The document provides information about transfer functions and their characteristics including time response, frequency response, stability, and system order. It discusses different types of systems including first order and second order systems. It also demonstrates how to analyze transfer functions and obtain step and impulse responses using MATLAB. Key points include:
- Transfer functions relate the input and output of a system in the Laplace domain
- Time and frequency responses provide information about a system's behavior over time and at different frequencies
- Stability depends on the locations of the poles - systems are stable if all poles have negative real parts
- First and second order systems have distinguishing characteristics like rise time, settling time, overshoot
- MATLAB commands like step, impulse, pole can
State space analysis, eign values and eign vectorsShilpa Shukla
State space analysis concept, state space model to transfer function model in first and second companion forms jordan canonical forms, Concept of eign values eign vector and its physical meaning,characteristic equation derivation is presented from the control system subject area.
State space analysis, eign values and eign vectorsShilpa Shukla
State space analysis concept, state space model to transfer function model in first and second companion forms jordan canonical forms, Concept of eign values eign vector and its physical meaning,characteristic equation derivation is presented from the control system subject area.
This presentation explains about the introduction of Polar Plot, advantages and disadvantages of polar plot and also steps to draw polar plot. and also explains about how to draw polar plot with an examples. It also explains how to draw polar plot with numerous examples and stability analysis by using polar plot.
This presentation gives complete idea about definitions of stability, BIBO, Absolute and relative stability, Routh-Hurwitz Criterion, Special Cases and numerical examples.
This presentation explains about the introduction of Nyquist Stability criterion. It clearly shows advantages and disadvantages of Nyquist Stability criterion and also explains importance of Nyquist Stability criterion and steps required to sketch the Nyquist plot. It explains about the steps required to sketch Nyquist plot clearly. It also explains about sketching Nyquist plot and determines the stability by using Nyquist Stability criterion with an example.
Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively
Z Transform And Inverse Z Transform - Signal And SystemsMr. RahüL YøGi
The z-transform is the most general concept for the transformation of discrete-time series.
The Laplace transform is the more general concept for the transformation of continuous time processes.
For example, the Laplace transform allows you to transform a differential equation, and its corresponding initial and boundary value problems, into a space in which the equation can be solved by ordinary algebra.
The switching of spaces to transform calculus problems into algebraic operations on transforms is called operational calculus. The Laplace and z transforms are the most important methods for this purpose.
Root locus is a graphical representation of the closed-loop poles as a system parameter is varied.
It can be used to describe qualitatively the performance of a system as various parameters are changed.
It gives graphic representation of a system’s transient response and also stability.
We can see the range of stability, instability, and the conditions that cause a system to break into oscillation.
This presentation explains about the introduction of Polar Plot, advantages and disadvantages of polar plot and also steps to draw polar plot. and also explains about how to draw polar plot with an examples. It also explains how to draw polar plot with numerous examples and stability analysis by using polar plot.
This presentation gives complete idea about definitions of stability, BIBO, Absolute and relative stability, Routh-Hurwitz Criterion, Special Cases and numerical examples.
This presentation explains about the introduction of Nyquist Stability criterion. It clearly shows advantages and disadvantages of Nyquist Stability criterion and also explains importance of Nyquist Stability criterion and steps required to sketch the Nyquist plot. It explains about the steps required to sketch Nyquist plot clearly. It also explains about sketching Nyquist plot and determines the stability by using Nyquist Stability criterion with an example.
Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively
Z Transform And Inverse Z Transform - Signal And SystemsMr. RahüL YøGi
The z-transform is the most general concept for the transformation of discrete-time series.
The Laplace transform is the more general concept for the transformation of continuous time processes.
For example, the Laplace transform allows you to transform a differential equation, and its corresponding initial and boundary value problems, into a space in which the equation can be solved by ordinary algebra.
The switching of spaces to transform calculus problems into algebraic operations on transforms is called operational calculus. The Laplace and z transforms are the most important methods for this purpose.
Root locus is a graphical representation of the closed-loop poles as a system parameter is varied.
It can be used to describe qualitatively the performance of a system as various parameters are changed.
It gives graphic representation of a system’s transient response and also stability.
