# Multiple Choice Questions (MCQ) on Control Systems with Answer Key - Top Picks

### Types of Control Systems and MCQs

A control system is a collection of interconnected components that work together to accomplish a particular function with input controlling the output. Two main types of control systems are open-loop control systems and closed-loop control systems.

#### Open-Loop Control System:

- Advantages:
- Simple and cost-effective
- Easy to construct
- Stable
- Disadvantages:
- Inaccurate
- No automatic compensation for changes in the output

#### Closed-Loop Control System:

- Advantages:
- Accurate
- Less susceptible to noise
- Disadvantages:
- Complicated and expensive
- Feedback lowers the overall gain of the system
- Stability can be a challenge

There are different types of control systems, such as linear and non-linear systems, time variant and time invariant systems, linear time-variant systems, and linear time-invariant systems. MCQs can be used to test understanding and knowledge of control systems.

### Application of Automatic Control Theory

The major part of the automatic control theory is applied to linear time-invariant systems.

```
// Example code for illustrating a linear time-invariant system
double[] input = {1.0, 2.0, 3.0}; // input signal
double[] output = new double[input.length]; // output signal
// System function
double[] b = {0.5, 0.6, 0.7}; // numerator coefficients of transfer function
double[] a = {1.0, 0.3, 0.2}; // denominator coefficients of transfer function
// Calculate system response
for (int n = 0; n < input.length; n++) {
double y = 0.0;
for (int k = 0; k < b.length; k++) {
if (n - k >= 0) {
y += b[k] * input[n - k];
}
}
for (int k = 1; k < a.length; k++) {
if (n - k >= 0) {
y -= a[k] * output[n - k];
}
}
output[n] = y / a[0];
}
// Output system response
for (int n = 0; n < output.length; n++) {
System.out.println("Output[" + n + "] = " + output[n]);
}
```

### Understanding Traffic Light Systems

A traffic light system is an example of an open-loop system. In this type of system, the output signal is not connected back to the input for further correction. Instead, the output signal is determined by a set of predetermined parameters.

In the context of traffic lights, these parameters might include the length of time that each light stays green, the length of time for yellow lights, and the intervals between lights changing color. Once these parameters are set, the traffic light system will operate according to them, regardless of actual traffic conditions.

Open-loop systems like traffic lights can be less flexible than closed-loop systems, which use feedback to adjust the system's output based on real-time observations. However, open-loop systems may be simpler and more reliable for certain applications, such as traffic control.

`// Example code for a simple traffic light system`

```
void trafficLightSystem() {
int greenLightDuration = 30; // in seconds
int yellowLightDuration = 5; // in seconds
int redLightDuration = 25; // in seconds
// loop indefinitely
while (true) {
turnGreenOn();
delay(greenLightDuration * 1000); // convert duration to milliseconds
turnGreenOff();
turnYellowOn();
delay(yellowLightDuration * 1000);
turnYellowOff();
turnRedOn();
delay(redLightDuration * 1000);
turnRedOff();
}
}
```

### Understanding Loop Gain in Control Systems

In control systems, loop gain is defined as the product of every branch gain while traversing the forward path. It is denoted by the symbol 'G'. The forward path is the path that originates from the input and terminates at the output. The feedback path, on the other hand, originates from the output and returns to the input.

Mathematically, the loop gain formula can be expressed as G = G1G2G3...Gn, where G1, G2, G3, ... Gn are the gain values for each branch in the forward path.

It is important to calculate the loop gain because it helps to determine the stability of the control system. A low loop gain will result in a slow and sluggish response, while a high loop gain can lead to instability and oscillations. Therefore, a balanced loop gain is necessary for optimal control system performance.

In summary, the correct definition of loop gain in control systems is the product of every branch gain while traversing the forward path.

### Identifying the Impulse Response of an RL Circuit

One way to identify the impulse response of an RL (resistor-inductor) circuit is by using an input signal in the form of a step function. The impulse response can then be observed in the output signal, which takes the form of a decaying exponential function.

The other options listed - rising exponential function, parabolic function, and step function (which is listed as the input signal) - do not accurately describe the impulse response of an RL circuit.

