Several papers have been presented in conferences
and
two papers have been submitted to IEEE transactions.
- Robust Control
of
Time
Delay Systems
Time delay systems are
systems
in which the action of control inputs takes a certain time before it
affects
the measured outputs. The robust control of such systems are quite
difficult.
It involves quite complex mathematical tools, such as chain-scattering
representation, J-spectral factorizations, differential and algebraic
Riccati
equations, L2[0,h]-induced norm, frequency-domain techniques etc.
The
following four problems have been solved:
1.
Generic
J-spectral factorization: to find a bistable matrix W(s) such that
Z(s)=W~(s)JW(s)
where Z(s) is a para-Hermitian matrix with non-singular feed-through
matrix
and J is a signature matrix. Dually, the general J-spectral
co-factorization
problem is solved.
2.
Delay-type
Nehari problem: to find a stable, causal and proper transfer matrix
K(s)
such that the L-infinity norm of G(s)+K(s)exp(-sh) is less than a given
non-negative number, where h>0 is a delay and G(s) is an (unstable)
transfer
matrix;
3.
Extended
Nehari problem with a delay: to find a causal and proper transfer
matrix
K(s) such that the H-infinity norm of G(s)+K(s)exp(-sh) is less than a
given non-negative number, where h>0 is a delay and G(s) is an
(unstable)
transfer matrix;
4.
Standard
H-infinity control problem of processes with a single delay: to find a
causal and proper transfer matrix K(s) such that the H-infinity norm of
Fl(P,K(s)exp(-sh)) is less than a given non-negative number,
where h>0 is a delay, P(s) is an generalized plant and Fl
stands
for lower linear fractional transformation (LFT).
These
results have been published in IEEE Trans. on Automatic Control and
Automatica,
see Publications.
Further investigations will involve the H-infinity control of
multiple-delay
systems and the implementation of the controller etc.
Moreover,
a new performance evaluation scheme has been proposed for H-infinity
control
of time-delay systems (published in Automatica).
- Robust
Stability
Analysis
of Time-Delay Systems
The
robust stability analysis of time-delay systems is a very important
topic,
e.g. in communication networks and network-controlled systems etc. Both
delay-dependent and delay-independent stability criteria for a
congestion
control algorithm and a mass-spring-damper system
controlled-via-internet
have been obtained using a dual-locus diagram method.
Further
cooperative investigations will involve the stability analysis of
combustion
systems.
- Control
Using
Delay Elements (Time-delay control)
It
has been well known that delay is bad for control. However, it has also
been shown that using delay elements, intentionally and reasonably, can
improve some performances of systems, even stabilize a system.
This
project involves 3 branches:
1.Time Delay Filter (TDF): Using delay elements in a filter to reduce
the
residual vibration of flexible structures. It has been widely applied
to
spacecraft, robot, hard disk drive, servo system etc. A new analysis
method
and a new design method have been proposed.
2 Time Delay Observer (TDO): Using delay elements to observe
uncertainties
and disturbances.
3. Repetitive Control (or Time Delay Learning Control, TDLC): Using
delay
elements to learn periodic signals so that to track or reject periodic
signals.
This
idea has been extensively applied to the Control of Power Converters
and
Process Control. Various interesting results have been obtained.