We can see the range of stability, instability, and the conditions that cause a system to break into oscillation.
This paper outlines fundamental topics related to classical control theory. It moves from modeling simple mechanical systems to designing controllers to manage said system.
The following resources come from the 2009/10 BEng in Electrical Engineering (course number 2ELE0066) from the University of Hertfordshire. All the mini projects are designed as level two modules of the undergraduate programmes.
The objectives of this module are to demonstrate within an industrial environment:
• To use Matlab® (Simulink®)
• To implement an appropriate analogue computer for modelling dynamic systems.
A DC motor model, in specific prototyping stages, is more appropriate to use than the actual DC motor. This project aimed to design and implement a DC motor model by using a simulation package (CAD) such as Matlab and implement the equivalent electronic hardware platform.
Giving description about time response, what are the inputs supplied to system, steady state response, effect of input on steady state error, Effect of Open Loop Transfer Function on Steady State Error, type 0,1 & 2 system subjected to step, ramp & parabolic input, transient response, analysis of first and second order system and transient response specifications
Here's the continuation of the report:
3.2.1 Parallel Plate Capacitor (continued)
As the IV fluid droplets move between the plates of the capacitor, the capacitance increases due to the change in the dielectric constant, resulting in the observation of a peak in capacitance.
3.2.2 Semi-cylindrical Capacitor
The semi-cylindrical capacitor consists of two semi-cylindrical conductors (plates) facing each other with a gap between them. The gap between the plates is filled with a dielectric material, typically the IV fluid.
When a potential difference is applied across the plates, electric field lines form between them. The dielectric material between the plates enhances the capacitance by reducing the electric field strength and increasing the charge storage capacity.
3.2.3 Cylindrical Cross Capacitor
The cylindrical cross capacitor is composed of two cylindrical conductors (rods) intersecting at right angles to form a cross shape. The space between the rods is filled with a dielectric material, such as the IV fluid.
When a potential difference is applied between the rods, electric field lines form between them. The dielectric material between the rods enhances the capacitance by reducing the electric field strength and increasing the charge storage capacity, similar to the semi-cylindrical design.
3.3 Advantages of Capacitive Sensing Approach
Capacitive sensing for IV fluid monitoring offers several advantages over other automated monitoring methods:
1. Non-invasive operation: The sensors do not require direct contact with the IV fluid, reducing the risk of contamination or disruption to the therapy.
2. High sensitivity: Capacitive sensors can detect minute changes in capacitance, enabling precise tracking of IV fluid droplets.
3. Low cost: The sensors can be constructed using relatively inexpensive materials, making them a cost-effective solution.
4. Low power consumption: Capacitive sensors typically have low power requirements, making them suitable for continuous monitoring applications.
5. Ease of implementation: The sensors can be easily integrated into existing IV setups without significant modifications.
6. Stable measurements: Capacitive sensors can provide stable and repeatable measurements across different IV fluid types.
Chapter 4: Experimental Setup and Results
4.1 Description of Experimental Setup
To evaluate the performance of capacitive sensors for IV fluid monitoring, an experimental setup was constructed. The setup included various capacitive sensor designs, such as parallel plate, semi-cylindrical, and cylindrical cross capacitors, positioned around an IV drip chamber.
The sensors were connected to a capacitance measurement circuit, which recorded the changes in capacitance as IV fluid droplets passed through the sensor's electric field. Multiple experiments were conducted using different IV fluid types and flow rates to assess the sensors' accuracy, repeatability, and sensitivity.
4.2 Measurements with
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
control system Lab 01-introduction to transfer functions
1. Nalan Karunanayake 16/03/2015 1
EC - Control Systems
Laboratory 01 – Transfer Functions
Objective
The main purpose of this lab session is to be familiar with characteristics of transfer functions using
MATLAB software
TASK 1
To construct a transfer function as bellow (System variable conversions)
G(S) =
3(𝑠+7)
𝑠2+2𝑠+2
In MATLAB command window, type
(Assigning the numerator and denominator coefficient vectors)
>> num = [3 21];
>> den = [1 2 2];
>> G = tf(num,den)
OR
>>s = tf(‘s’);
>>G = ((3*s+21)/(s^2+2*s+2))
Try to obtain the following transfer functions:
G(S) =
5(𝑠+2)
(𝑠+1)(𝑠2+𝑠−6)
G(S) =
2(s+3)(s+5)2
(s+2)(s2+4)2
Time response of a system
2. Nalan Karunanayake 16/03/2015 2
The time response represents how the state of a dynamic system changes in time when subjected to a
particular input. The time response of a linear dynamic system consists of the sum of the transient
response which depends on the initial conditions and the steady-state response which depends on the
system input.
