Control Systems Laboratory
EEL308A
B.Tech. in EEE V Semester
Department: Electrical Engineering
Faculty of Engineering & Technology
Ramaiah University of Applied Sciences
Control Systems Laboratory
Laboratory Manual
Faculty Engineering & Technology
Department Electrical Engineering
Programme B. Tech.
Course Electrical and Electronics Engineering
Year/Semester 3rd Year/5th Semester
Name of the Laboratory Control Systems Laboratory
Laboratory Code EEL308A
List of Experiments:
Mathematical Model of Physical Systems-Automotive Cruise Control System
Mathematical Model of Physical Systems-RLC Circuit
Block Diagram Reduction
Time Response Analysis of First Order Systems
Time Response Analysis of Second Order Systems
Design of a P Controller
Design of a PI Controller
Design of a PID Controller
Root Locus Techniques
Lab Internal Test
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Name:
Reg No. :
Branch:
Experiment Experiment
VIVA Total
Name of the Experiment Write up Conduction
(10) (25)
(8) (7)
Mathematical Model of Physical Systems-
1 Automotive Cruise Control System
Mathematical Model of Physical Systems-RLC
2 Circuit
3 Block Diagram Reduction
Time Response Analysis of First Order
4
Systems
Time Response Analysis of Second Order
5
Systems
6 Design of a P Controller
7 Design of a PI Controller
8 Design of a PID Controller
9 Root Locus Techniques
10 Lab Internal Test
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Experiment No.1
Mathematical Modelling of Physical
Systems
1. Introduction and Purpose of Experiment
The experiment aims to create and validate a mathematical model for an automotive cruise control
system to study its dynamic behavior. It evaluates the system's performance under different conditions
to optimize control strategies. This helps identify design improvements and ensures better system
stability and responsiveness.
2. Aim and Objective
To mathematically model an automotive cruise control system by obtaining its transfer
function.
3. Software Required
MATLAB Simulink
4. Experimental Set Up
Figure 1: Automotive Cruise Control Systems
5. Experimental Procedure:
OPEN MATLAB
GO TO FILE->New Script->Script
Write your MATLAB Code:
Save the .m File
Save the file with a ‘.m’ extension
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Run the code in MATLAB Editor
Click the Run button in the MATLAB Editor Toolbar
6. Program or Simulation Model and Tabulation:
M=1000;
B=50;
U=500;
num=[1]
den=[M B]
sys = tf(num,den);
step(u*sys);
7. Calculations/Computations/Algorithms
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8. Presentation of Results
9. Analysis and Discussions
1. Integrating adaptive control techniques improves performance in varying conditions.
2. Continuous advancements in modeling tools expand the scope of control system designs.
10. Conclusions
Simulation tools facilitate the validation of cruise control models.
11. Comments
1. Limitations of Experiments
Environmental variables, such as weather and road conditions, may not be fully captured.
Limited availability of test scenarios reduces the scope of experimental validation.
Limitations of Results
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Simplifications in the mathematical model can cause deviations from real-world behavior.
Hardware limitations in testing setups may restrict accurate performance measurement
2. Learning happened
1. Understanding the impact of feedback mechanisms in control systems improved.
2. Techniques for balancing stability and responsiveness were clarified.
3. Recommendations
Employ advanced nonlinear modeling techniques for improved accuracy.
Integrate adaptive algorithms to handle varying road and load conditions effectively.
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Experiment No.2
Mathematical Modelling of Automotive
Cruise Control System
1. Introduction and Purpose of Experiment
Automatic cruise control is an excellent example of a feedback control system found in many modern vehicles. The
purpose of the cruise control system is to maintain a constant vehicle speed despite external disturbances, such as
changes in wind or road grade. This is accomplished by measuring the vehicle speed, comparing it to the desired
or reference speed, and automatically adjusting the throttle according to a control law.
2. Aim and Objective
To mathematically model an automotive cruise control system by obtaining its transfer
function.
3. Software Required
MATLAB Simulink
4. Experimental Set Up
Figure 1: RLC Circuit
5. Experimental Procedure:
OPEN MATLAB
• GO TO FILE->New Script->Script
• Write your MATLAB Code:
• Save the .m File
• Save the file with a ‘.m’ extension
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• Run the code in MATLAB Editor
• Click the Run button in the MATLAB Editor Toolbar
6. Program or Simulation Model and Tabulation:
7. Calculations/Computations/Algorithms
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8. Presentation of Results
9. Analysis and Discussions
The mathematical model of the RLC circuit captures the system's behavior by describing
the relationships between resistance, inductance, capacitance, and applied voltage. The analysis
highlights the dynamic response of the circuit to AC and DC inputs, emphasizing resonance
frequency and damping factors. Simulations validate the accuracy of the model, showing close
agreement with theoretical predictions under ideal conditions.
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10. Conclusions
The RLC circuit model successfully predicts system dynamics, including transient and
steady-state responses.Resonance frequency and damping ratio are critical parameters
for determining circuit performance.
11. Comments
4. Limitations of Experiments
Experimental results may be affected by non-ideal components like parasitic inductance and
resistance. Environmental factors, such as temperature, can influence the circuit's behavior.
5. Limitations of Results
The model assumes ideal components, which may not fully represent real-world variations.
6. Learning happened
Understanding the interplay between resistance, inductance, and capacitance in defining circuit
behavior
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Experiment No. 3
Block Diagram Reduction
1. Introduction and Purpose of Experiment
2. Aim and Objectives
To verify the validity of the transfer function obtained through hand calculations for a series and
parallel block diagram with feedback using MATLAB and Simulink.
