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Books > Reference & Interdisciplinary > Communication studies > Information theory > Cybernetics & systems theory
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Linear Systems Control - Deterministic and Stochastic Methods (Paperback, Softcover reprint of hardcover 1st ed. 2008)
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Linear Systems Control - Deterministic and Stochastic Methods (Paperback, Softcover reprint of hardcover 1st ed. 2008)
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Modern control theory and in particular state space or state
variable methods can be adapted to the description of many
different systems because it depends strongly on physical modeling
and physical intuition. The laws of physics are in the form of
differential equations and for this reason, this book concentrates
on system descriptions in this form. This means coupled systems of
linear or nonlinear differential equations. The physical approach
is emphasized in this book because it is most natural for complex
systems. It also makes what would ordinarily be a difficult
mathematical subject into one which can straightforwardly be
understood intuitively and which deals with concepts which
engineering and science students are already familiar. In this way
it is easy to immediately apply the theory to the understanding and
control of ordinary systems. Application engineers, working in
industry, will also find this book interesting and useful for this
reason. In line with the approach set forth above, the book first
deals with the modeling of systems in state space form. Both
transfer function and differential equation modeling methods are
treated with many examples. Linearization is treated and explained
first for very simple nonlinear systems and then more complex
systems. Because computer control is so fundamental to modern
applications, discrete time modeling of systems as difference
equations is introduced immediately after the more intuitive
differential equation models. The conversion of differential
equation models to difference equations is also discussed at
length, including transfer function formulations. A vital problem
in modern control is how to treat noise in control systems.
Nevertheless this question is rarely treated in many control system
textbooks because it is considered to be too mathematical and too
difficult in a second course on controls. In this textbook a simple
physical approach is made to the description of noise and
stochastic disturbances which is easy to understand and apply to
common systems. This requires only a few fundamental statistical
concepts which are given in a simple introduction which lead
naturally to the fundamental noise propagation equation for dynamic
systems, the Lyapunov equation. This equation is given and
exemplified both in its continuous and discrete time versions. With
the Lyapunov equation available to describe state noise
propagation, it is a very small step to add the effect of
measurements and measurement noise. This gives immediately the
Riccati equation for optimal state estimators or Kalman filters.
These important observers are derived and illustrated using
simulations in terms which make them easy to understand and easy to
apply to real systems. The use of LQR regulators with Kalman
filters give LQG (Linear Quadratic Gaussian) regulators which are
introduced at the end of the book. Another important subject which
is introduced is the use of Kalman filters as parameter estimations
for unknown parameters. The textbook is divided into 7 chapters, 5
appendices, a table of contents, a table of examples, extensive
index and extensive list of references. Each chapter is provided
with a summary of the main points covered and a set of problems
relevant to the material in that chapter. Moreover each of the more
advanced chapters (3 - 7) are provided with notes describing the
history of the mathematical and technical problems which lead to
the control theory presented in that chapter. Continuous time
methods are the main focus in the book because these provide the
most direct connection to physics. This physical foundation allows
a logical presentation and gives a good intuitive feel for control
system construction. Nevertheless strong attention is also given to
discrete time systems. Very few proofs are included in the book but
most of the important results are derived. This method of
presentation makes the text very readable and gives a good
foundation for reading more rigorous texts. A complete set of
solutions is available for all of the problems in the text. In
addition a set of longer exercises is available for use as
Matlab/Simulink 'laboratory exercises' in connection with lectures.
There is material of this kind for 12 such exercises and each
exercise requires about 3 hours for its solution. Full written
solutions of all these exercises are available.
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