Chapter 10 â An introduction to digital control. This book has been written for controls students at Cal Poly quite simply to save them money. A flyâbyâwire system vs. A cruise control system, iconic examples of the positioner and the regulator. Below table provides you Control System Notes and Books Pdf Free pdf download. Disclaimer: Erexams.Com Website Is Not the Original Publisher Of all Book pdf On Net. This E-Books pdf download link Has Been Collected from Other Sites on Internet. This book is intended to give the senior or beginning graduate student in mechanical engineering an introduction to digital control of mechanical systems with an emphasis on applications. The desire to write this book arose from my frustration with the existing texts on digital control, which while.
Get New Updates Alerts Through Whatsapp, FB & TG Join Our Official Pages
Students JOIN OUR Whatsapp Group| Telegram Channel & Group
Jobs seekers :Visit to Get all upcoming Government & Teaching Jobs Updates Regularly
Download Control Systems Engineering By I.J. Nagrath,â M. Gopal â The book provides comprehensive coverage of various issues under control systems engineering. The book is suitable for courses at both the undergraduate and postgraduate level of engineering. Since the subject matter is inter-disciplinary, examples in the book are based on different branches of engineering.
The book discusses a wide range of topics including Mathematical Models of Physical Systems, Control Systems and Components, Concepts of Stability and Algebraic Criteria, Root Locus Technique, Frequency Response Analysis, Liapunovâs Stability Analysis, Optimal Control Systems, and Advances in Control Systems. In this revised edition, the book includes a host of new topics such as Neural Network Control, Nonlinear Systems, and Robotics Modeling and Control. In depth coverage has been given to classical and modern approaches on Digital Control. Explanations on PID tuning procedure and Robust Control have been improved and are accompanied by illustrations where necessary. Care has been taken to remove examples based on outdated technologies and to update the same with more relevant cases.
Control Systems Engineering By I.J. Nagrath,â M. Gopal â PDF Free Download
Contents
(Share & Gain Knowledge)Join EasyEngineering Whatsapp/Telegram Group
..Sharing is Caring..
Suggestion to Viewers: If youâre little serious about your studies, you should never consider eBooks/Books in PDF. The reason is the electronic devices divert your attention and also cause strains while reading eBooks. Kindly, Switch to hard copy of this Book & Buy it officially from the publishers and utilize your potential efficiently and with more confident.
Book Contents
About Author
I. J. Nagrath is the Adjunct Professor and former Deputy Director, BITS, Pilani. He has authored several leading books on engineering such as Modern Power System Analysis, Robotics and Control, Analog Computation and Simulation, and Basic Electrical Engineering. His research papers have been published in prominent technical journals. Prof. Nagrath received his M.S. from Wisconsin University, USA. He has also worked widely in the fields of robotics, signals and systems, and power.
M. Gopal is Professor of Electrical Engineering at the Indian Institute of Technology (IIT), New Delhi. His research focuses on Robust Control, Neural, and Fuzzy Technologies, Process Control, and Robotics. He has authored many books on Control Engineering including Modern Control System Theory, Digital Control Engineering, and Control Systems: Principles and Design. He has previously taught at IIT, Bombay, BITS, Pilani, and REC, Jaipur. He has also worked as an Honorary Visiting Professor in the Control Engineering Center at City University.
Book Details
Download Link
Visitor Kindly Note :This website is created solely for the engineering students and graduates to download an engineering e-books, Competitive Study Notes & other Study materials for free of cost. EasyEngineering team try to Helping the students and others who cannot afford buying books is our aim. If You think this Study Material/Book is Useful, Please Get It Legally from the publishers & If you feel good Share this Website with Others.
Disclaimer : EasyEngineering does not own this book/materials, neither created nor scanned. we provide the links which is already available on the internet. For any quarries, Disclaimer are requested to kindly contact us, We assured you we will do our best. We DO NOT SUPPORT PIRACY, this copy was provided for students who are financially troubled but deserving to learn. Thank you
Link is Successfully Activated to save the Book/Material (PDF)
Kindly Note : For Security purpose (Spam Protections), You need to Verify the below Captcha to Active your Download Link.
Click below the linkâDOWNLOADâ to save the Book/Material (PDF)
DOWNLOAD â Control Systems Engineering By I.J. Nagrath,â M. Gopal â Free Download PDF
If you face above Download Link error try this Link
DOWNLOAD â Control Systems Engineering By I.J. Nagrath,â M. Gopal â Free Download PDF
IS THIS MATERIAL IS HELPFUL, KINDLY SHARE IT & RATE IT
Jobs seekers :Visit to Get all upcoming Government & Teaching Jobs Updates Regularly
Preview
We need Your Support, Kindly Share this Web Page with Other Friends
If you have any Engg study materials with you kindly share it, It will be useful to other friends & We Will Publish The Book Submitted By You Immediately Including The Book Credits (Your Name) Soon After We Receive It (If The Book Is Not Posted Already By Us)
If You Think This Materials Is Useful, Please get it legally from the PUBLISHERS.
A GOOD MATERIAL ALONG WITH WELL EXPLAINED TEXTBOOKS PLAYS A KEY ROLE IN FETCHING APPRECIABLE GOOD RANK.
WISHING EVERY PERSON WHO GETS THIS MATERIAL FROM OUR SITE ALL THE VERY BEST !!
DISCLAIMER : I am not the original publisher of this Book/Material on net. This e-book/Material has been collected from other sources of net.
Where in the world is carmen sandiego episodes watch. Thank you for visiting my thread. Hope this post is helpful to you. Have a great day !
Kindly share this post with your friends to make this exclusive release more useful.
Related Posts You May Also LikeYour Comments About This Post
The latest reviewed version was checked on 14 June 2017. There are template/file changes awaiting review.
Digital Systems[edit]
Digital systems, expressed previously as difference equations or Z-Transform transfer functions can also be used with the state-space representation. Also, all the same techniques for dealing with analog systems can be applied to digital systems, with only minor changes.
Digital Systems[edit]
For digital systems, we can write similar equations, using discrete data sets:
Zero-Order Hold Derivation[edit]
If we have a continuous-time state equation:
We can derive the digital version of this equation that we discussed above. We take the Laplace transform of our equation:
Now, taking the inverse Laplace transform gives us our time-domain system, keeping in mind that the inverse Laplace transform of the (sI - A) term is our state-transition matrix, Φ:
Now, we apply a zero-order hold on our input, to make the system digital. Notice that we set our start time t0 = kT, because we are only interested in the behavior of our system during a single sample period:
We were able to remove u(kT) from the integral because it did not rely on Ï. We now define a new function, Î, as follows:
Inserting this new expression into our equation, and setting t = (k + 1)T gives us:
Now Φ(T) and Î(T) are constant matrices, and we can give them new names. The d subscript denotes that they are digital versions of the coefficient matrices:
We can use these values in our state equation, converting to our bracket notation instead:
Relating Continuous and Discrete Systems[edit]
Continuous and discrete systems that perform similarly can be related together through a set of relationships. It should come as no surprise that a discrete system and a continuous system will have different characteristics and different coefficient matrices. If we consider that a discrete system is the same as a continuous system, except that it is sampled with a sampling time T, then the relationships below will hold. The process of converting an analog system for use with digital hardware is called discretization. We've given a basic introduction to discretization already, but we will discuss it in more detail here.
Discrete Coefficient Matrices[edit]
Of primary importance in discretization is the computation of the associated coefficient matrices from the continuous-time counterparts. If we have the continuous system (A, B, C, D), we can use the relationship t = kT to transform the state-space solution into a sampled system:
Now, if we want to analyze the k+1 term, we can solve the equation again:
Separating out the variables, and breaking the integral into two parts gives us:
If we substitute in a new variable β = (k + 1)T + Ï, and if we see the following relationship:
We get our final result:
Digital Control System Book Pdf System
Comparing this equation to our regular solution gives us a set of relationships for converting the continuous-time system into a discrete-time system. Here, we will use 'd' subscripts to denote the system matrices of a discrete system, and we will use a 'c' subscript to denote the system matrices of a continuous system.
