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This monograph presents a simple and efficient two-relay control
algorithm for generation of self-excited oscillations of a desired
amplitude and frequency in dynamic systems. Developed by the
authors, the two-relay controller consists of two relays switched
by the feedback received from a linear or nonlinear system, and
represents a new approach to the self-generation of periodic
motions in underactuated mechanical systems. The first part of the
book explains the design procedures for two-relay control using
three different methodologies - the describing-function method,
Poincare maps, and the locus-of-a perturbed-relay-system method -
and concludes with stability analysis of designed periodic
oscillations. Two methods to ensure the robustness of two-relay
control algorithms are explored in the second part, one based on
the combination of the high-order sliding mode controller and
backstepping, and the other on higher-order sliding-modes-based
reconstruction of uncertainties and their compensation where
Lyapunov-based stability analysis of tracking error is used.
Finally, the third part illustrates applications of
self-oscillation generation by a two-relay control with a Furuta
pendulum, wheel pendulum, 3-DOF underactuated robot, 3-DOF
laboratory helicopter, and fixed-phase electronic circuits.
Self-Oscillations in Dynamic Systems will appeal to engineers,
researchers, and graduate students working on the tracking and
self-generation of periodic motion of electromechanical systems,
including non-minimum-phase systems. It will also be of interest to
mathematicians working on analysis of periodic solutions.
This monograph presents a simple and efficient two-relay control
algorithm for generation of self-excited oscillations of a desired
amplitude and frequency in dynamic systems. Developed by the
authors, the two-relay controller consists of two relays switched
by the feedback received from a linear or nonlinear system, and
represents a new approach to the self-generation of periodic
motions in underactuated mechanical systems. The first part of the
book explains the design procedures for two-relay control using
three different methodologies - the describing-function method,
Poincare maps, and the locus-of-a perturbed-relay-system method -
and concludes with stability analysis of designed periodic
oscillations. Two methods to ensure the robustness of two-relay
control algorithms are explored in the second part, one based on
the combination of the high-order sliding mode controller and
backstepping, and the other on higher-order sliding-modes-based
reconstruction of uncertainties and their compensation where
Lyapunov-based stability analysis of tracking error is used.
Finally, the third part illustrates applications of
self-oscillation generation by a two-relay control with a Furuta
pendulum, wheel pendulum, 3-DOF underactuated robot, 3-DOF
laboratory helicopter, and fixed-phase electronic circuits.
Self-Oscillations in Dynamic Systems will appeal to engineers,
researchers, and graduate students working on the tracking and
self-generation of periodic motion of electromechanical systems,
including non-minimum-phase systems. It will also be of interest to
mathematicians working on analysis of periodic solutions.
The inverted pendulum is a classic problem in dynamics and control
theory and is widely used as a benchmark for testing control
algorithms. It is also an area of active study, with many new
innovations and applications - for example the problem is solved in
the technology of the Segway, a self-balancing transportation
device. This book provides an overall picture of historical and
current trends and developments in nonlinear control theory, based
on the simple structure and rich nonlinear model of the inverted
pendulum. After an introduction to the system and open/current
problems, the book covers the topic in four parts: applications of
robust state estimation and control to pendulum-cart systems;
controllers for under-actuated mechanical systems; nonlinear
controllers for mobile inverted pendulum systems; and robust
controllers based observers via Takagi-Sugeno or linear approaches.
With contributions from international researchers in the field, The
Inverted Pendulum in Control Theory and Robotics is essential
reading for researchers, scientists, engineers and students in the
field of control theory, robotics and nonlinear systems.
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