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
Time Response Analysis of system
Standard Test Signals
What is time response ?
Types of Responses
Analysis of First order system
Analysis of Second order system
State variable analysis (observability & controllability)SatheeshCS2
Mr. C.S.Satheesh, M.E.,
State Variable Analysis
Observability
Controllability
Concept of state variables
State models for linear and time invariant Systems
Solution of state and output equation in controllable canonical form
Concepts of controllability and observability
Effect of state feedback.
Ch5 transient and steady state response analyses(control)Elaf A.Saeed
Chapter 5 Transient and steady-state response analyses. From the book (Ogata Modern Control Engineering 5th).
5-1 introduction.
5-2 First-Order System.
5-3 second-order system.
5-6 Routh’s stability criterion.
5-8 Steady-state errors in unity-feedback control systems.
Time Response Analysis of system
Standard Test Signals
What is time response ?
Types of Responses
Analysis of First order system
Analysis of Second order system
State variable analysis (observability & controllability)SatheeshCS2
Mr. C.S.Satheesh, M.E.,
State Variable Analysis
Observability
Controllability
Concept of state variables
State models for linear and time invariant Systems
Solution of state and output equation in controllable canonical form
Concepts of controllability and observability
Effect of state feedback.
Ch5 transient and steady state response analyses(control)Elaf A.Saeed
Chapter 5 Transient and steady-state response analyses. From the book (Ogata Modern Control Engineering 5th).
5-1 introduction.
5-2 First-Order System.
5-3 second-order system.
5-6 Routh’s stability criterion.
5-8 Steady-state errors in unity-feedback control systems.
This presention is about one of the most important concept of control system called State space analysis. Here basic concept of control system and state space are discussed.
Mr. C.S.Satheesh, M.E.,
Time Response in systems
Time Response
Transient response
Steady-state response.
Delay Time (td)
Rise Time (tr)
Peak Time (tp)
Maximum Overshoot (Mp)
Settling Time (tS)
Standard Test Signals
Impulse signal
Step signal
Ramp signal
Parabolic signal
state space modeling of electrical systemMirza Baig
Introduction
As systems become more complex, representing them with differential equations or transfer functions becomes cumbersome. This is even more true if the system has multiple inputs and outputs. This document introduces the state space method which largely alleviates this problem. The state space representation of a system replaces an nth order differential equation with a single first order matrix differential equation. The state space representation of a system is given by two equations :
The first equation is called the state equation, the second equation is called the output equation. For an nth order system (i.e., it can be represented by an nth order differential equation) with r inputs and m outputs the size of each of the matrices is as follows:
Several features:The state equation has a single first order derivative of the state vector on the left, and the state vector, q(t), and the input u(t) on the right. There are no derivatives on the right hand side.The output equation has the output on the left, and the state vector, q(t), and the input u(t) on the right. There are no derivatives on the right hand side.
q is nx1 (n rows by 1 column)q is called the state vector, it is a function of timeA is nxn; A is the state matrix, a constantB is nxr; B is the input matrix, a constant u is rx1; u is the input, a function of time C is mxn; C is the output matrix, a constant D is mxr; D is the direct transition matrix, a constant y is mx1; y is the output, a function of time
Derivation of of State Space Model (Electrical)
To develop a state space system for an electrical system, they choosing the voltage across capacitors, and current through inductors as state variables. Recall that
so if we can write equations for the voltage across an inductor, it becomes a state equation when we divide by the inductance (i.e., if we have an equation for einductor and divide by L, it becomes an equation for diinductor/dt which is one of our state variable). Likewise if we can write an equation for the current through the capacitor and divide by the capacitance it becomes a state equation for ecapacitor
There are three energy storage elements, so we expect three state equations. Try choosing i1, i2 and e1 as state variables. Now we want equations for their derivatives. The voltage across the inductor L2 is e1 (which is one of our state variables)so our first state variable equation is
This equation has our input (ia) and two state variable (iL2 and iL1) and the current through the capacitor. So from this we can get our second state equation
Our third, and final, state equation we get by writing an equation for the voltage across L1 (which is e2) in terms of our other state variables
references:
http://lpsa.swarthmore.edu/Representations/SysRepSS.html
https://en.wikipedia.org/wiki/State-space_representation
In this chapter, let us discuss the stability analysis in the ‘s’ domain using the RouthHurwitz stability criterion. In this criterion, we require the characteristic equation to find the stability of the closed loop control systems.
