الفهرس 
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Abstract
The control of a flexible robot arm pose new control technology
problems. One major problem area is the closed-loop stability of the arm
that has been mode led with truncated modal dynamics. Stability problems
arise due to the control design process beginning with a deficient model.
One possible method of circumventing the problems resultingfrom
the increased number of modes to be controlled is by avoiding modal
models. Working directly with partial-differential equation (PDE) models
of continuous structure (flexible robot arm) is a viable (workable)
alternative for preliminary control designs.
This work provides a PDE control problem formulation that
contains sufficient generality to encompass a wide variety of continuous
control system problems within a single analyticalframework. The method
of Lyapunov optimal feedback control is applied to a flexible one link
robot arm, whose control torque is limited to be at the arm joint. This
method combines junction minimization with lyapunov stability criteria
and produces a closed loop feedback control directly.
The stability of the system under the proposed control law is derived
in terms of energy dissipation properties of the system and is independent
of physical parameters of the plant. The control law is applicable to linear,
as well as nonlinear mechanical robot arm with any number of vibrational
modes. It’s, therefore, unaffected by modal truncation, and as, the stability
of the proposed controlleris based on globalpropertiesofthe arm, so, it’s
robust with respect to plant parameters.