[406d] - Effect of Input Rate Limitation on Controllability
- Espen Storkaas
- Norwegian University of Science
and Technology
- Dep. of Chemical Engineering,
NTNU
- Trondheim, 7491
- Norway
- Phone:
+4773596391
- Fax:
- Email: espen.storkaas@chemeng.ntnu.no
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- Sigurd
Skogestad (speaker)
- Norwegian University of Science
and Technology (NTNU)
- Sem Sealands vei
4
- Trondheim, N7491
- Norway
- Phone:
+4773594154
- Fax:
- Email: skoge@chemeng.ntnu.no
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Abstract:
Controllability is the ability to achieve
acceptable control performance under the influence of disturbances
and using available inputs and measurements. The controllability of
a system is independent of the controller(s) and can hence be
regarded as a property of the system itself. Thus, it can also be
used as a tool in process design, for example when choosing
actuators and measurement devices.
The conventional
controllability analysis has almost exclusively focused on signal
magnitudes. Design parameters like valve size (e.g. CV value) that
would ensure a controllable system can be determined by a systematic
controllability analysis. However, valve rates (stroke time) can in
many cases be just as important as valve size, especially when large
valves are used for stabilizing control and/or suppression of
(relatively) fast disturbances. Input (and output) rate issues have
yet to be included into the controllability analysis framework,
possibly because it has been viewed as a nonlinear phenomenon.
We will in this work show how to describe the effect of
input rate limitations in a linear framework. The key step is to
realize that the magnitude of sinusoidal input signals are limited
by the rate of change of the input signal, resulting in a linear
reduction of available input magnitude above a critical frequency in
a Bode magnitude plot. This representation of frequency dependent
available input signals can be included into a controllability
analysis, and used to determine both the required size and rate of
actuators. Analytic expressions for perfect and acceptable control
can be used to give explicit expressions for the required input
rate.
The actuator properties can similarly be transformed
into a first order bound on input magnitude and used as a bound on
the sensitivity function KS from reference r to input u, u = KSr
=K(I+GK)-1r. This bound can be used explicitly in controller design,
i.e. as in mixed sensitivity H∞ controller design. This will yield a
controller that utilizes the available input in an optimal matter,
and at the same time fulfilling other design criteria such as output
disturbance sensitivity reduction as in the case of the typical S/KS
mixed sensitivity optimization. Such a controller would also keep
the input away from saturation due to either rate or magnitude, and
by that ensure that stabilizing controller does not loose their
feedback properties.
The above concepts will be illustrated
by considering the stabilization of severe slugging in a
pipeline-riser system for multiphase transport of oil and gas. The
flow in the system is unstable for low rates, but can be stabilized
using a choke valve located at the end of the pipe. The valve rate
needed for stabilization and disturbance rejection is determined,
and a controller that satisfies the bounds on the input usage is
designed. This controller is compared with a conventional PI
controller, both by comparing the shape of the sensitivity functions
and by simulations.
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