ME-314 Introduction to Control Engineering is a course taught to Mechanical Engineering senior undergrads. The course is taught by Dr. Bilal Siddiqui at DHA Suffa University. This lecture is about time response of systems derived by inspection of poles and zeros. Stability concepts and steady state errors are taught.
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.
Mr. C.S.Satheesh, M.E.,
Frequency response analysis
Frequency Domain Specifications
Resonant Peak Mr
Resonant Frequency ωr
Bandwidth ωh
Cut – off Rate
Gain margin Kg
Phase margin γ
POLAR PLOT
Bode PLOT
Transient and Steady State Response - Control Systems EngineeringSiyum Tsega Balcha
. Two crucial aspects of this behavior are transient and steady-state responses. These concepts encapsulate how a system behaves over time, from the moment an input is applied to when the system settles into a stable state. The transient response of a system characterizes its behavior during the initial phase after a change in input. It reflects how the system reacts as it transitions from one state to another. This phase is marked by dynamic changes in the system's output as it adjusts to the new conditions imposed by the input.
Characteristics of Transient Response are Time Constant, overshoot, settling time and damping.
Once the transient effects have subsided, the system enters the steady-state, where its behavior becomes constant over time. In this phase, the system operates under stable conditions, and its output remains within a narrow range around the desired value, despite fluctuations in input or external disturbances. Characteristics of Steady-State Response are Steady-State Error, stability, accuracy, robustness,.
This presention is about one of the most important concept of control system called State space analysis. Here basic concept of control system and state space are discussed.
Mr. C.S.Satheesh, M.E.,
Time Response in systems
Time Response
Transient response
Steady-state response.
Delay Time (td)
Rise Time (tr)
Peak Time (tp)
Maximum Overshoot (Mp)
Settling Time (tS)
Standard Test Signals
Impulse signal
Step signal
Ramp signal
Parabolic signal
state space modeling of electrical systemMirza Baig
Introduction
As systems become more complex, representing them with differential equations or transfer functions becomes cumbersome. This is even more true if the system has multiple inputs and outputs. This document introduces the state space method which largely alleviates this problem. The state space representation of a system replaces an nth order differential equation with a single first order matrix differential equation. The state space representation of a system is given by two equations :
The first equation is called the state equation, the second equation is called the output equation. For an nth order system (i.e., it can be represented by an nth order differential equation) with r inputs and m outputs the size of each of the matrices is as follows:
Several features:The state equation has a single first order derivative of the state vector on the left, and the state vector, q(t), and the input u(t) on the right. There are no derivatives on the right hand side.The output equation has the output on the left, and the state vector, q(t), and the input u(t) on the right. There are no derivatives on the right hand side.
q is nx1 (n rows by 1 column)q is called the state vector, it is a function of timeA is nxn; A is the state matrix, a constantB is nxr; B is the input matrix, a constant u is rx1; u is the input, a function of time C is mxn; C is the output matrix, a constant D is mxr; D is the direct transition matrix, a constant y is mx1; y is the output, a function of time
Derivation of of State Space Model (Electrical)
To develop a state space system for an electrical system, they choosing the voltage across capacitors, and current through inductors as state variables. Recall that
so if we can write equations for the voltage across an inductor, it becomes a state equation when we divide by the inductance (i.e., if we have an equation for einductor and divide by L, it becomes an equation for diinductor/dt which is one of our state variable). Likewise if we can write an equation for the current through the capacitor and divide by the capacitance it becomes a state equation for ecapacitor
There are three energy storage elements, so we expect three state equations. Try choosing i1, i2 and e1 as state variables. Now we want equations for their derivatives. The voltage across the inductor L2 is e1 (which is one of our state variables)so our first state variable equation is
This equation has our input (ia) and two state variable (iL2 and iL1) and the current through the capacitor. So from this we can get our second state equation
Our third, and final, state equation we get by writing an equation for the voltage across L1 (which is e2) in terms of our other state variables
references:
http://lpsa.swarthmore.edu/Representations/SysRepSS.html
https://en.wikipedia.org/wiki/State-space_representation
In this chapter, let us discuss the stability analysis in the ‘s’ domain using the RouthHurwitz stability criterion. In this criterion, we require the characteristic equation to find the stability of the closed loop control systems.