Therefore, option D - decaying exponential function - is the correct answer.

```
// Example code for determining the impulse response of an RL circuit
float resistance = 10.0; // value in Ohms
float inductance = 0.5; // value in Henrys
// Calculate time constant of circuit
float time_constant = resistance * inductance;
// Simulate input signal (step function)
float input_signal = 1.0; // assume step of amplitude 1.0
// Simulate output signal (impulse response)
float output_signal;
for (float t = 0.0; t < 5*time_constant; t += time_constant/10.0) {
output_signal = input_signal * (1.0 - exp(-t/time_constant));
}
```

### Calculating Gain Margin of a Second-Order System

To calculate the gain margin of a second-order system, we need to determine the system's transfer function and substitute s=jw, where w is the frequency of operation. After doing so, we need to find the gain margin by calculating the value of K at which the phase shift is -180 degrees.

If we end up with no value of K at which the phase shift is -180 degrees, then the gain margin is infinite. Therefore, the correct answer is **Option A) Infinite**.

```
// Sample code to calculate gain margin of a second-order system
float omega = 100; // frequency of operation
float zeta = 0.5; // damping ratio
float GM; // gain margin
float K; // gain of the system
K = sqrt(1/(1-zeta^2)); // calculate gain
GM = 1/K; // calculate gain margin
if (isnan(GM)) {
GM = INFINITY; // if no gain value satisfies phase shift of -180 degrees, set gain margin to infinity
}
```

### Identifying the Most Powerful Controller

In the list of controllers given, the most powerful one is the PID controller.

```
// PID controller code example:
double kp = 0.5; // proportional gain
double ki = 0.2; // integral gain
double kd = 0.1; // derivative gain
double last_error = 0;
double integral = 0;
while(true) {
double error = setpoint - process_variable;
double derivative = error - last_error;
last_error = error;
integral += error;
double output = kp*error + ki*integral + kd*derivative;
// apply output to control system
}
```

The PID controller is a control loop feedback mechanism widely used in industrial control systems. It calculates an error value as the difference between a measured process variable and a desired set point. The controller tries to minimize the error by adjusting the process control inputs.

It generally combines a proportional term, an integral term, and a derivative term. The proportional term is proportional to the current error value and provides the main driving force for the control output. The integral term takes into account past errors and accumulates them, helping to eliminate steady-state errors. The derivative term looks at the rate of change of error and can improve the stability of the system.

### Controller for Fast Process Load Changes

In terms of handling fast process load changes, the PD controller is the most suitable among the given options. The PID controller and the PI PI controller, though effective in controlling process parameters, may not respond well to sudden changes in the load. Therefore, option A, PD controller, is the correct answer to this question.

### True or False: Mechanism of Control of Body Temperature

The statement "The mechanism of control of body temperature is a non-feedback system" is:

False.

The mechanism of control of body temperature is actually a feedback system.

### Comparison of closed and open-loop control systems

In a closed-loop control system, the bandwidth is higher than in an open-loop control system. This means that the system can respond to changes in input signals faster and is more efficient in regulating its output. On the other hand, in an open-loop control system, the bandwidth is limited and the response time is slower.

Out of the given options, the correct answer is D) Bandwidth.

### Effects of Feedback on System Performance

The statement is true: feedback can reduce the effects of noise and disturbance on system performance.

In a control system, feedback is the process of comparing the output of a system with the desired output and adjusting the system accordingly. When external noise or disturbance is introduced to the system, feedback can help to correct the system and prevent errors from accumulating.

By constantly measuring and adjusting the output of the system, feedback can improve system stability, accuracy, and overall performance. Therefore, the effects of noise and disturbance can be reduced through the use of feedback in a control system.

### Identifying System Capable of Using Multiple Signals

The correct answer is B) In feedback systems, multiple signals can be used.

```
// Example code of a feedback system using multiple signals
int signal1 = 5;
int signal2 = 10;
int threshold = 15;
// Calculate the sum of the signals
int sum = signal1 + signal2;
// Check if the sum is greater than the threshold
if (sum > threshold) {
// Take action
doAction();
}
```

In the code example above, a feedback system is used to take action based on the sum of two signals. The system uses both signal1 and signal2 to determine if the sum exceeds the threshold. If the sum is greater than the threshold, the system takes action by executing the doAction() function.

