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Email : Relaxc@appedge.com
elaxc
•Change of paradigm: In contrast with the other
approaches, Relaxc is an implicit algebraic controller. The control
U is evaluated by numerical convergence. This is why U does not
depend of the mathematical structure of the process, so that
we can apply it for tuning (almost) all the kind of processes,
without modification or complex parameter rules .
•Thus by his mathematical nature, Relaxc allows to control
effortless and without overshoot complex processes including
Non minimal phase, small and large pure d e lay, unstable
processes, variable static gain, strongly non-linearities,
constraints on U, speed saturations, discontinuities, load
disturbances, etc. while minimizing the operational costs, the
energy peaks of U with a more reliable control.
•A Few words about Relaxc tuning.
To work with Relaxc, you have to identify the pure delay and
the “reactivity” time(1) of the process to build (named relax
time too) and the max speed of your process (v). With this
information, we deduce the time constant of the reference
trajectory to get the best dynamic that the process can
secure. Then , we just use the pretty formula to compute it.
=
(
). This methodology seems close to that of
Ziegler & Nichols. But Relaxc is not a PID and in particular all its
parameters have a physical meaning, are clearly discernable
and easily identifiable in the mathematical structure of Relaxc
with respect to open-loop or impulse response or by auto-
tuning identification. For this reason, the parameters of Relaxc
predict directly the response time in closed-loop and the time
response of the active disturbance rejection(2) without
involving numerous trial-and-error tests or complicated calculus
to determine them.
=, +(
+)
•Plug and control: Relaxc is available in Unity Pro
software (Schneider Electric). It can be embedded in small
controllers with less than 10 arithmetic operations by cycle.
The tracking mode functionality is available too and allows to
switch in confidence your controller to Relaxc.
•Example : Split range with pneumatic valves
It is a strongly non-linear process (Cavitation phenomenon ,
5000 liter/h ). From scratch, in only 15 minutes after two
open-loop responses, we estimates =
= 0.8, =
1.5= 1/ and =0.25. We obtain an adequate closed-
loop response for different operating ranges. Notice how
Relaxc follows the variation of the process dynamic with
robustness. It is not the case for the PID (Kp=0.8 and Ti=2s).
There are excessive oscillations and overshoots even if the
response seems better for a step between 10% and 15%.
(1) “reactivity” time(1) of the process is not exactly the “apparent” time delay that we see in the literature.
(2) Relaxc provides a better rejection behavior than many other controllers.
Relaxc technology can be used in all sectors of the industry where processes control is needed: chemistry, aerospace, drone, pharmaceutical, automotive, petrochemical, electric or combustion or rocket engine, etc
Relaxc Equation : the reactivity function, e=(yref-ym) with
yref the reference trajectory and ym the process
More information about Relaxc:
https://www.researchgate.net/publication/
335652545_Relaxc_vs_Real_processes
https://www.researchgate.net/publication/
326649670_RelaxC_and_the_other_control
lers
https://www.researchgate.net/publication/
321918636_RelaxC_Controller_The_Ultimat
e_controller_The_origin
J.Masse 13/09/2019