A Panel Session is scheduled on the
evening of Tuesday 06.
The Panel session is entitled “What are sliding modes and sliding mode control? New challenges in
emerging topics”
To
stimulate a more fruitful session, all
conference attendees are invited to submit via email to the conference
secretariat [vss06@diee.unica.it] possible hints for
discussion, which will be posted on this page as soon as they arrive.
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Prof. V. Utkin gave the following
considerations which motivated the title of the panel session.
I still believe that "What are sliding mode and
sliding mode control?", which was matter of
discussion at VSS'04 is still an interesting topic
to discuss.
Indeed, originally this concept was associated with
continuous finite dimensional systems with discontinuous right hand sides.
Within the last decade the term "sliding
mode" has been used in the context of discrete-time systems, systems with
delay, infinite-dimensional systems; the term "high order sliding
mode" has become popular.
It may lead to "uncertainties" in
understanding the potential of sliding mode control and even more to doubts
that it has any novelty if compared with the other control methodologies.
As an example, you can meet term "continuous
sliding mode" associated with the idea to design control such that sdot=-(lambda)s.
Then the question "What is new?" looks
natural.
Similar situation takes place for the other
non-conventional sliding modes.
Prof.
L. Fridman produced
a short document entitled “About the definition of the sliding modes
and the order of sliding”
[PDF]
Dr. S. Janardhanan gave
the following considerations:
Discussion of the essence of sliding mode is very much necessary
in the present state where the definition of sliding mode and variable
structure / switched mode control systems have become non-coincidental.
I would like to suggest the topic of defintion of 2-sliding mode and its difference from the
definition of the classical definition of sliding mode.
I would also suggest that the difference between
sliding mode control and variable structure control be clarified ( I have seen many instances where the two are not equivalent,
but the literature using SMC and VSC interchangably)
Dr.
Jan Wolff ”On
Discrete-Time Sliding Mode [PDF]
I would like to contribute a note, which I think is of
interest for discussion of the discrete-time case.
The system described is compatible with the classical
definition of discrete-time sliding mode. But in constrast
to established sliding
mode, the system order is
not reduced and the sliding set and state space have equal dimension [DOWNLOAD]
Recollections by Prof. Fridman
of the history of his work on the paper referenced as #1 in his note made me
ponder on whether the second-order sliding mode (SM) is a natural phenomenon
indeed or to what degree it is natural. This is also closely related with the
problem posed by Prof. Utkin.
Apparently consideration of the second-order SM being
a natural phenomenon came from analysis of a first-order SM control system
perturbed by additional dynamics of the first order (I apologize if my
assumptions about other people reasoning are not quite precise). If the
additional dynamics are attributed to the actuator then, indeed, a mode
featuring s_dot=0 would occur in that system, and
therefore it might be concluded that the second-order SM
“naturally” occurred. However, we must remember that the
first-order model of the actuator is an approximation. If we consider a smaller
detail we will find that actuator model is of much higher order. The same would
be true with respect to sensors, transducers, amplifiers, and other elements of
every control system. Inevitable existence of chattering in a SM system may
serve as a proof of existence of higher-order dynamics (otherwise, we should
expect infinite frequency of chattering, and I presume that nobody would expect
it from a real control system). Now, knowing that every real SM would be
manifested as chattering – regardless of whether it is a first-order SM
or second-order SM, and neither s=0 nor s_dot=0 would
be satisfied exactly – then what is the difference between the first- and
second-order SM control? It looks like the presence of parasitic dynamics
“practically” eliminates this difference?
The answer to this question should, of course, depend
on what dynamics we analyze and compare. Segregating system dynamics into
principal and parasitic would be helpful in that respect. SM design should,
apparently, be done for principal dynamics only.
However, existence of parasitic dynamics should also be kept in mind. With this
being said, the second-order SM can hardly be considered a natural phenomenon,
as actuator dynamics are normally considered parasitic and first-order model is
not sufficient for the actuator description. The nature of parasitic dynamics
is that on the one hand they are much faster than the principal dynamics and
their contribution to the system dynamics is smaller, but on the other hand the
order of parasitic dynamics is high and, I think, is probably even infinite
– we would obtain a higher order of the model of parasitic dynamics every
time we consider a smaller detail of the implementation. Therefore, segregation
of the system dynamics into principal and parasitic is needed for practical
reasons. With this segregation, only principal dynamics should be considered
when the SM algorithm is designed (which is a commonly used approach now). What
is the place of parasitic dynamics then? I think that existence of parasitic
dynamics with some proper model of these dynamics must be accounted for at
analysis of robustness of the SM system. This analysis should include not only
effect of parameter uncertainties but also effect of parasitic dynamics. The
notion of robustness, which is interpreted now in many different ways, should
probably also include robustness with respect to introducing parasitic
dynamics. I believe that this type of analysis would help to bridge the gap
between the SM theory and applications of this theory.
Some ideas for the panel
session.
The ideal task for an ideal control engineer is to
attain everything from a system of which one knows nothing. In practice we have to face less
ambitious questions like what I need to know about the system to be able to achieve a specific
performance?
The evaluation of a new development of the control
methodology results in a complex mixture of criteria regarding the class of systems tractable,
the degree of knowledge required,
the implementation aspects and the practically achieved performance.
Now it is the moment to give evaluation of the present
of sliding modes just to have some ideas for future developments.
It is my precise duty, as one of the
“nominal” organizers of VSS06, to invite all of us to prepare
some thought, a single period, the title of a book or what else to increase the
probability of a fruitful discussion during the panel session. Just to give an
example I winn my natural timidity sending you some
points of
view of mine (I’m ready to immediately refuse them at the
first criticism)
I believe it is important to reflect on the fact that
sliding modes is a technique aimed at forcing to a constrained motion an
originally free uncertain system. The constraints are so chosen that the
reduced order motion has some good properties.
Usually we start from the desired reduced order
motion, then we try to find the constraint to be imposed and finally we try to
identify a control forcing the actual (uncertain) system to satisfy such
constraints.
The whole problem can be modelled as an uncertain
differential/algebraic system with non consistent initial conditions. With this
representation some of the features of the sliding modes (semigroup
properties of the constrained motion, higher order sliding modes, well and ill
posed problems, regularization/approximabilty ) can be accounted in an unified framework . The problem
can be solvable or not.
The last case corresponds to the failure of some step
in the procedure. The discovery of the way to avoid failure is the task for the
researches in the future.
From a good knowledge of the drawbacks of our
methodology we can expect some new developments( I do
not know but I know that I do not know).
Some good combination of sliding modes with existing
methodologies could some time help so we cannot be unaware of what has been
done by the other.
The second aspect which I think of the same importance
is the implementability of the achieved results. The
nature is very generous of examples of controlled system able to perform with
extraordinary precision with existing ( They do exist!
even if we do not know so much about them) control techniques, sensors and
actuators.
I conclude my quick contribution hoping to have been
of some help to the discussion