### Stability of a system with feedback

It is true that an originally stable system can become either unstable or more stable due to feedback.

```
// Example code showing how feedback can affect system stability
```

double originalSystemOutput = 10; // output of the system without feedback double feedbackGain = 0.5; // the amount of feedback to be added

// With negative feedback, the system output can become more stable double systemOutputWithFeedback = originalSystemOutput * (1 + feedbackGain); if (systemOutputWithFeedback originalSystemOutput) { System.out.println("The system is now unstable with positive feedback."); }

### Regenerative Feedback and Its Sign

In a feedback system, regenerative feedback occurs when a portion of the output signal is fed back to the input with positive feedback. This means that the feedback signal reinforces the input signal.

A regenerative feedback is characterized by a positive sign or a sign that is the same as that of the input signal. This type of feedback can lead to instability and oscillations in the system.

Therefore, the answer is **positive sign**.

```
// code implementation in a feedback system
int outputSignal = 0;
int inputSignal = 0;
int feedbackSignal = 0;
// Regenerative feedback occurs when feedbackSignal reinforces inputSignal
feedbackSignal = outputSignal * 0.5; // assume a gain of 0.5
inputSignal += feedbackSignal; // add feedback signal to input
outputSignal = someFunction(inputSignal); // calculate the output based on input
// This type of feedback can lead to instability and oscillations in the system
```

### Identifying the Output of Feedback Control

When it comes to feedback control, the output is determined by the function of output and feedback signal.

`output = f(output signal, feedback signal)`

Therefore, answer D, "The function of output and feedback signal," is correct.

### Effects of Control System with Excessive Noise

A control system can experience various effects when there is excessive noise. One of the likely effects is the saturation in amplifying stages. This can result in a distortion of the output signal, which can lead to inaccurate readings and measurements.

Other possible effects include oscillations and vibrations, which can cause instability and fluctuations in the system. Loss of gain may also occur, reducing the system's ability to respond to changes in the input signal and affecting its performance.

It is therefore essential to identify and address noise-related issues early on to maintain the effectiveness and reliability of a control system.

```
// Example of identifying and addressing noise in a control system
int gain = 10; // initialize gain variable
int noiseLevel = 5; // initialize noise level variable
if (noiseLevel > 3) { // if noise level is excessive
gain -= 2; // reduce gain by 2
// implement noise reduction techniques
}
```

### Understanding Zero Initial Condition for a System

Zero initial condition for a system refers to a state where the system is at rest, and no energy is stored. It means that the system is in its initial state, and there is no external stimulus acting upon it. When a system is in zero initial condition, it is considered stable and ready to receive input signals or energy to perform its intended function.

### Understanding the Transfer Function

The transfer function is a mathematical representation of a system that relates the system's output to its input. It is represented by the ratio of the Laplace transform of the output to the Laplace transform of the input, assuming all initial conditions are zero.

The transfer function is primarily used for finding the system's output for any given input. By applying the input to the transfer function, one can obtain the output of the system in Laplace domain.

Therefore, the correct answer is B) The transfer function is used for finding the output for any given input.

### Sensitivity of Closed-Loop System Factors

The sensitivity of the closed-loop system to gain changes and load disturbances depends on the forward gain, loop gain, and frequency. All three factors contribute to the overall behavior of the system and affect its response to changes.

### Optimal Damping Ratio for Second-Order Systems

For a desirable transient response of a second-order system, it is recommended that the damping ratio falls between the range of 0.4 and 0.8.

`Example:`

```
python
# Setting damping ratio to 0.6 for optimal transient response
damping_ratio = 0.6
# Further code implementation here...
```

### Identifying the Correct Feature of a Minimum Phase System

In a minimum phase system, all zeros lie in the left half-plane. This is the correct feature of a minimum phase system.

### Understanding Poles and Zeros in Transfer Function

When analyzing a transfer function, it is common to look at its poles and zeros. Poles and zeros give us information about the stability and behavior of the system.

