This monograph provides readers with tools for the analysis, and
control of systems with fewer control inputs than degrees of
freedom to be controlled, i.e., underactuated systems. The text
deals with the consequences of a lack of a general theory that
would allow methodical treatment of such systems and the ad hoc
approach to control design that often results, imposing a level of
organization whenever the latter is lacking.
The authors take as their starting point the construction of a
graphical characterization or control flow diagram reflecting the
transmission of generalized forces through the degrees of freedom.
Underactuated systems are classified according to the three main
structures by which this is found to happen chain, tree, and
isolated vertex and control design procedures proposed. The
procedure is applied to several well-known examples of
underactuated systems: acrobot; pendubot; Tora system; ball and
beam; inertia wheel; and robotic arm with elastic joint.
The text is illustrated with MATLAB(r)/Simulink(r) simulations
that demonstrate the effectiveness of the methods detailed.
Readers interested in aircraft, vehicle control or various forms
of walking robot will be able to learn from "Underactuated
Mechanical Systems" how to estimate the degree of complexity
required in the control design of several classes of underactuated
systems and proceed on to further generate more systematic control
laws according to its methods of analysis."
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