Adaptive Control of Systems with Hard Nonlinearities
- Robust and Adaptive Control of Systems with Backlash and Flexibility
This report summarizes our recent work on control of
gun-turret systems with backlash and flexibility. In the first part of the
report, we formulate the control problem and
propose two control schemes for a rigid gun-turret system which has backlash
between a driving gear and a driven gear. The first scheme is for the system
with known parameters and the second scheme is for the
system with unknown parameters. Both schemes have a backlash compensation
design to cancel the undesirable backlash effect for improving system
In the second part, the assumption of a rigid system is relaxed and the effects
of flexibility on system performance and stability with and without backlash
are analyzed. Utilizing a root-locus and partial state-feedback
approach it is shown that with the proper choice of feedback gains, the
designs of Part I for known and unknown parameters can be made robust
with respect to flexibility.
- Optimal Control of Tracking Systems with Backlash and Flexibility
A system with backlash and flexibility is compensated with an
optimal control law combined with a linear partial-state feedback law.
The compensation of backlash is treated as a rendezvous
problem in optimal control, while the linear controller for
flexibility is designed using techniques from classical control theory
and singular pertubation theory.
Simulation results show significant
improvements in system tracking performance when backlash compensation
- Adaptive Control and Identification of A Flexible System with
Friction and Backlash
In control of a real-life system consisting of two mechanical bodies
with flexibility, backlash and friction, there are several important issues
such as design of low-order adaptive controllers, friction compensation
in the presence of flexibility, and backlash compensation.
An adaptive state feedback control scheme is developed for systems with
unknown parameters in non-canonical forms, by employing static state feedback
for pole placement and dynamic output feedback for parameter adaptation.
The developed control scheme does not need a restrictive state space model
matching condition for an adaptive state feedback design. The adaptive
parameter update law is derived based on a desirable linear output tracking
error equation. Such an adaptive control scheme, whose order is considerably
lower than an output feedback design, ensures closed-loop stability and output
The developed model reference adaptive control scheme is then applied to the
control of a two-body system with flexibility and damping. Simulation
results indicate that the adaptive state feedback model reference
control scheme ensures desired tracking performance in the presence of
An extended model reference adaptive control scheme is developed for control
of the two-body system with nonlinear friction compoments. New parametrization schemes
are proposed for adaptive friction compensation in the presence of
flexibility which imposes some new challenge.
In the presence of backlash, a two-body system operates in two
modes: a backlash mode and an impact mode. While an adaptive controller can
be used for a system in impact mode, optimal control designs are favorable
for a system in backlash mode. Several such optimal controllers are
compared. Backlash compensation in the presence of friction is
also addressed. Finally, algorithms are developed
for identifying system parameters needed for backlash compensation.