ME-314 Introduction to Control Engineering is a course taught to Mechanical Engineering senior undergrads. The course is taught by Dr. Bilal Siddiqui at DHA Suffa University. This lecture is about time response of systems derived by inspection of poles and zeros. Stability concepts and steady state errors are taught.
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.
Mr. C.S.Satheesh, M.E.,
Frequency response analysis
Frequency Domain Specifications
Resonant Peak Mr
Resonant Frequency ωr
Bandwidth ωh
Cut – off Rate
Gain margin Kg
Phase margin γ
POLAR PLOT
Bode PLOT
Transient and Steady State Response - Control Systems EngineeringSiyum Tsega Balcha
. Two crucial aspects of this behavior are transient and steady-state responses. These concepts encapsulate how a system behaves over time, from the moment an input is applied to when the system settles into a stable state. The transient response of a system characterizes its behavior during the initial phase after a change in input. It reflects how the system reacts as it transitions from one state to another. This phase is marked by dynamic changes in the system's output as it adjusts to the new conditions imposed by the input.
Characteristics of Transient Response are Time Constant, overshoot, settling time and damping.
Once the transient effects have subsided, the system enters the steady-state, where its behavior becomes constant over time. In this phase, the system operates under stable conditions, and its output remains within a narrow range around the desired value, despite fluctuations in input or external disturbances. Characteristics of Steady-State Response are Steady-State Error, stability, accuracy, robustness,.
ME-314 Introduction to Control Engineering is a course taught to Mechanical Engineering senior undergrads. The course is taught by Dr. Bilal Siddiqui at DHA Suffa University. This lecture is about time response of systems derived by inspection of poles and zeros. First and second order systems are considered, along with higher order and nonminimum phase systems
This presentation gives complete idea about time domain analysis of first and second order system, type number, time domain specifications, steady state error and error constants and numerical examples.
Combustion Chamber for Compression Ignition EnginesKaushal Patel
Description of various types of combustion chambers for compression ignition engines, various types of swirls, primary combustion considerations, advantages and disadvantages of various types of swirls and combustion chambers.
describe how elliptical trammel work and mathematics behind it, some calculations. you can make your own elliptical trammel some define range by using mathematics for controlling shape of ellipse.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
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
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
2. What is Time Response?
•Time response of system is defined as the output of a system when subjected when to an input
which is a functions of time.
•In the block diagram representation and signal flow graphs we studied how to obtain the
transfer function of a physical system. We have also seen how to combine individual transfer
functions to get a single transfer function using block diagram reduction and signal flow graphs.
We shall now study how this block responds to different inputs, i.e. we will now take closer look
at the response characteristics of the control system.
2
3. Inputs Supplied to a System
1. Impulse input :
Impulse represents a sudden change in input. An Impulse is infinite at t = 0 and zero
everywhere else. The area under the curve is 1. A unit impulse has magnitude 1 at t = 0.
r(t) = δ(t) = 1 t = 0
= 0 t ≠ 0
In the Laplace domain we have
L[r(t)] = L[δ(t)] = 1
Impulse inputs are used to derived a mathematical model of the system.
3
4. Inputs Supplied to a System
2. Step input :
A step input represents a constant command such as position. The input given to an elevator
is step input. Another example of a step input is setting the temperature of an air
conditioner.
A step signal is given by the formula,
r(t) = u(t) = A t ≥ 0
= 0 otherwise , If A = 1, it is called step.
