FCS Practicals [Third Year Instrumentation/Electrical]
Practical List
2. Compare and plot the unit-step responses of the unity-feedback closed-loop systems with the given forward path transfer function. Assume zero initial conditions. Use any computer simulation program.
3. Study of the effect of damping factor on system performance by obtaining unit step response and unit impulse response for a prototype standard second-order system. Consider five different values for zeta= 0.1, 0.3, 0.5, 0.7 and 1.0. Also, study the effect of varying undamped natural frequency by taking three different values. Comment on the simulations obtained.
4. Write a program that will compute the step response characteristics of a second-order system i.e. percent overshoot, rise time, peak time, and settling time. Generalize it for accepting different values of undamped natural frequency and damping factor.
5. Study and plot the unit step responses of the addition of a pole and a zero to the forward path transfer function for a unity feedback system. Plot the responses for four different values of poles and zeros. Comment on the simulations obtained.
6. Study and plot the unit step responses of the addition of a pole and a zero to the closed-loop transfer function. Plot the responses for four different values of poles and zeros. Comment on the simulations obtained.
7. Program for compensator design using Bode plot.
8. Program for Compensator design using Root Locus Analysis.
9. Plot and comment on various properties of any three systems (Problems) using the Routh-Hurwitz criterion, Root locus technique, Bode plots, Nyquist plots.
Practical number # 1
Introduction to MATLAB and SIMULINK
1. Introduction to MATLAB. What is MATLAB? (Search on google)2. How we initialize variables in MATLAB? Write all theory whichever you have written in a notebook in your words.
3. Matrices initialization and extraction of elements from matrices.
4. How to assign polynomials? How to get equation from polynomials and vice versa?
5. How do we plot any graphs with all labels? Explain with an example.
6. How we write transfer functions in the editor window and SIMULINK? Explain with some examples.
7. What is the Final value theorem? What it signifies? Write any conclusion whichever you have found during the study of a transfer function.
Only for Reference (Write, what you learned only):-
Modeling of physical systems using SIMULINK and subplot the response of various types of inputs applied to the model.
Revision of first practical (Time delay systems and its response at its steady-state) Write theory as per practical session understanding.Theory consist of
1. Explain zpk instruction with example.
2. When do we use zp2tf and tf2zp instruction? Explain as per your understanding in detail.
3. Write a program for various inputs apply on model using 'subplot' and 'lsim' instructions, assume necessary data.
4. Explain mathematical proof using the Final value theorem for each case (i.e., when applying (a) Impulse (b) Step (c) ramp (d) exponential inputs applied to systems).
5. Prints to be attach- (a) Script file of the program (b) Output generate from that program (only figures not command window) --- (Write your Name and Reg. no. before print)
Practical number # 3
Performance of first-order and second-order systems.
Aim:- Study of the effect of damping factor on system performance by obtaining unit step response and unit impulse response for a prototype standard second-order system. Consider five different values for ξ = 0.1, 0.3, 0.5, 0.7 and 1.0. Also, study the effect of varying undamped natural frequency by taking three different values. Comment on the simulations obtained.
Objective:- The objective of this exercise will be to study the performance characteristics of first and second-order systems using MATLAB.
Theory:-
Revision of second practical and necessary instructions (ramp signal, take Laplace and inverse Laplace, find a response in the time domain when an input to a system is ramp)
1. Linear and non linear identification...(Necessary conditions of linearity i.e., homogeneity (scaling) and additivity) Take example:- (1) x=u+2 (2) dx/dt+x=u take x(0)=0......where u is input=t
Check the responses on MATLAB.
2. What are the differential equations?
3. Mathematical model some real-time examples (1) Disposal of packed radioactive elements in the sea (2) Vehicles shock absorber when hit to particular objects.
4. Generalized second-order differential equations of any physical systems and effects of damping in it.
5. Prints to be attach- (a) Script file of the program (b) Output generate from that program (only figures not command window) --- (Write your Name and Reg. no. before print)
Dates of completion:- (A batch Instru- 21/07/2018), (B batch Instru- 30/07/2018), (C batch Instru- 01/08/2018), (A batch EE- 26/07/2018), (B batch EE- 30/07/2018)
Overview of second-order systems:-
The above system is known as a second-order system.