If we equate the denominator of the transfer function to 0, we get the poles of the transfer function. Therefore, the answer is **b) Poles**.

```
# Example of obtaining poles and zeros in Python
import control
# Define transfer function
G = control.tf([1],[1, 2, 1])
# Get poles and zeros
zeros = control.zero(G)
poles = control.pole(G)
print("Zeros:", zeros)
print("Poles:", poles)
```

### Definition of Maximum Overshoot

Maximum overshoot refers to the maximum peak of a response curve relative to the target, and it is a function of both the damping ratio and the natural frequency of oscillation.

`// Example code demonstrating max overshoot calculation`

`double dampingRatio = 0.5; double naturalFrequency = 2.3; double maxOvershoot = Math.Exp((-1 * dampingRatio * Math.PI) / Math.Sqrt(1 - Math.Pow(dampingRatio, 2))) * 100; Console.WriteLine("Max Overshoot: {0}%", maxOvershoot);`

In the above code, the maximum overshoot is calculated using the given damping ratio and natural frequency, using the equation for the maximum overshoot function. The result is then printed to the console as a percentage value.

## Preferred System Condition

Generally, the underdamped system condition is preferred.

`// Example implementation in code:`

`java public class SystemConditions { private String damping; public SystemConditions() { this.damping = "underdamped"; } public String getDamping() { return damping; } public void setDamping(String damping) { this.damping = damping; } }`

## Sensitivity to parameter in feedback systems

In a feedback system, the sensitivity to a parameter tends to decrease.

## Explanation of Damping Ratio

The damping ratio is a measure of the rate of decay of oscillations in a system. If the damping ratio is too high, the system will take longer to settle into a steady state, resulting in slow response times. Conversely, if the damping ratio is too low, the system will overshoot its steady-state value, resulting in a slow-but-steady oscillation.

When the overshoot is excessive, the damping ratio is less than 0.4.

`= 0.4`

is not the correct answer because a damping ratio of 0.4 would actually result in a moderate overshoot, not excessive. Therefore, the correct answer is

`< 0.4`

.

## Understanding the Term "Controller"

The term "controller" is used to refer to the combination of error detector and control elements. They work together to maintain the output of a system within a desired range by detecting deviations from the reference signal and adjusting the control input accordingly.

Therefore, option B - "The term "controller" includes error detector and control elements" - is the correct answer.

## Automated Control System with Variable Output

In the field of engineering and automation, the automated control system which can vary or adjust its output is referred to as a process control system.

Other types of automated control systems include: - Servomechanism: used to control the position or motion of a part of a machine. - Closed-loop system: characterized by a feedback loop, where the output of the system is continuously monitored and adjusted based on the desired input. - Automatic regulating system: designed to maintain a specific setpoint or reference value regardless of any disturbances in the system.

However, for an automated control system that varies its output, the correct term is a process control system.

## Which Device is used to Obtain Output Position in a Position Control System?

In a position control system, the load gauge is used to obtain the output position. The load gauge measures force or torque and converts it into an electrical signal, which can be used to calculate the position of the load being controlled. Other devices such as thermistors, strain gauges, and synchros can be used for different purposes but not specifically to determine output position in a position control system.

## Calculating damping ratio from phase margin

To calculate damping ratio from phase margin:

- Use the formula - damping ratio = tan(phase angle) * sqrt(1-pow(sin(phase angle), 2))
- Substitute phase angle as 45 degrees in the formula.
- Solve the equation to get the answer:
`phase_angle = 45 damping_ratio = tan(phase_angle) * sqrt(1 - pow(sin(phase_angle), 2)) # damping_ratio = 0.42`

Therefore, the damping ratio of a system where the phase margin is 45 degrees is 0.42.

## Definition of Eigenvalues of a Matrix

The Eigenvalues of a matrix are defined as the values of lambda for which the matrix A when multiplied by a vector v, results in a scaled version of the same vector i.e. Av = λv. In simpler terms, Eigenvalues are the values of the matrix such that when the matrix is applied to a vector, the vector changes by only a scalar factor.

The sum of elements of principal diagonal elements is not the correct definition. It is related to the trace of a matrix, which is the sum of elements on the diagonal.

