Control system
PRACTICAL FILE
HIMANSHU
41821025
B. TECH MECHATRONICS
CONTROL SYSTEM LAB FILE
ND TH
2 YEAR,4 SEMESTER
List of Experiments
1. Introduction to software commands used in control system.
2. To calculate the transfer function for a given block diagram.
3. To find unit step response, unit ramp parabolic response for second order
transfer function with unity feedback.
4. To find poles, zeros and gain of a given transfer function and to find to find
transfer function of a system whose zeros, poles and gain are given.
5. To determine the steady state error of a unity feedback control system in case of
step, ramp and parabolic inputs.
6. To plot the root locus for a given open loop transfer function.
7. To find phase and gain margin using bode plot for a given transfer function.
8. To draw polar plot for a given transfer function.
9. To study of ac servomotor.
10. To study the torque-speed characteristics and determine the transfer function of a
dc motor.
EXPERIMENT NO: - 1
Object: Introduction to software commands used in control system.
Software used: MATLAB
Theory: MATLAB is software package which is being used by the scientific and
engineering community all over the world. This is one of the most versatile and user —
friendly software useful for solving large and complex problem. MATLAB is developed by
The Math Work Inc., stands for matrix Laboratory. It is a software package used to
perform scientific computations and visualization. Its capability for analysis of various
scientific problems, flexibility and powerful graphics makes it a very useful software
package. It provides an integrated Development Environment (IDE) for programming
with numerous predefined functions for technical computations and visualization.
Besides available built-in-functions, user-defined functions can also be included which
can be used just like any other built-in-function.
It provide collections of functions that act as tools for specific applications such as
control system Design, power systems, Design , Power system, Digital Signal Processing.
MATLAB includes C and C++ Math libraries that support the development of stand -alone
applications. It provides an external interface to run FORTRAN, C and C++ programs from
within MATLAB programs. It also acts as the foundation for powerful simulation software
such as simulink and state flow. Moreover, more than 125 third-party software product
and services have interface with MATLAB.
As the name MATLAB comes from the two words 'MAT', which stand for Matrix, and
'LAB', which stands for Laboratory, MATLAB is Matrix Laboratory implying that it deals in
matrices.
Various types of tool box available in MATLAB as shown below:-
Aerospace Toolbox
Antenna Toolbox
Statistics and Machine Learning Toolbox
Curve Fitting Toolbox
Control System Toolbox
Signal Processing Toolbox
Mapping Toolbox
System Identification Toolbox
Deep Learning Toolbox
DSP System Toolbox
Data feed Toolbox
Financial Toolbox
Image Processing Toolbox
Text Analytics Toolbox
Predictive Maintenance Toolbox
Communications Toolbox
Embedded Coder
Filter Design HDL Coder
Robotics System Toolbox
Control Toolbox:
Control System ToolboxTM provides algorithms and apps for systematically analyzing,
designing, and tuning linear control systems. You can specify your system as a transfer
function, state-space, zero-pole-gain, or frequency-response model. Apps and functions,
such as step response plot and Bode plot, let you analyze and visualize system behavior
in the time and frequency domains.
You can tune compensator parameters using interactive techniques such as Bode loop
shaping and the root locus method. The toolbox automatically tunes both SISO and
MIMO compensators, including PID controllers. Compensators can include multiple
tunable blocks spanning several feedback loops. You can tune gain-scheduled
controllers and specify multiple tuning objectives, such as reference tracking,
disturbance rejection, and stability margins. You can validate your design by verifying
rise time, overs hoot, settling time, gain and phase margins, and other requirements.
Key Features
Transfer-function, state-space, zero-pole-gain, and frequency-response models
of linear systems.
Step response, Nyquist plot, and other time-domain and frequency-domain
tools for analyzing stability and performance.
Automatic tuning of PID, gain-scheduled, and arbitrary SISO and MIMO
control systems.
Root locus, Bode diagrams, LQR, LQG, and other classical and state-space
design techniques.
Model representation conversion, continuous-time model discretization, and
low- order approximation of high-order systems.
Commands used in control system:
Program-I
clearall
clc
A= [1 10 20;2 5 6; 7 8 9]; %Take any Matrix A
Determinant_A=det(A); %Determinant of Matrix
A Rank_A=rank(A); %Rank of Matrix A
Trace_A=trace(A); %Trace of Matrix A
Square_A=A*A; %Square of Matrix A
Transpose_A=transpose(A); %Transpose of Matrix
A Inverse_A=inv(A); %lnverse of Matrix A
Eigenvalue_A=eig(A); %Eigen Values of Matrix
A [v x]= eig(A) %Eigen Vector of Matrix
A
Orthogonal_A=orth(A); %Orthogonal Matrix of Matrix A
EXPERIMENT NO: - 2
Object: Introduction to software commands used in control system.