Revision of second practical and necessary instructions (ramp signal, take Laplace and inverse Laplace, find a response in the time domain when an input to a system is ramp)
1. Linear and non linear identification...(Necessary conditions of linearity i.e., homogeneity (scaling) and additivity) Take example:- (1) x=u+2 (2) dx/dt+x=u take x(0)=0......where u is input=t
Check the responses on MATLAB.
2. What are the differential equations?
3. Mathematical model some real-time examples (1) Disposal of packed radioactive elements in the sea (2) Vehicles shock absorber when hit to particular objects.
4. Generalized second-order differential equations of any physical systems and effects of damping in it.
5. Prints to be attach- (a) Script file of the program (b) Output generate from that program (only figures not command window) --- (Write your Name and Reg. no. before print)
Dates of completion:- (A batch Instru- 21/07/2018), (B batch Instru- 30/07/2018), (C batch Instru- 01/08/2018), (A batch EE- 26/07/2018), (B batch EE- 30/07/2018)
Consider the
following the Mass-Spring system shown in Figure 2. Where K is the spring constant, B is the friction coefficient, x(t) is the displacement, and F(t) is the applied force:
 |
| A mass damper spring system |
The differential equation for the above Mass-Spring the system can be derived as follows
 |
| Equation 1 |
Applying the Laplace transformation we get
 |
| Laplace transform of above Equation 1 |
provided that, all the initial
conditions are zeros.
Then the transfer function representation of the system is given by
 |
| The transfer function of a system |
The above system is known as a second-order system.
The generalized notation for a second-order system described above can be written as
 |
| Generalized second order system |
for
which the transient output, as obtained from the Laplace transform table, is
Where,
0 < ζ < 1. The transient response
of the system changes for different values
of damping ratio, ζ. Standard
performance measures for a second-order feedback system are defined in terms of
step response of a system
Only for Reference (Write, what you learned only):-
Matlab Code:- (Attach Print)
Output:- (Attach figure print and include command window result)
Conclusion:-
Practical number # 4
Time-domain specifications of the second-order system.
Aim:- Write a program that will compute the step response characteristics of a second-order system i.e. percent overshoot, rise time, peak time, and settling time. Generalize it for accepting different values of undamped natural frequency and damping factor.
Objective:- The objective of this exercise will be to study the step response characteristics of second-order systems using MATLAB.
Theory:- The response of the second-order system is shown below.
Revision of practical 3 (Variation in zeta and variation in natural frequency wn, what is the difference?)
1. What is the effect of a time constant on the first-order system? Chart of the time constant.
2. Effect of zeta values on poles of the system. Also, plot the unit step response for second-order
system. comment on the magnitude of the system for various values of zeta and wn.
3. Check Rise time, Peak time, Maximum overshoot, Settling time, and steady-state value.
4. Write an observation table for all cases.
5. Prints to be attach- (a) Script file of the program (b) Output generate from that program (only figures not command window) --- (Write your Name and Reg. no. before print)
Dates of completion:- (A batch Instru- 31/07/2018), (B batch Instru- 06/08/2018), (C batch Instru- ), (A batch EE- 02/08/2018), (B batch EE- 06/08/2018)
The performance measures could be described as follows:
1) Delay time (td):- It is the time required to reach at 50% of its final value by a time response signal during its first cycle of oscillation.
2) Rise Time (tr):- The time for a system to respond to a step input and attains a response equal to a percentage of the magnitude of the input. The 0-100% rise time, Tr, measures the time to 100% of the magnitude of the input. Alternatively, Tr1, measures the time from 10% to 90% of the response to the step input.
3) Peak Time (tp):- The time for a system to respond to a step input and rise to peak response.
4) Maximum overshoot (Mp): The amount by which the system output response proceeds beyond the desired response and it is calculated as
5) Settling time (ts):- The time required for the system’s output to settle within a certain percentage of the input amplitude (which is usually taken as 2%). Then, settling time, Ts is calculated as Ts= (4÷(ζωn)).
Characteristic table:-
Write the Table only for Zeta=0.4 and Zeta=0.7 in journal pages. (All values you have to calculate in MATLAB)
Assignment for Practical 4 - Implement the RLC circuit on a breadboard and give it a step input (Square wave) and observe the response on CRO.
Refer this link- https://www.youtube.com/watch?v=zfh2WKCNoeo
Aim:- Study and plot the unit step responses of the addition of a pole and a zero to the transfer function for a unity feedback system. Plot the responses for four different values of poles and zeros. Comment on the simulations obtained.