## Identification of Element Not Used in Automatic Control System

In an automatic control system, the following elements are used:

- Sensor
- Final control element
- Error detector
- Oscillator

Out of these elements, the one that is not used in an automatic control system is **oscillator**.

Hence, option C is the correct answer.

### Bandwidth Requirements for a Good Control System

The suitable nature of the bandwidth for a good control system depends on the specific system. However, it is generally recommended that the bandwidth should be medium. This allows for a balance between the responsiveness and stability of the control system. If the bandwidth is too small, the system will be too sluggish in its response. On the other hand, if the bandwidth is too large, the system may become unstable and oscillate. Therefore, it is important to select an appropriate bandwidth to ensure an efficient and effective control system.

### Incorrect Features of a Good Control System

A good control system is an essential component in many engineering and industrial applications. There are some particular features that are considered necessary for a control system to function effectively. These include:

- Good stability
- Good accuracy
- Sufficient power for handling large capacity control systems
**Fast response time (not slow response)**

Note that a good control system should be a negative feedback closed-loop control system to ensure efficiency.

### Effect of Feedback on Sensitivity in Open-Loop Control System

In an open-loop control system, the effect of feedback on sensitivity is minimum. Open-loop control systems do not have a feedback loop, which means they cannot adjust or correct errors that occur during operation. Any changes in the input signal will not be compensated by the system, so the output signal will always depend on the accuracy of the original setpoint.

On the other hand, closed-loop control systems have a feedback loop that compares the actual output to the desired setpoint and adjusts the system accordingly. This means that any errors or changes in the input signal can be detected and corrected, resulting in higher sensitivity and accuracy.

Therefore, the correct answer is A) Open-loop control system.

### When is Sampling Necessary?

Sampling is necessary in systems where high accuracy is required. This ensures that the measurements taken are representative of the entire system and that the data collected is accurate and reliable.

Sampling may not be necessary in non-automated control systems, but in complex and automated control systems, it becomes imperative to ensure that the readings obtained are precise and reflect the true conditions of the system.

Therefore, knowing when and where to employ sampling techniques is crucial in obtaining useful and applicable results.

```
// Example of sampling in a control system
double[] samples = new double[10];
double sum = 0;
for (int i = 0; i < 10; i++) {
samples[i] = takeMeasurement();
sum += samples[i];
}
double average = sum / 10; // calculate the average value of the measurements taken
```

### Definition of Stochastic Control System

A stochastic control system refers to a type of control system where the system operates under unknown and random actions or disturbances. It is a control theory utilized to examine and design a feedback or control system when the signals are partly random in nature.

Stochastic control systems are useful in various fields, including engineering, physics, economics, and finance.

Out of the options provided, the correct answer is B) Stochastic control system.

### Where is the Output of Control Given?

The output of control is given to the final control element.

In other words, the final control element receives the output of a control system, which includes all the necessary actions to maintain or regulate a process. This output is the result of the comparison between the desired state and the actual state of the system being controlled.

Therefore, option A is the correct answer.

### Feedback Control System as a Low Pass Filter

A feedback control system is a **low pass filter**, not a high pass filter. Therefore, the correct answer is **False**. Feedback control systems are designed to reduce the difference between the desired signal and the actual output signal. The feedback loop will attenuate high-frequency signals and allow low-frequency signals to pass through. This property is what makes it a low pass filter.

### Measurement of Peak Overshoot and Damping Ratio

Peak overshoot and damping ratio are two measures commonly used to assess the behavior of a control system.

The peak overshoot is a measure of how much the response of a system exceeds its steady-state value in response to a step input. It is expressed as a percentage of the steady-state value.

The damping ratio, on the other hand, is a measure of how quickly the response of a system returns to its steady-state value after a disturbance. It is a dimensionless quantity that is expressed as a ratio of the damping coefficient to the critical damping coefficient.

Both measures are important in assessing the speed of response of a control system. A high peak overshoot indicates that the system is taking longer to settle down to its steady-state value, whereas a low damping ratio indicates that the system oscillates for a longer period before returning to its steady-state value.