3. Software Required
MATLAB Simulink
4. Experimental Set Up
R(s) Y(s)
G1 G2
Figure 1: Blocks in Series with feedback
G1
R(s) Y(s)
G2
Figure 2: Blocks in parallel with feedback
5. Experimental Procedure
OPEN MATLAB
• GO TO FILE->New Script->Script
• Write your MATLAB Code:
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• Save the .m File
• Save the file with a ‘.m’ extension
• Run the code in MATLAB Editor
• Click the Run button in the MATLAB Editor Toolbar
Program or Simulation Model and Tabulation
1. Calculations/Computations/Algorithms
2. Expected Graph
3. Presentation of Results
4. Analysis and Discussions
5. Conclusions
6. Comments
Limitations of Experimen
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1. ts
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2. Limitations of Results
3. Learning happened
4. Recommendations
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Experiment No. 4
Time Response Analysis – First Order System
1. Introduction and Purpose of Experiment
2. Aim and Objectives
To analyse the system time response of an RLC circuit by fulfilling the following objectives:
Obtaining the Transfer Function for the case in question
Comparing the Transfer Function with the general first order equation
Finding the Rise Time, Peak Time, Maximum Overshoot and Settling Time where ever
necessary
Comparing the results by plotting the same on MATLAB
3. Apparatus Required
MATLAB
4. Experimental Procedure
5. Program or Simulation Model and Tabulation
6. Calculations/Computations/Algorithms
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7. Presentation of Results
8. Analysis and Discussions
9. Conclusions
10. Comments
1. Limitations of Experiments
2. Limitations of Results
3. Learning happened
4. Recommendations
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Experiment No. 5
Time Response Analysis – Second Order System
1. Introduction and Purpose of Experiment
2. Aim and Objectives
To analyse the system time response of a general second order system and a mass spring
damper system by fulfilling the following objectives:
Obtaining the Transfer Function for the case in question
Comparing the Transfer Function with the general second order equation
Identifying the values of the variables Zeta and Omega
Finding the Rise Time, Peak Time, Maximum Overshoot and Settling Time where ever
necessary
Comparing the results by plotting the same on MATLAB
3. Software Required
MATLAB
4. Experimental Procedure
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5. Program or Simulation Model and Tabulation
6. Calculations/Computations/Algorithms
Case: 1
General Second Order equation
𝜔𝑛2
𝑠22𝜔𝑛𝜁𝑠 + 𝜔𝑛2
Given equation
𝐾
𝑠2 + 10𝑠 + 𝐾
Presentation of Results
7. Analysis and Discussions
8. Conclusions
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9. Comments
1. Limitations of Experiments
2. Limitations of Results
3. Learning happened
4. Recommendations
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Experiment No. 6
Design of a Proportional Controller
1. Introduction and Purpose of Experiment
2. Aim and Objectives
To design a controller for the given Transfer Function the following objectives need to be met:
Convert the given block diagram to a transfer function
Plot the step response of the system to understand the existing parameters of the system
Arrive the values for gain to obtain the appropriate results
Plot the new system on MATLAB
Arrive at appropriate conclusions
3. Apparatus Required
MATLAB
4. Experimental Procedure
5. Calculations/Computations/Algorithms
With the specifications given:
1
𝑇𝐹 =
𝑚𝑠 + 𝑏
6. Presentation of Results
7. Analysis and Discussions
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8. Conclusions
9. Comments
1. Limitations of Experiments
2. Limitations of Results
3. Learning happened
4. Recommendations
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Experiment No. 7
Design of a PI Controller
1. Introduction and Purpose of Experiment
2. Aim and Objectives
To design a controller for the given Transfer Function the following objectives need to be met:
Convert the given block diagram to a transfer function
Plot the step response of the system to understand the existing parameters of the system
Arrive the values for gain to obtain the appropriate results
Plot the new system on MATLAB
Arrive at appropriate conclusions
3. Apparatus Required
MATLAB
4. Experimental Procedure
5. Calculations/Computations/Algorithms
6. Presentation of Results
7. Analysis and Discussions
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8. Conclusions
9. Comments
1. Limitations of Experiments
2. Limitations of Results
3. Learning happened
4. Recommendations
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Experiment No. 8
Design of a PID Controller
1. Introduction and Purpose of Experiment
2. Aim and Objectives
To design a controller for the given Transfer Function the following objectives need to be met:
Convert the given block diagram to a transfer function
Plot the step response of the system to understand the existing parameters of the system
Arrive the values for gain to obtain the appropriate results
Plot the new system on MATLAB
Arrive at appropriate conclusions
3. Apparatus Required
MATLAB
4. Experimental Procedure
5. Calculations/Computations/Algorithms
6. Presentation of Results
7. Analysis and Discussions
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8. Conclusions
9. Comments
5. Limitations of Experiments
6. Limitations of Results
7. Learning happened
8. Recommendations
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Experiment No. 9
Root Locus Techniques
1. Introduction and Purpose of Experiment
2. Aim and Objectives
To obtain the root locus of a given system by determining the following:
Finding the poles and zeros of the open loop transfer function
Finding the centroid of the given poles
Determining the angle of asymptotes for the given poles
Determining the breakaway point
Validation of the results using MATLAB
3. Apparatus Required
MATLAB
4. Experimental Procedure
5. Calculations/Computations/Algorithms
Open Loop Transfer Function
𝑘
𝐺(𝑠) =
𝑆(𝑠 + 2)(𝑠 + 4)
6. Presentation of Results
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7. Analysis and Discussions
8. Conclusions
9. Comments
1. Limitations of Experiments
2. Limitations of Results
3. Learning happened
4. Recommendations
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