Objective:- The objective of this exercise will be to study the time response analysis of addition of pole & zero to forwarding path transfer function for unity feedback the system using MATLAB.
Objective:-
Matlab Code:- (Attach Print)
Aim:- Write a program for obtaining a bode plot of the open-loop transfer function.
Objective:- The objective of this experiment is to investigate practical use of the frequency response analysis tool for a compensator design and to simulate this process in MATLAB for Bode Plot.
General procedure:-
1) Rewrite the sinusoidal function in the time constant form.
2) Identify the corner frequencies associated with each factor of the transfer function.
3) Knowing the corner frequencies, draw the asymptotic magnitude plot.
5) Dawn the smooth curve through connected points.
Matlab Code:- (Attach Print)
Objective:- The objective of this experiment is to study the SISO tool for the design purpose of controllers in the control system.
Revision of practical 3 (Variation in zeta and variation in natural frequency wn, what is the difference?)
1. What is the effect of a time constant on the first-order system? Chart of the time constant.
2. Effect of zeta values on poles of the system. Also, plot the unit step response for second-order
system. comment on the magnitude of the system for various values of zeta and wn.
3. Check Rise time, Peak time, Maximum overshoot, Settling time, and steady-state value.
4. Write an observation table for all cases.
5. Prints to be attach- (a) Script file of the program (b) Output generate from that program (only figures not command window) --- (Write your Name and Reg. no. before print)
Dates of completion:- (A batch Instru- 31/07/2018), (B batch Instru- 06/08/2018), (C batch Instru- ), (A batch EE- 02/08/2018), (B batch EE- 06/08/2018)
 |
| The response of the second-order system |
The performance measures could be described as follows:
1) Delay time (td):- It is the time required to reach at 50% of its final value by a time response signal during its first cycle of oscillation.
2) Rise Time (tr):- The time for a system to respond to a step input and attains a response equal to a percentage of the magnitude of the input. The 0-100% rise time, Tr, measures the time to 100% of the magnitude of the input. Alternatively, Tr1, measures the time from 10% to 90% of the response to the step input.
3) Peak Time (tp):- The time for a system to respond to a step input and rise to peak response.
4) Maximum overshoot (Mp): The amount by which the system output response proceeds beyond the desired response and it is calculated as
Characteristic table:-
Write the Table only for Zeta=0.4 and Zeta=0.7 in journal pages. (All values you have to calculate in MATLAB)
Matlab Code:- (Attach Print)
Output:- (Attach figure print and include command window result)
Assignment for Practical 4 - Implement the RLC circuit on a breadboard and give it a step input (Square wave) and observe the response on CRO.
Refer this link- https://www.youtube.com/watch?v=zfh2WKCNoeo
Conclusion:-
For Reference-
For Reference-
 |
| Characteristics of unit step response for a first-order and second-order system |
Practical number # 5
Stability analysis using Routh Hurwitz Criteria
Program script file and result
Advanced script file for all cases (Find error and correct it)
Program script file and result
Advanced script file for all cases (Find error and correct it)
Aim:- Write a program to check stability from Routh Hurwitz table from MATLAB
Theory:- Write a theory by yourself.
Matlab Code:- (Attach Print of code from the updated link)
Output:- Write output for example 1, 2, 3, and 4. (No need to print output from the command window, write as per your own understanding)
Conclusion:-
Practical number # 6
Time response analysis of the addition of pole and zero to the transfer function of the system also study the root locus plot of the respective system.
Aim:- Study and plot the unit step responses of the addition of a pole and a zero to the transfer function for a unity feedback system. Plot the responses for four different values of poles and zeros. Comment on the simulations obtained.
Objective:- The objective of this exercise will be to study the time response analysis of addition of pole & zero to forwarding path transfer function for unity feedback the system using MATLAB.
Theory:-
1. Effect of addition of pole and zeros in transfer functions.
2. Comment on Stability and nature of system depends on poles of a system, explain.
3. Prints to be attach- (a) Script file of the program (b) Output generate from that program (only figures not command window) --- (Write your Name and Reg. no. before print)
Addition of pole to forward path transfer function:
The forward path transfer of the second-order system is given by
when we add a pole to it we get the transfer function as
Now when p is large the pole addition has very little effect on the transient response as p approaches the imaginary axis, the overshoot increases. This effect is just opposite to that of the addition
of a pole to CLTF. If p is sufficiently closed to the origin the close loop system may even go unstable.