In Laplace domain, we have
L[r(t)] = R(s) =
𝐴
𝑠
In case of a unit step, we get L [ r(t)] = R(s) =
1
𝑠
4
5. Inputs Supplied to a System
3. Ramp input :
The ramp input represents a linearly increasing input command. It is given by the formula,
r(t) = At t ≥ 0 ; Here A is the slope.
= 0 t < 0
If A = 1, it is called a unit ramp.
In the Laplace domain we have,
L [r(t)] = R(s) =
𝐴
𝑠2
In case of unit ramp, we have R(s) =
1
𝑠2
System are subjected to Ramp inputs when we need to study the system behavior for linear
increasing functions like velocity.
5
6. Inputs Supplied to a System
4. Parabolic input :
Rate of change of velocity is acceleration. Acceleration is a parabolic function. It is given by
the formula,
r(t) =
𝐴𝑡2
2
t ≥ 0
= 0 t < 0
If A = 1, it is called a unit parabola. In the Laplace domain we have
L [r(t)] = R(s) =
𝐴
𝑠3
In case of unit parabola, we have R(s) =
1
𝑠3
6
7. Inputs Supplied to a System
5. Sinusoidal input :
There are application where we need to subject the control system to sinusoidal inputs of
varying frequencies and study the system frequency response. A typical example is when we
want to check the quality of speakers of music system. In this we play different frequencies
(sinusoidal waves) and study their attenuations.
It is given by the equation, r(t) = A sin (ωt)
7
8. Steady State Response
•“Steady state response is that part of the output response where the output signal remains
constant.”
•The parameter that is important in the steady state response is the steady state error (𝑒𝑠𝑠).
•Error in general is the difference between the input and desirable output. Steady state error is
the error at t → ∞.
∴ 𝑒𝑠𝑠 = lim
𝑡 →∞
𝐸𝑟𝑟𝑜𝑟
•By derivation of formula for steady state error,
𝑒𝑠𝑠 = lim
𝑠 →0
𝑠 ∙
𝑅(𝑠)
1+𝐺 𝑠 𝐻(𝑠)
8
9. Effect of Input R(s) on Steady State Error
1. Step input :
The system subjected to a step input, the steady state error is controlled by position error
coefficient 𝑘 𝑝. Refer the figure Ignore the transient part. The input is shown by dotted line while
response is shown by a firm line. The equation below is describe steady state error for step input.
𝑒𝑠𝑠 =
𝐴
1+ 𝑘 𝑝
9
10. Effect of Input R(s) on Steady State Error
2. Ramp input :
For ramp input; the velocity error coefficient 𝑘 𝑣 will control the steady state error. Refer
figure ignore the transient part. The input is shown by a dotted line while the response is shown
by a firm line. The equation below describe the steady state transient error for the ramp input.
𝑒𝑠𝑠 =
𝐴
𝑘 𝑣
10
11. Effect of Input R(s) on Steady State Error
3. Parabolic input :
When parabolic input signal is applied, the acceleration error coefficient controls the steady state
error of the system. Refer figure ignore transient time. The parabolic input is shown by dotted line and
response by a firm line. The equation below is show the steady state error for the parabolic time
response.
𝑒𝑠𝑠 =
𝐴
𝑘 𝑎
11
12. Effect of Open Loop Transfer Function on
Steady State Error
•The steady state error(𝑒𝑠𝑠) also depends on G(s)H(s). Actually 𝑒𝑠𝑠 depends on the Type of system
G(s)H(s).
•Type of system is defined by the number of open loop Poles i.e., poles of G(s)H(s) that are present at
the origin.
•The open loop transfer function written in time constant form is,
𝐺 𝑠 𝐻 𝑠 =
𝑘1 1+𝑇𝑧1 𝑠 1+𝑇𝑧2 𝑠 …
𝑠 𝑛 1+𝑇𝑝1 𝑠 1+𝑇𝑝2 𝑠 …
•The open loop transfer function written in pole-zero form is written as
𝐺 𝑠 𝐻 𝑠 =
𝑘 𝑠+𝑧1 𝑠+𝑧2 …
𝑠 𝑛 𝑠+𝑝1 𝑠+𝑝2 …
•Here n is number of poles at the origin. It is very easy to obtain one from the other.