Software used: MATLAB
Theory: MATLAB is software package which is being used by the scientific and
engineering community all over the world. This is one of the most versatile and user —
friendly software useful for solving large and complex problem. MATLAB is developed by
The Math Work Inc., stands for matrix Laboratory. It is a software package used to
perform scientific computations and visualization. Its capability for analysis of various
scientific problems, flexibility and powerful graphics makes it a very useful software
package. It provides an integrated Development Environment (IDE) for programming
with numerous predefined functions for technical computations and visualization.
Besides available built-in-functions, user-defined functions can also be included which
can be used just like any other built-in-function.
It provides collections of functions that act as tools for specific applications such as
control system Design, power systems, Design, Power system, Digital Signal Processing.
MATLAB includes C and C++ Math libraries that support the development of stand -alone
applications. It provides an external interface to run FORTRAN, C and C++ programs from
within MATLAB programs. It also acts as the foundation for powerful simulation software
such as simulink and state flow. Moreover, more than 125 third-party software product
and services have interface with MATLAB.
As the name MATLAB comes from the two words 'MAT', which stand for Matrix, and
'LAB', which stands for Laboratory, MATLAB is Matrix Laboratory implying that it deals in
matrices.
Control System ToolboxTM provides functions for creating four basic representations of
linear time- interval (LTI) models:
Transfer function (T F) models
Zero-pole-gain (ZPK) models
State-space (SS) models
Frequency response data (FRD) models
Creating Transfer Function Models a1sn+a2sn-1+….an+1
Transfer functions (T F) are frequency-domain representations of L TI systems. A SISO
transfer function is a ratio of polynomials:
H(s)= A(s) a1sn+a2sn−1+...an+1
=
B(s) 𝑏1𝑠𝑚+𝑏2𝑠𝑚−1+...+𝑏𝑚+1
Transfer functions are specified by their numerator and denominator polynomials A(s)
and B(s). In MATLAB, a polynomial is represented by the vector of its coefficients, for
example, the polynomial
s2+2s+10
is specified as [1 2 10]
To create a TF object representing the transfer function:
𝑠
H(s)=𝑠2+2𝑠+10
Specify the numerator and denominator polynomials and use TF to construct the TF
object:
num = [1 0 ];
den = [1 2 25];
H = fts(num,den)
𝑠
H=
𝑠2+2𝑠+25
Continuous-time transfer function
Input
Output
EXPERIMENT NO: - 3
Objective- Plot unit step response of given transfer function and find peak
time, overshoot time, rise time and delay time using met lab.
Software used: MATLAB
Theory: The response of a system (with all initial conditions equal to zero at
t=0-, i.e., a zero-state response) to the unit step input is called the unit step
response.
Peak overshoot- Peak overshoot Mp is defined as the deviation of the
response at peak time from the final value of response. It is also called the
maximum overshoot. Where, c(tp) is the peak value of the response
Delay Time
It is the time required for the response to reach half of its final value from the
zero instant. It is denoted by td.
Consider the step response of the second order system for t ≥ 0, when ‘δ’ lies
between zero and one.
Rise Time
It is the time required for the response to rise from 0% to 100% of its final
value. This is applicable for the under-damped systems. For the over-damped
systems, consider the duration from 10% to 90% of the final value. Rise time is
denoted by tr.
Peak Time
It is the time required for the response to reach the peak value for the first
time. It is denoted by tp. At t=tp, the first derivate of the response is zero
INPUT
OUTPUT
EXPERIMENT NO :- 4
Object: To find poles, zeros and gain of a given transfer function and to find ystem.
Software used: MATLAB
Theory: The transfer function provides a basis for determining important system
response characteristics without solving the complete differential equation. As defined.
the transfer function is a rational function in the complex variable
N(s) 𝑎𝑛𝑠𝑚 +𝑎𝑛−1𝑠𝑚−1+....+𝑎1𝑠+𝑎0
H(s) = D(s) = 𝑏𝑛𝑠𝑛+𝑏𝑛−1𝑠𝑛−1+....+𝑏1𝑠+𝑏0
It is often convenient to factor the polynomials in the numerator and denominator. and
to write the transfer function in terms of those factors
N(s)
H(s) = = 𝐾(𝑠−𝑧1)(𝑠−𝑧2)……..(𝑠−𝑧𝑚−1)(𝑠−𝑧𝑚)
D(s)
(𝑠−𝑝1)(𝑠−𝑝2)……..(𝑠−𝑝𝑛−1)(𝑠−𝑝𝑛)
where the numerator and denominator polynomials, N(s)and D(S) have real coefficients
defined by the system's differential equation and K is gain. As written in Eq. (2), the zi's
and Pi's are the poles and zeros respectively with the equations.
N(s)=0
D(s)=0
Program:
Plot the pole-zero configuration in s-plane for the given transfer function:
(5S2+15S+10)
G(s) = 2𝑆
Input
Output