For infinity, the step response is the same as the step response of the system of only the forward path transfer function. As p reduces the plot moves away from the step response of this system.
Addition of zeros to Forward path transfer function:
The transfer function after adding zeros to second-order FPTF is given as,
on further simplification we get,
1) Addition of FP zeros on the left-hand side increases a speed response
. But a large overshoot may result if the zero is sufficiently close to the origin.
2) The order of the system does not increase with the addition of zero to FPTF.
3) The zero in the right half-plane retards the system & produces an undershoot. The percent overshoot decreases as the zero moves along with the positive real axis towards infinity, again the system oscillates for a longer time.
Matlab Code:- (Attach Print)
1. Effect of addition of pole and zeros in transfer functions.
2. Comment on Stability and nature of system depends on poles of a system, explain.
3. Prints to be attach- (a) Script file of the program (b) Output generate from that program (only figures not command window) --- (Write your Name and Reg. no. before print)
Addition of pole to forward path transfer function:
 |
| Forward path gain |
when we add a pole to it we get the transfer function as
For infinity, the step response is the same as the step response of the system of only the forward path transfer function. As p reduces the plot moves away from the step response of this system.
Addition of zeros to Forward path transfer function:
The transfer function after adding zeros to second-order FPTF is given as,
2) The order of the system does not increase with the addition of zero to FPTF.
3) The zero in the right half-plane retards the system & produces an undershoot. The percent overshoot decreases as the zero moves along with the positive real axis towards infinity, again the system oscillates for a longer time.
Matlab Code:- (Attach Print)
Output:- (Attach figure print and include command window result)
Conclusion:-
Practical
number # 7
Program for obtaining root locus plot.
Aim:- Write a
program for obtaining
root locus plot of the open-loop transfer function.
Objective:-
- The objective of this experiment is to investigate practical use of the root locus analysis tool.
- To simulate this process in MATLAB for poles and zero location, in addition to Simulink for dynamical system simulation.
Theory:-
Control system engineers have utilized a number of techniques to analyze and design a controller for a typical closed-loop control system. One of the most employed approaches is the Root Locus. In particular, Root Locus shows graphically the location of closed-loop poles through the knowledge of the open-loop poles and zeros. In addition to this, it shows also the location of the closed-loop poles as a loop gain k varies from zero up to infinity. Once the desired response is known, hence it will be then an easy task to find from the Root Locus the associated gain to achieve such response.
Matlab Code:- (Attach Print)
Output:- (Attach figure print and include command
window result)
Conclusion:-
Dates of completion:- (A batch Instru- ), (B batch Instru- ), (C batch Instru- ), (A batch EE- ), (B batch EE- )
Practical number # 8
Program for obtaining bode plot
Aim:- Write a program for obtaining a bode plot of the open-loop transfer function.
Objective:- The objective of this experiment is to investigate practical use of the frequency response analysis tool for a compensator design and to simulate this process in MATLAB for Bode Plot.
Theory:- Frequency response methods have been used to analyze closed-loop dynamic systems, in addition, to design typical controllers. Magnitude
and phase play important measures for quantifying the mount of energy a system has. Once the response of the system is known
for over a large range of frequencies, this gives an insight about how
to attach a typical controller at some frequencies to make the system acting in the required manner.
This experiment looks in details on how to obtain a
typical
the frequency response of a
a system, experimentally and theoretically.
General procedure:-
1) Rewrite the sinusoidal function in the time constant form.
2) Identify the corner frequencies associated with each factor of the transfer function.
3) Knowing the corner frequencies, draw the asymptotic magnitude plot.
5) Dawn the smooth curve through connected points.
Matlab Code:- (Attach Print)
Output:- (Attach figure print and include command window result)
Conclusion:-
Practical number # 9
Study of the SISO tool in MATLAB.
Aim:- Study SISO tool in MATLAB used for the design purpose of the control system.
Objective:- The objective of this experiment is to study the SISO tool for the design purpose of controllers in the control system.
Theory:-
Write in your own understanding. (It must include information on starting procedure of SISO tool, syntax, necessary plots used for checking stability and nature of the response.)
Write in your own understanding. (It must include information on starting procedure of SISO tool, syntax, necessary plots used for checking stability and nature of the response.)
Conclusion:-
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