Frequency response of a system
In linear time invariant (LTI) systems have the extremely important property that if the input to the
system is sinusoidal, then the steady-state output will also be sinusoidal at the same frequency but in
general with different magnitude and phase. These magnitude and phase differences as a function of
frequency comprise the frequency response of the system.
The frequency response of a system can be found from the transfer function in the following way: create
a vector of frequencies (varying between zero or "DC" to infinity) and compute the value of the plant
transfer function at those frequencies. If 𝐺(𝑠) is the open-loop transfer function of a system and is the
frequency vector, we then plot 𝐺(𝑗𝜔) versus 𝜔. Since 𝐺(𝑗𝜔)is a complex number, we can plot both its
magnitude and phase (the Bode Plot) or its position in the complex plane (the Nyquist Diagram). Both
methods display the same information in different ways.
Stability of a system
The transfer function representation is especially useful when analyzing system stability. If all poles of
the transfer function (values of s at which the denominator equals zero) have negative real parts, then
the system is stable. If any pole has a positive real part, then the system is unstable. If we view the poles
on the complex s-plane, then all poles must be in the left half plane (LHP) to ensure stability. If any
pair of poles is on the imaginary axis, then the system is marginally stable and the system will oscillate.
The poles of a LTI system model can easily be found in MATLAB using the pole command.
>>s = tf(‘s’);
>>G = 1/(s^2 + 2*s + 5)
>>pole(G)
ans =
-1.0000 + 2.0000i
-1.0000 - 2.0000i
If we use pole-zero map using the pzmap command on MATLAB:
3. Nalan Karunanayake 16/03/2015 3
>>pzmap(G)
Thus this system is stable since the real parts of the poles are both negative.
Exercise 1
Check the following transfer functions stability
1. 𝐺𝑠 =
1
𝑠2−2𝑠+9
2. 𝐺𝑠 =
1
𝑠2 + 1
3. 𝐺𝑠 =
1
(𝑠 − 6)(𝑠 − 4)
4. Nalan Karunanayake 16/03/2015 4
System Order
The order of a dynamic system is the order of the highest derivative of its governing differential
equation. Equivalently, it is the highest power of s in the denominator of its transfer function.
First Order System
The first order system can take the general form
𝐺(𝑆) =
𝑏
(𝑠 + 𝑎)
+
𝐾𝑑𝑐
(𝑡. 𝑠 + 1)
DC gain:𝑲𝒅𝒄 , is the ratio of the magnitude of the steady-state step response to the magnitude of the
step input. From the Final Value Theorem, for stable transfer functions the DC gain is the value of the
transfer function when s=0. For first order systems equal to 𝐾𝑑𝑐 =
𝑏
𝑎
.
Time constant t: is the time to reach 63% of the steady state value for a step input or to decrease to
37% of the initial value and 𝑡 =
1
𝑎
is found. It is special for the first order system only.
Rise Time (Tr): 𝑻 𝒓 =
𝟐.𝟐
𝒂
Settling Time (Ts): 𝑻 𝒔 =
𝟒
𝒂
The first order system has no overshooting but can be stable or not depending on the location of its pole.
The first order system has a single pole at -a. If the pole is on the negative real axis (LHP), then the
system is stable. If the pole is on the positive real axis (RHP), then the system is not stable. The zeros
of a first order system are the values of s which makes the numerator of the transfer function equal to
zero.
5. Nalan Karunanayake 16/03/2015 5
Second Order System
Second order systems are commonly encountered in practice, and are the simplest type of dynamic
system to exhibit oscillations. In fact many real higher order systems are modeled as second order to
facilitate analysis.