Matrix Dimensions:
A: p à p B: p à q C: r à p D: r à q
This operation can be performed using this MATLAB command:
If the Ac matrix is nonsingular, and we can find it's inverse, we can instead define Bd as:
The differences in the discrete and continuous matrices are due to the fact that the underlying equations that describe our systems are different. Continuous-time systems are represented by linear differential equations, while the digital systems are described by difference equations. High order terms in a difference equation are delayed copies of the signals, while high order terms in the differential equations are derivatives of the analog signal.
![]()
If we have a complicated analog system, and we would like to implement that system in a digital computer, we can use the above transformations to make our matrices conform to the new paradigm.
Digital Control System Book Pdf In HindiNotation[edit]
Because the coefficent matrices for the discrete systems are computed differently from the continuous-time coefficient matrices, and because the matrices technically represent different things, it is not uncommon in the literature to denote these matrices with different variables. For instance, the following variables are used in place of A and B frequently:
These substitutions would give us a system defined by the ordered quadruple (Ω, R, C, D) for representing our equations.
As a matter of notational convenience, we will use the letters A and B to represent these matrices throughout the rest of this book.
Converting Difference Equations[edit]
Now, let's say that we have a 3rd order difference equation, that describes a discrete-time system:
From here, we can define a set of discrete state variables x in the following manner:
Which in turn gives us 3 first-order difference equations:
Again, we say that matrix x is a vertical vector of the 3 state variables we have defined, and we can write our state equation in the same form as if it were a continuous-time system:
Solving for x[n][edit]
We can find a general time-invariant solution for the discrete time difference equations. Let us start working up a pattern. We know the discrete state equation:
Starting from time n = 0, we can start to create a pattern:
With a little algebraic trickery, we can reduce this pattern to a single equation:
Substituting this result into the output equation gives us:
[General Output Equation Solution]
Time Variant Solutions[edit]
If the system is time-variant, we have a general solution that is similar to the continuous-time case:
Where Ï, the state transition matrix, is defined in a similar manner to the state-transition matrix in the continuous case. However, some of the properties in the discrete time are different. For instance, the inverse of the state-transition matrix does not need to exist, and in many systems it does not exist.
State Transition Matrix[edit]
The discrete time state transition matrix is the unique solution of the equation:
Where the following restriction must hold:
From this definition, an obvious way to calculate this state transition matrix presents itself:
Or,
MATLAB Calculations[edit]
MATLAB is a computer program, and therefore calculates all systems using digital methods. The MATLAB function lsim is used to simulate a continuous system with a specified input. This function works by calling the c2d, which converts a system (A, B, C, D) into the equivalent discrete system. Once the system model is discretized, the function passes control to the dlsim function, which is used to simulate discrete-time systems with the specified input.
Because of this, simulation programs like MATLAB are subjected to round-off errors associated with the discretization process.
Sampler Systems[edit]
Let's say that we introduce a sampler into our system:
Notice that after the sampler, we must introduce a reconstruction circuit (described elsewhere) so that we may continue to keep the input, output, and plant in the laplace domain. Notice that we denote the reconstruction circuit with the symbol: Gr(s).
Now, Let's show the transfer function of this equation:
Now, this is going to get a little tricky, so follow along:
And we convert into the star domain because each term on the right-hand side of this equation has a star-domain term:
And next we can change variables into the Z-domain:
And we can solve for Y(z):
The preceding was a particularly simple example. However, the reader is encouraged to solve for the transfer function for a system with a sampler (and it's associated reconstructor) in the following places:
Retrieved from 'https://en.wikibooks.org/w/index.php?title=Control_Systems/Digital_Control_Systems&oldid=3231047'
Comments are closed.
|
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |