31-01-2013, 09:41 AM
Posicast Control Past and Present
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Abstract
Renewed attention to Posicast control has spawned
new feedback based approaches and applications for what was
orignally a feedforward control technique. In this paper, the basic
principles of Posicast control, some of its past history, and new
methods and fields of application are presented.
THE BASIC CONCEPT
INVENTED in the late 1950’s, Posicast is a feedforward
control method that dampens oscillations in systems whose
other transient specifications are otherwise acceptable. When
properly tuned, the controlled system yields a transient response
that has deadbeat nature.
Consider a system having a lightly damped step response
as shown in Fig. 1(a). The overshoot in the response can be
described by two parameters. First, the time to the first peak
is one half the underdamped response period Td. Second, the
peak value is described by 1 + , where is the normalized
overshoot, which ranges from zero to one. Zero overshoot
corresponds to critical damping.
Posicast splits the original step input command into two
parts, as illustrated in Fig. 1(b). The first part is a scaled
step that causes the first peak of the oscillatory response to
precisely meet the desired final value. The second part of
the reshaped input is full scale and time-delayed to precisely
cancel the remaining oscillatory response, thus causing the
system output to stay at the desired value. Such is the idea
behind “half-cycle Posicast,” which can be modeled using just
the two parameters and Td. The resulting system output is
sketched in Fig. 1©; the uncompensated output is also shown
for comparison.
A BRIEF HISTORY OF POSICAST RESEARCH AND
APPLICATIONS
The invention of Posicast control is due to Prof. Otto J. M.
Smith (currently Professor Emeritus – University of California
at Berkeley), who described the basic principles in the Sept.
1957 Proceedings of the IRE (Institute of Radio Engineers,
forerunner of today’s IEEE) [1]. Prof. Smith, best known for
inventing the “Smith Predictor” for control of systems having
time delay, also described Posicast in his 1958 textbook on
feedback control [3].
A decade later, Gerald Cook, then a student at the Massachusetts
Institute of Technology (MIT), published an article
in the IEEE Transactions on Automatic Control, in which
he described application of half-cycle Posicast to vibrating
structures. Cook offered an excellent frequency domain interpretation
for the Posicast element [2]. An example application
of Posicast is the suppression of vibrations on a guided missile
launcher [4]. Nearly twenty years later, Prof. Cook presented
additional variations of Posicast, with application to the control
of flexible structures [5].
REDISCOVERY AND NEW APPLICATIONS
Over the past five years, a method for designing feedback
systems that incorporate Posicast has emerged, and is being
applied to new engineering problems. Researchers have also
implemented these techniques on a variety of technologies
with encouraging results.
Posicast in Feedback Control
The sensitivity problem can be reduced if Posicast compensation
is applied within a feedback system rather than in the
classical feedforward configuration [9], [10]. A block diagram
explaining the control method is shown in Fig. 5. Whereas
the classical applications placed Posicast before the lightly
damped system, recent work suggests that Posicast be used
within a feedback system. The proposed control method is
a significant departure from classical Posicast. Note that the
overall system characteristic polynomial using classical halfcycle
Posicast is found by simply removing the dominant
lightly damped poles of the plant G(s). In the feedback
approach, the closed loop characteristic polynomial is given by
1+C(s)[1+P(s)]G(s). The primary purpose of the Posicast
function is to cancel undesirable plant poles, thus minimizing
the effect of lightly damped poles in the closed loop response.
Poles of the closed-loop system would be determined by the
remaining open-loop poles and zeros.
Recent Developments
Application of Posicast in the feedback configuration was
first demonstrated on dc-dc power converters. These systems
can exhibit nonlinear behaviors, and the natural damping is
strongly dependent on the load. PID type controllers implemented
around specialized analog integrated circuits are the
standard solution, although digital controllers being reported
in the research literature [11]–[14].
CONCLUDING REMARKS
Invented 50 years ago, Posicast was originally designed
as a feedforward compensator for lightly damped systems.
The first reported applications were for mechanical structures.
The technique is also closely related to input pre-shaping
control, which has been widely studied and reported in the
robotics research community. More recently, Posicast has been
proposed for use within feedback loops, to take advantage of
its superior damping qualities while also reducing Posicast’s
sensitivity to modeling error. Modern digital signal processors
make it easy to accurately implement the time delay element
that is at the heart of Posicast. Furthermore, the computing
power of the digital signal processor has enabled engineers
to apply Posicast based feedback control to new applications,
such as power converters and inverters that interface to power
grids. Classical application of Posicast is very simple, but
the complex resonances of modern applications may make it
more difficult to design Posicast. There remain opportunities to
explore and apply intelligent design approaches with Posicast.