The general form of second order system is:
𝐺(𝑠) =
𝑎
(𝑠2 + 𝑏𝑠 + 𝑐)
=
𝐾 𝑑𝑐. 𝜔 𝑛
2
(𝑠2 + 2𝜀𝜉𝜔 𝑛 𝑠 + 𝜔 𝑛
2)
Natural frequency 𝝎 𝒏 is the frequency of oscillation of the system without damping.
Damping Ratio
The damping ratio is a dimensionless quantity characterizing the energy losses in the system due to
such effects as viscous friction or electrical resistance.
𝝃 =
𝒃
𝟐𝝎 𝒏
Poles and zeros
Note that the system has a pair of complex conjugate poles at:
𝑆 = −𝝃𝝎 𝒏 ± 𝒋𝝎 𝒏√𝟏 − 𝝃 𝟐 = −𝝈 ± 𝒋𝝎
𝝎 : damped frequency of oscillation.
DC gain
The DC gain,𝐾𝑑𝑐 =
𝑎
𝑐
, again is the ratio of the magnitude of the steady-state step response to the
magnitude of the step input, and for stable systems it is the value of the transfer function when s = 0.
For second order systems
𝐾𝑑𝑐 =
𝑎
𝑐
Percent Overshoot
The percent overshoot is the percent by which a system exceeds its final steady-state value. For a second
order under damped system, the percent overshoot is diretly related to the damping ratio by the
following equation:
𝑂𝑆% = 𝑒
−
𝜋𝜉
√1−𝜉2
∗ 100
6. Nalan Karunanayake 16/03/2015 6
Settling Time
The settling time, , is the time required for the system ouput to fall within a certain percentage of the
steady state value for a step input or equivalently to decrease to a certain percentage of the initial value
for an impulse input. For a second order, underdamped system, the settling time can be approximated
by the following equation:
𝑻 𝒔 =
𝟒
𝝃𝝎 𝒏
=
𝟒
𝝈
Rise Time: 𝑻 𝒓 =
𝟏 − 𝟎.𝟒𝟏𝟔𝟕𝝃 +𝟐.𝟗𝟏𝟕𝝃 𝟐
𝝎 𝒏
General Form of a Denominator: S2
+ 2ςωnS + ωn2
(Second order system)
Then, S = -ςωn ± √(ςωn)2 − ωn2
∆ = (ςωn)2
− ωn2
Step time response:
If the input is step function then the output or the response is called step time response. The system can
be represented by a transfer function which has poles (values make the denominator equal to zero),
depending on these poles the step response divided into four cases:
1. Underdamped response:
In this case the response has an overshooting with a small oscillation which results from complex poles
in the transfer function of the system. i.e. ∆ < 0 or ς < 1
2. Critically response:
In this case the response has no overshooting and reaches the steady state value (final value) in the
fastest time. In other words it is the fastest response without overshooting and is resulted from the
existence of real & repeated poles in the transfer function of the system. i.e. ∆ = 0 or ς =1
3. Overdamped response:
In this case no overshooting will appear and reach the final value in a time larger than critically case.
This response is resulted from the existence of real & distinct poles in the transfer function of the system.
i.e. ∆ > 0 or ς > 1
7. Nalan Karunanayake 16/03/2015 7
4. Undamped response:
In this case a large oscillation will appear at the output and will not reach a final value and this because
of the existence of imaginary poles in the transfer function of the system and the system in this case is
called "Marginally stable".
8. Nalan Karunanayake 16/03/2015 8
MATLAB Work
Step and Impulse Responses of a Transfer Function
To get the step response of a transfer function: use,
1 . 𝐺𝑠 =
2
𝑠 + 3
>> G = tf ([2], [1 3])
>> step (G)
To obtain impulse response: use,
>> impulse (G)
stepinfo(sys): this command is used to Compute
step response characteristics.