In conclusion, peak overshoot and damping ratio are both measures of the transient response of a system, and they provide important information about the speed and stability of a control system.

`Code:`

There is no code to show for this lesson, as it is a conceptual topic.

### Types of Control Systems

In control engineering, there are two types of control systems:

`1. Open-loop control system`

`2. Closed-loop control system`

Therefore, the correct answer is B) 2.

### Disadvantages of Closed-Loop Control Systems

In closed-loop control systems, there exist some disadvantages that can affect the performance of the system. The disadvantages are as follows:

- Instability
- Complexity and high cost
- Feedback reduces the system gain

All of the above mentioned are the disadvantages of a closed-loop control system.

### Advantages of a Closed-Loop Control System

A closed-loop control system has the following advantages:

- It is accurate
- It is less affected by noise

Therefore, the correct answer is D, which indicates that both accuracy and less sensitivity to noise are advantages of a closed-loop control system.

### Identifying Time-Variant Systems

In the field of signal processing and control theory, systems are classified based on their characteristics. One of the main classifications is based on whether a system is time-invariant or time-variant. Time-variant systems are those in which the output varies with time.

For example, if a system's output changes with time due to changes in its input or internal parameters, it can be considered a time-variant system. On the other hand, if the output remains constant with time, it is a time-invariant system.

Answer: **Time-variant system**

### Correct Formula for Transfer Function of Positive Feedback

The transfer function of positive feedback can be calculated through the following formula:

`T = G / (1 - GH)`

Therefore, the correct answer is A).

### Identifying Nodes in a Circuit

In electrical engineering, a node is a point in a circuit where two or more circuit elements are connected together. It represents a variable or a signal. The term "node" is commonly used to refer to the connection point in a network of electrical components, but it can also be applied to any other interconnected system.

A node is often represented by a dot in circuit diagrams. The number of nodes in a circuit is equal to the number of wires or connections between components in the circuit. Nodes are important for analyzing and designing circuits, and they play a vital role in circuit analysis and design.

To identify the nodes in a circuit, one can look for dots or the intersection points of wires in the circuit diagram. It is important to understand the concept of a node in order to analyze and design electrical circuits accurately.

### Types of Time-Domain Analysis

In time-domain analysis, there are two main types of responses:

`1. Transient response`

`2. Steady-state response`

Therefore, the correct answer is B - 2 types of time-domain analysis.

### Identifying a Mixed Node

A mixed node is a type of node in a graph or network that has both incoming and outgoing branches. It is also referred to as a junction node or branching node. A mixed node is important in determining the overall connectivity of a network.

When analyzing a graph or network, it is important to recognize the different types of nodes, including input and output nodes, as well as mixed nodes. By identifying the type of node, we can better understand the structure and behavior of the network.

### Features of a Test Signal

A test signal may have various features that are important in analyzing the performance of a system or device. These features include:

**Sudden change:**At times, a system may encounter sudden changes in input or output signals. A test signal that has this feature can help determine how the system responds to such changes.**Sudden shock:**Similar to sudden change, a sudden shock can also be used to analyze a system's ability to handle sudden disturbances or disruptions.**Constant velocity and acceleration:**When testing mechanical or electrical systems, it is often important to know how a system responds to constant velocity and acceleration. A test signal with this feature can help determine the limits of such responses.

Therefore, the correct answer is **D) All of the above**, as all of these features are important in a test signal.

### Number of Types of Static Error Constants

The total number of static error constants is 3, which includes position constant, velocity constant, and acceleration constant.

```
const int POSITION_CONSTANT = 0;
const int VELOCITY_CONSTANT = 1;
const int ACCELERATION_CONSTANT = 2;
```

### Applicability of State-Space Method

The state-space method can be applied to both non-linear and time-variant systems. This means that it can be used to model and analyze a wide range of systems, including those that exhibit complex and dynamic behavior.

By representing a system in state-space form, it is possible to derive mathematical models that can be used to predict system behavior, design controllers, and optimize performance.

Therefore, if you are dealing with a non-linear or time-variant system, the state-space method is a powerful tool that can help you understand and control its behavior.

`// No code provided for this question`

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