Control Systems Question 5:
What is the actuating error signal in a closed loop control system?
Answer (Detailed Solution Below)
Basics of Control Systems Question 5 Detailed Solution
- In a closed-loop control system, the actuating error signal is the difference between the input (reference) signal and the feedback signal.
- This error signal is used by the controller to adjust the output and minimize the difference between the desired and actual outputs.
- E(t) = R(t) - C(t)
Where:
E(t) = Error signal
R(t) = Reference or input signal
C(t) = Feedback signal (typically the output signal or a portion of it) - The error signal represents the deviation between the desired output (as set by the input signal) and the actual output (as measured by the feedback signal).
- This signal is used to adjust the system's parameters and bring the output closer to the desired value.
- In a closed-loop system, feedback is continuously used to compare the output with the desired input.
- The controller uses the error signal to generate the appropriate control action to minimize the error over time.
Explanation:
System input of the Close loop circuit is the output of the Controller after measuring the error.
- A controller is essentially the comparator that compares the given input with the reference input and generates the error signal.
- The reference input is the actual signal input to the control system.
- The error signal is the input to the controller, and it causes the output to be the desired output.
- The controller is used in closed-loop control systems.
Closed-loop control system:
The closed-loop control system can be described by a block diagram as shown in the figure below.
r(t) is the error signal given to the input of the controller.
These are the systems in which the control action depends on the output. These systems have a tendency to oscillate.
Ex: Temperature controllers, speed control of the motor, systems having sensors, etc.
Advantages:
- More accurate
- Non-linear distortions are less
- The output is less sensitive to parameter changes within the system
- Bandwidth increases
Disadvantages:
- Design is complicated
- More expensive
- May become unstable, if there are malfunctions in the feedback.
Top Basics of Control Systems MCQ Objective Questions
Consider a linear time-invariant system whose input r(t) and output y(t) are related by the following differential equation:
\(\frac{{{d^2}y\left( t \right)}}{{d{t^2}}} + 4y\left( t \right) = 6r\left( t \right)\)
The poles of this system are atAnswer (Detailed Solution Below)
Basics of Control Systems Question 6 Detailed Solution
Download Solution PDFConcept:
A transfer function is defined as the ratio of Laplace transform of the output to the Laplace transform of the input by assuming initial conditions are zero.
TF = L[output]/L[input]
\(TF = \frac{{C\left( s \right)}}{{R\left( s \right)}}\)
For unit impulse input i.e. r(t) = δ(t)
⇒ R(s) = δ(s) = 1
Now transfer function = C(s)
Therefore, the transfer function is also known as the impulse response of the system.
Transfer function = L[IR]
IR = L-1 [TF]
Calculation:
Given the differential equation is,
\(\frac{{{d^2}y\left( t \right)}}{{d{t^2}}} + 4y\left( t \right) = 6r\left( t \right)\)
By applying the Laplace transform,
s2 Y(s) + 4 Y(s) = 6 R(s)
\( \Rightarrow \frac{{Y\left( s \right)}}{{R\left( s \right)}} = \frac{6}{{{s^2} + 4}}\)
Poles are the roots of the denominator in the transfer function.
⇒ s2 + 4 = 0
⇒ s = ±2jThe open loop DC gain of a unity negative feedback system with closed-loop transfer function \(\frac{s+4}{s^2+7s+13}\) is
Answer (Detailed Solution Below)
Basics of Control Systems Question 7 Detailed Solution
Download Solution PDFConcept:
Closed-loop transfer function = \(\frac{G(s)}{1+G(s)H(s)}\)
For unity negative feedback system Open-loop transfer function (G(s) H(s)) can be found by subtracting the numerator term from the denominator term
Application:
Open-loop transfer Function
\(= \frac{{s + 4}}{{{s^2} + 7s + 13 - s - 4}} = \frac{{s + 4}}{{{s^2} + 6s + 9}}\)
For DC gain s = 0
∴ open-loop gain \(= \frac{4}{{9}} \)
The transfer function of a system is defined as:
Answer (Detailed Solution Below)
Basics of Control Systems Question 8 Detailed Solution
Download Solution PDFThe transfer function of a control system is defined as the ratio of the Laplace transform of the output variable to Laplace transform of the input variable assuming all initial conditions to be zero.
It is also defined as the Laplace transform of the impulse response.
If the input is represented by R(s) and the output is represented by C(s), then the transfer function will be:
\(\frac{T}{F} = \frac{{C\left( s \right)}}{{R\left( s \right)}}\)
Open loop transfer function of a closed loop control system is defined as:
Answer (Detailed Solution Below)
Basics of Control Systems Question 9 Detailed Solution
Download Solution PDFClosed-loop control system:
These are the systems in which the control action depends on the output. These systems have a tendency to oscillate.
Ex: Temperature controllers, speed control of the motor, systems having sensors, Human eye, etc.
The closed-loop control system can be described by a block diagram as shown in the figure below.
Where, R(s) is Reference Input,
Actuating Signal E(s) = R(s) - C(s)
G(s) is unity feedback open loop gain.
H(s) is Feedback gain.
C(s) is the Output and it is given as a feedback signal to input through the feedback gain function H(s)
From the above figure, we can find out closed-loop transfer function.
CLTF = C(s) / R(s)
From this open-loop transfer function is calculated as,
\(OPLT = \dfrac{CLTF}{1-CLTF}=\dfrac{\frac {C(s)}{R(s)}}{1-\frac {C(s)}{R(s)}}\)
\(OLTF=\dfrac{C(s)}{R(s)-C(s)}=\dfrac{C(s)}{E(s)}\)
OLTF = Output / actuating signal
In the force-current analogy, capacitance C corresponds to:
Answer (Detailed Solution Below)
Basics of Control Systems Question 10 Detailed Solution
Download Solution PDFThe various relation in force voltage and force current analogy is given in the table below:
|
Electrical Qty. |
Force current |
Force Voltage |
|
Voltage, e |
Velocity, v |
Force,f |
|
Current, i |
Force, f |
Velocity,v |
|
Resistance, R |
Lubricity, 1/B |
Friction,B |
|
Capacitance, C |
Mass, M (I, Inertia) |
Compliance, 1/K (inverse spring constant) |
|
Inductance, L |
Compliance, 1/K (inverse spring constant) |
Mass M |
|
Transformer, N1:N2 |
Lever L1:L2 |
Lever L1:L2 |
The unit step response for a relaxed system is c(t) = 1 – e-3t; t ≥ 0; What will be its transfer function?
Answer (Detailed Solution Below)
Basics of Control Systems Question 11 Detailed Solution
Download Solution PDFConcept:
The transfer function is defined as the ratio of Laplace transform of the output to the Laplace transform of the input by assuming initial conditions are zero.
TF = L[output]/L[input]
\(TF = \frac{{C\left( s \right)}}{{R\left( s \right)}}\)
For unit impulse input i.e. r(t) = δ(t)
⇒ R(s) = δ(s) = 1
Now transfer function = C(s)
Therefore, transfer function is also known as impulse response of the system.
Transfer function = L[IR]
IR = L-1 [TF]
Calculation:
c(t) = 1 – e-3t
Applying Laplace transform, i.e. time domain into s- domain
\(\Rightarrow C\left( s \right) = \frac{1}{s} - \frac{1}{{s + 3}} = \frac{3}{{s\left( {s + 3} \right)}}\)
Input is unit step, i.e. r(t) = u(t)
\(\Rightarrow R\left( s \right) = \frac{1}{s}\)
Transfer function \(= \frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{3}{{s + 3}}\)If the value of (1 + GH) is less than 1, then sensitivity is/has _____.
Answer (Detailed Solution Below)
Basics of Control Systems Question 12 Detailed Solution
Download Solution PDFTransfer Function
The transfer function is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input keeping initial conditions zero.
The transfer function of the closed-loop system is:
\({C(s)\over R(s)}={G\over 1+GH}\)
where, G = Open loop gain
H = Feedback gain
Sensitivity of the transfer function
Case 1: Sensitivity with respect to the open loop gain (G)
\(S={1\over 1+GH}\)
Case 2: Sensitivity with respect to the feedback gain (H)
\(S={-GH\over 1+GH}\)
In both cases, if the value of (1 + GH) is less than 1, then sensitivity increases.
Which of the following is the transfer function of:
\(\frac{{dc\left( t \right)}}{{dt}} + 2c\left( t \right) = r\left( t \right)\)
Where, r(t) is the unit impulse signal
Answer (Detailed Solution Below)
Basics of Control Systems Question 13 Detailed Solution
Download Solution PDFConcept:
A transfer function is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input by assuming initial conditions are zero.
TF = L[output]/L[input]
\(TF = \frac{{C\left( s \right)}}{{R\left( s \right)}}\)
For unit impulse input i.e. r(t) = δ(t)
⇒ R(s) = δ(s) = 1
Now transfer function = C(s)
Therefore, the transfer function is also known as the impulse response of the system.
Transfer function = L[IR]
IR = L-1 [TF]
Calculation:
The given differential equation is,
\(\frac{{dc\left( t \right)}}{{dt}} + 2c\left( t \right) = r\left( t \right)\)
By applying the Laplace transform, we get
⇒ s C(s) + 2 C(s) = R(s)
\( \Rightarrow G\left( s \right) = \frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{1}{{s + 2}}\)
Which of the following options is correct for the system shown below?
Answer (Detailed Solution Below)
Basics of Control Systems Question 14 Detailed Solution
Download Solution PDFFrom the block diagram,
\(G\left( s \right) = \frac{1}{{{s^2}\left( {s + 1} \right)}}\)
\(H\left( s \right) = \frac{{20}}{{\left( {s + 20} \right)}}\)
As the given feedback is negative, the transfer function of the closed loop system is
\(\frac{{Y\left( s \right)}}{{R\left( s \right)}} = \frac{{G\left( s \right)}}{{1 + G\left( s \right)H\left( s \right)}}\)
\( = \frac{{\frac{1}{{{s^2}\left( {s + 1} \right)}}}}{{1 + \frac{1}{{{s^2}\left( {s + 1} \right)}}\frac{{20}}{{\left( {s + 20} \right)}}}}\)
\( = \frac{{s + 20}}{{{s^2}\left( {s + 1} \right)\left( {s + 20} \right) + 20}}\)
\( = \frac{{s + 20}}{{{s^4} + 21{s^3} + 20{s^2} + 20}}\)
The denominator of the above transfer function has the highest degree of 4. Therefore, the order of the system is 4.
The coefficient of ‘s’ term is zero in the characteristic equation (denominator of above transfer function). Therefore, the system is unstable.The Laplace of the response is the same as the system function for:
Answer (Detailed Solution Below)
Basics of Control Systems Question 15 Detailed Solution
Download Solution PDFConcept:
\(\begin{array}{l} r\left( t \right) = \delta \left( t \right),\;R\left( s \right) = 1\\ TF = \frac{{L\left[ {C\left( s \right)} \right]}}{{L\left[ {R\left( s \right)} \right]}} \end{array}\)
Transfer function \(= L\left[ {C\left( s \right)} \right]\)
Hence, the Laplace of the response is the same as the system function for unit impulse input.