12
13. Subjecting a Type 0,1 & 2 Systems to a
Step, Ramp & Parabolic Input
Sr. No. Type Step Input Ramp Input Parabolic Input
𝒌 𝒑 𝒆 𝒔𝒔 𝒌 𝒗 𝒆 𝒔𝒔 𝒌 𝒂 𝒆 𝒔𝒔
(1) Type Zero K 𝐴
1 + 𝑘
0 ∞ 0 ∞
(2) Type One ∞ 0 k 𝐴
𝑘
0 ∞
(3) Type Two ∞ 0 ∞ 0 K 𝐴
𝑘
13
14. Transient Response
•In the earlier section, we discussed the steady state response in detail and found a method of
calculating the steady state error.
•We realized that 𝑒𝑠𝑠 was dependent on the Type of the system i.e. the number of poles, the
system had at the origin.
•The transient response of the system depends on the order of system. Order of a system is the
highest power of s in the denominator of closed loop transfer function.
•Hence for transient response, we need to work with the closed loop transfer function,
𝐺(𝑠)
1+𝐺 𝑠 𝐻(𝑠)
14
15. Analysis of First Order Systems
15
•General form:
•Problem: Derive the transfer function for the following circuit
1)(
)(
)(
s
K
sR
sC
sG
1
1
)(
RCs
sG
16. 16
Analysis of First Order Systems
•Transient Response: Gradual change of output from initial to the desired
condition.
•Block diagram representation:
•By definition itself, the input to the system should be a step function which is
given by the following:
C(s)R(s)
1s
K
s
sR
1
)(
Where,
K : Gain
: Time constant
17. 17
Analysis of First Order Systems
•General form:
•Output response:
1)(
)(
)(
s
K
sR
sC
sG
1
1
1
)(
s
B
s
A
s
K
s
sC
t
e
B
Atc
)(
)()()( sRsGsC
18. Analysis of Second Order Systems
18
•General form:
•Roots of denominator:
22
2
2 nn
n
ss
K
sG
Where,
K : Gain
ς : Damping ratio
n : Undamped natural frequency
02 22
nnss
12
2,1 nns
19. 19
Analysis of Second Order Systems
•Natural frequency, n
◦ Frequency of oscillation of the system without damping.
•Damping ratio, ς
◦ Quantity that compares the exponential decay frequency of the envelope to the
natural frequency.
(rad/s)frequencyNatural
frequencydecaylExponentia
20. Analysis of Second Order Systems
20
•Step responses for second-order system damping cases
21. Analysis of Second Order Systems
21
•When 0 < ς < 1, the transfer function is given by the following.
•Pole position:
dndn
n
jsjs
K
sG
2 Where,
2
1 nd
22. Transient Response Specifications
1. Delay time (Td) :
It is the time required for the response to reach 50% of the final value in the first attempt. It
is given by the formula,
1+0.7𝜉
𝜔 𝑛
sec
2. Rise time (Tr) :
It is the time required by response to rise from 10% to 90% of the final value for a
overdamped system. For a underdamped system (our case) the rise time is the taken for the
response to rise from 100% of the final value in the attempt. It is given by the formula,
𝜋−Θ
𝜔 𝑑
sec
22
23. Transient Response Specifications
3. Peak time (Tp) :
It is the time required by the response to reach its first peak. The first peak is always the
maximum peak,
𝜋
𝜔 𝑑
sec
4. Setting time (Ts) :
It is defined as the time required for the transient damped oscillations to reach and stay
within a specified tolerance band (usually 2% of the input value).
4
𝜉𝜔 𝑛
sec
23
24. Transient Response Specifications
5. Peak overshoot (Mp) :
It is the maximum peak value of the response measured from the input signal value. It is
also maximum error between input and output. It is generally written in terms of percentage,
%𝑀 𝑝 = 𝑒
−𝜉𝜋
1−𝜉2
∗ 100
24