For the following transfer functions we will find
the settling time, rise time, overshoot and steady
state error:
>> stepinfo(G)
Result
10. Nalan Karunanayake 16/03/2015 10
Undamped Response
𝐺𝑠 =
9
𝑠2 + 3
>> G = tf ([9], [1 0 3])
>> step (G)
>> figure, impulse (G)
>>stepinfo(G)
Exercise 2
Obtain the step response of the following transfer functions given below and find the step info using
MATLAB and calculations
1. 𝐺𝑠 =
21
2𝑠2 + 16𝑠 + 21
2. 𝐺𝑠 =
2
3𝑠2 + 4𝑠 + 6
3. 𝐺𝑠 =
√6
𝑠2+8𝑠+ √6
11. Nalan Karunanayake 16/03/2015 11
Step Response using Matlab Simulink
Starting Simulink
Simulink is started from the MATLAB command prompt by entering the following command:
>>Simulink
Alternatively, you can hit the Simulink button at the top of the MATLAB window as shown here
When it starts, Simulink brings up a single window, entitled Simulink Library Browser which can be
seen here.
12. Nalan Karunanayake 16/03/2015 12
Then goto NewSimulink Model
Construct the following Simulink model using Simulink library components as follows
The simple model consists of three blocks: Step, Transfer Function, and Scope. The Step is
a Source block from which a step input signal originates. This signal is transferred through the line in
the direction indicated by the arrow to the Transfer Function Continuous block. The Transfer
Function block modifies its input signal and outputs a new signal on a line to the Scope. The Scope is
a Sink block used to display a signal much like an oscilloscope.
Modifying blocks
A block can be modified by double-clicking on it. For example, if you double-click on the Transfer
Function block in the Simple model, you will see the following dialog box.
Modify the transfer function block as follows
13. Nalan Karunanayake 16/03/2015 13
Running simulation
To run the simulation hit the play button
The simulation should run very quickly and the scope window will appear as shown below.
Note that the simulation output (shown in yellow) is at a very low level relative to the axes of the scope.
To fix this, hit the auto scale button (binoculars), which will rescale the axes as shown below.
14. Nalan Karunanayake 16/03/2015 14
Exercise 3
1. Obtain the step response of the following transfer functions using Simulink.
1. 𝐺𝑠 =
12
(𝑠2+6𝑠+9)
2. 𝐺𝑠 =
15
(𝑠2+7𝑠+12)
3. 𝐺𝑠 =
9
𝑠2+3
The effect of varying damping ratio on a second-order system
15. Nalan Karunanayake 16/03/2015 15
Exercise 4
Review Questions
1. What is the different between steady state response and transient response of a control
system?
2. The pole-zero plot for the two transfer functions are given below, obtain their unit step
response and comment on it.
3. How damping ratio (zeta) affects the time response of a second order system?
16. Nalan Karunanayake 16/03/2015 16
NOTE
What is time response?
It is an equation or a plot that describes the behavior of a system and contains much information about
it with respect to time response specification as overshooting setting time, peak time, rise time and
steady state error. Time response is formed by the transient response and the steady state response.
𝑻𝒊𝒎𝒆 𝒓𝒆𝒔𝒑𝒐𝒏𝒔𝒆 = 𝑻𝒓𝒂𝒏𝒔𝒊𝒆𝒏𝒕 𝒓𝒆𝒔𝒑𝒐𝒏𝒔𝒆 + 𝑺𝒕𝒆𝒂𝒅𝒚 𝒔𝒕𝒂𝒕𝒆 𝒓𝒆𝒔𝒑𝒐𝒏𝒔𝒆
Transient time response describes the behavior of the system in its first short time until arrives the
steady state value and this response will be our study focus.
If the input is step function then the output or the response is called step time response and if the input
is ramp, the response is called ramp time response … etc.
Delay Time (Td): is the time required for the response to reach 50% of the final value.
Rise Time (Tr): is the time required for the response to rise from 0 to 90% of the final value.
Settling Time (Ts): is the time required for the response to reach and stay within a specified tolerance
band (2% or 5%) of its final value.
Peak Time (Tp): is the time required for the underdamped step response to reach the peak of time
response (Yp) or the peak overshoot.
Percent Overshoot (OS%): is the normalized difference between the response peak value and the
steady value This characteristic is not found in a first order system and found in higher one for the
underdamped step response.
Steady State Error (ess): indicates the error between the actual output and desired output as‘t’ tends to
infinity, and is defined as: