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Discrete-time control system design with applications. (English) Zbl 1402.93013

New York, NY: Springer (ISBN 978-1-4614-9289-4/hbk; 978-1-4939-4095-0/pbk; 978-1-4614-9290-0/ebook). xvii, 170 p. (2014).
The book ‘Discrete-time Control System Design with Applications’ presents and studies several issues in the field of digital control. In the process of designing a control system, a designer needs to take into account that most control systems are implemented using digital hardware. Based on hardware capabilities, the sampling and update rates may not be optimal, but are subject to limitations. Thus, the conversion of a continuous system to a digital one needs to be studied, since there are several issues that emerge during this design process that need to be addressed, to ensure stability, accurate representation of the continuous system, and overall performance. This book addresses many of those issues and discusses suitable design techniques, along with real time applications.
The first part of the book provides a review of preliminary results of control systems. Chapters 1 and 2 present the basics of signal analysis, \(Z\) and \(\Gamma\) transforms, along with sample and hold techniques such as zero and first order hold, dual-rate generalized holds and lifting.
Chapter 3 studies different discretization techniques like numerical approximation, hold equivalence, pole zero matching. Attention is given to multivariable systems and nonlinear systems.
In Chapter 4, the connection between continuous systems and their sampled-data and discrete time analogues is studied. The problem of convergence of these models as sampling time decreases is studied, for single and dual rate systems.
Chapter 5 presents the global digital redesign technique. Again, issues like stability, sampling rate and efficient fast implementation, order reduction and other issues are considered for single and dual rate systems.
The last two chapters implement the previous results to two real time control problems. In Chapter 8, the motion control problem for a wheeled mobile robot is studied using flatness-based averaging control. A general model for a wheeled robot is given and extensive numerical simulations are carried out to compare flatness based control and feedback linearization linear control. The results are then discussed and observations are made on the effects of different sampling times, gain, hold techniques, processing burden and single or dual rate designs.
The second application in Chapter 8 deals with the problem of digital redesign of autopilots, for tracking an acceleration signal. Numerous simulations are made and several issues are again discussed, like sampling rates and the effect on stability, controller order, pole zero locations and more.
Overall, the book will be of great interest to researchers, academics and industry engineers since it combines theory and practise and outlines control techniques along with the many issues that arise when implementing them. It also includes several explanatory figures and many numerical simulations in the last two chapters.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93C55 Discrete-time control/observation systems
93C95 Application models in control theory
93C57 Sampled-data control/observation systems
93B18 Linearizations
93C35 Multivariable systems, multidimensional control systems
93B36 \(H^\infty\)-control
93C62 Digital control/observation systems
93C10 Nonlinear systems in control theory
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