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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