Control Engineering Problems with Solutions

1 Derek P. AthertonControl Engineering Problems with SolutionsDownload free books atDownload free eBooks at Derek P. AthertonControl Engineering Problems with SolutionsDownload free eBooks at Control Engineering Problems with Solutions1st edition 2013 Derek P. Atherton & 978-87-403-0374-2 Download free eBooks at on the ad to read moreControl Engineering Problems with Solutions4 ContentsContents Preface 71 Introduction Purpose 82 Mathematical Models and Block Diagrams Introduction Examples Problems 263 Transfer Functions and their Time Domain Responses Introduction Examples Problems e Graduate Programme for Engineers and GeoscientistsMonth 16I was a constructionsupervisor in the North Sea advising and helping foremen solve problemsI was ahesReal work International opportunities ree work placementsal Internationaor ree woI wanted real responsibili I joined MITAS because

2 E Graduate Programme for Engineers and GeoscientistsMonth 16I was a constructionsupervisor in the North Sea advising and helping foremen solve problemsI was ahesReal work International opportunities ree work placementsal Internationaor ree woI wanted real responsibili I joined MITAS because e Graduate Programme for Engineers and GeoscientistsMonth 16I was a constructionsupervisor in the North Sea advising and helping foremen solve problemsI was ahesReal work International opportunities ree work placementsal Internationaor ree woI wanted real responsibili I joined MITAS because e Graduate Programme for Engineers and GeoscientistsMonth 16I was a constructionsupervisor in the North Sea advising and helping foremen solve problemsI was ahesReal work International opportunities ree work placementsal Internationaor ree woI wanted real responsibili I joined MITAS because free eBooks at on the ad to read moreControl Engineering Problems with Solutions5 Contents4 Frequency Responses and their Plotting Introduction Examples Problems 595 Feedback Loop Stability Introduction Examples Problems 846 State Space Models and Transformations Introduction Examples Problems 1167 Control system Design Introduction Examples Problems free eBooks at on the ad to read moreControl Engineering Problems with Solutions6 Contents8 Phase Plane Analysis

3 Introduction Examples Problems 1689 The Describing Function and Exact Relay Methods Introduction Examples Problems 195it s an interestingworldGet under the skin of opportunitiesCheltenham | 24,945 + benefitsOne of the UK s intelligence services, GCHQ s role is two-fold: to gather and analyse intelligence which helps shape Britain sresponse to global events, and, to provide technical advice for theprotection of Government communication and information doing so, our specialists in IT, internet, Engineering , languages,information assurance, mathematics and intelligence get wellbeneath the surface of global affairs. If you thought the world was an interesting place, you really ought to explore our world of must be British citizens.

4 GCHQ values diversity and welcomes applicants fromall sections of the community. We want our workforce to reflect the diversity of our free eBooks at Engineering Problems with Solutions7 Preface PrefaceThe purpose of this book is to provide both worked examples and additional Problems , with answers only, which cover the contents of the two Bookboon books Control Engineering : An introduction with the use of Matlab and An Introduction to Nonlinearity in Control Systems . Although there was considerable emphasis in both books on the use of Matlab/Simulink, such usage may not always be possible, for example for students taking examinations. Thus in this book there are a large number of Problems solved long hand as well as by Matlab/Simulink. A major objective is to enable the reader to develop confidence in analytical work by showing how calculations can be checked using Matlab/Simulink.

5 Further by plotting accurate graphs in Matlab the reader can check approximate sketching methods, for say Nyquist and Bode diagrams, and by obtaining simulation results see the value of approximations used in solving some nonlinear Control Problems . I wish to acknowledge the influence of many former students in shaping my thoughts on many aspects of Control Engineering and in relatively recent years on the use of Matlab. In particular, Professor Dingyu Xue whose enthusiasm for Matlab began when he was a research student and who has been a great source of knowledge and advice for me on its use since that time, and to Dr. Nusret Tan for his assistance and advice on some Matlab routines. I wish to thank the University of Sussex for the facilities they have provided to me in retirement which have been very helpful in writing all three bookboon books and finally to my wife Constance for her love and support over many P.

6 AthertonUniversity of SussexBrighton May free eBooks at Engineering Problems with Solutions8 Introduction1 PurposeThe purpose of this book is to provide both worked examples and additional Problems , with answers only, which cover the contents of the two Bookboon books Control Engineering : An introduction with the use of Matlab[1] and An Introduction to Nonlinearity in Control Systems [2], which will be referred to as references 1 and 2, respectively, throughout this book. In reference 1 the emphasis in the book was to show how the use of Matlab together with Simulink could avoid the tedium of doing some calculations, however, there are situations where this may not be possible, such as some student examinations. Thus in this book as well as working out in many cases the examples long hand , the Solutions obtained using Matlab/Simulink are also given.

7 Matlab not only allows confirmation of the calculated results but also provides accurate graphs of say Nyquist plots or root locus diagrams where an examination question may ask for a sketch. Academics have been known to say they gained significant knowledge of a topic from designing exercises for students. Unlike 50 years ago when slide rules and logarithmic tables were used to solve Problems designing exercises is now much easier because in most instances results can be checked using appropriate computer programs, such as Matlab. Thus with these tools students can build their own exercises and gain confidence in solving them by doing appropriate checks with software. The examples and Problems have been carefully chosen to try and bring out different aspects and results of problem solving without, hopefully creating too much repetition, which can turn off the most ardent enthusiast.

8 Before the examples in each chapter a very brief overview of aspects of the topics covered is given but more details can be found in the relevant chapters of references 1 or 2, which are referred to in the relevant chapters of this Control Engineering : An introduction with the use of Matlab, Atherton. Bookboon An Introduction to Nonlinearity in Control Systems. Atherton. Bookboon OverviewThe examples and Problems are included under the following topic Mathematical Models and Block Transfer Functions and their Time Domain Responses. 4. Frequency Responses and their Plotting5. Feedback Loop Stability6. State Space Models and Transformations7. Control system Phase Plane Analysis9. The Describing Function and Exact Relay free eBooks at Engineering Problems with Solutions9 Mathematical Models and Block Diagrams2 Mathematical Models and Block IntroductionBlock diagrams are used by engineers to show how the possibly large number of components, which are present in many systems, are interconnected.

9 The information in a block may be purely descriptive, such as that shown in Figure , which describes the components of a typical measurement system , or contain a mathematical model of the various components which is required if any dynamic analysis is to be undertaken, which will be our concern here. TransducerVariableconversionelementSigna lprocessingSignaltransmissionSignalutili zationPhysical variableUsedoutputFigure Components of a typical measurement basic mathematical model of a component with lumped parameters is a differential equation. Although all component models are nonlinear one may often be able to approximate them under certain conditions by a linear differential equation. Control engineers usually work with two equivalents of a linear differential equation, a transfer function or a state space model, as described in chapter 2 of reference 1.

10 Thus a component model is typically shown by a block and labelled with its transfer function )(sG as shown in Figure , where the input to the block is labelled )(sU and the output )(sY. This means that )()()(sUsGsY=, where)(sUis the Laplace transform of the input signal )(tu and )(sYis the Laplace transform of the output signal )(ty. The corresponding relationship in the time domain is the convolution integral, see appendix A reference 1, given by = =ttdtugdutgty00)()()()()( , where )(tg the weighting function, or impulse response, of the block has the Laplace transform )(sG. It is normally understood that when the lower case is used, u, it is a function of t and when the upper cases is used, U it is a function of free eBooks at Engineering Problems with Solutions10 Mathematical Models and Block DiagramsThe first set of examples will be concerned with model representations for a single block.