Offset Free Tracking with MPC under Uncertainty: Experimental Verification

1

• Offset Free Tracking with MPC under Uncertainty
  Experimental Verification
• Audun Faanes and Sigurd Skogestad
• Department of Chemical Engineering
• Norwegian University of Science and Technology
• N-7491 Trondheim N, Norway
• Also affiliated with Statoil ASA, TEK, Process
  Control, N-7005 Trondheim, Norway
• Author to whom all correspondence should be
  addressed. E-mail skoge_at_chemeng.ntnu.no, Tel.
  47 73 59 41 54, Fax. [phone]

Abstract A laboratorial experiment is used to
investigate some aspects related to integral
action in MPC. MPC is used for temperature
control of a process with two tanks in series.
Since this often improves performance, an extra
the temperature measurements was applied. To
avoid outlet temperature steady-state offset,
estimates of input disturbances have been used in
the calculation of the steady-state control
input. Simulations may indicate that integral
action is present and that disturbances are
handled well, but in practice unmodelled
phenomena may give a poor result in the actual
plant, also at steady-state. If should be
verified that integral action (feedback) is
actually present and not an apparent effect of
perfect feedforward control. The experiments
verify that output feedback through input
disturbance estimation is efficient, provided
that it is correctly done. To obtain integral
action, care must be taken when choosing which
input disturbance estimates to include. It is not
sufficient to estimate a disturbance or bias in
the control input(s), even if the control
input(s) are sufficient to control the process.
The present work verifies that the number of
independent disturbance estimates must equal the
number of measurements. In our experiment the use
of estimates of input disturbances to both tanks
gave satisfactory performance with no
steady-state error. Experimental set-up Hot and
cold water are mixed in two tanks in series, and
the temperature of the outlet water (y) shall be
kept constant despite disturbances d1 (variation
in hot water flow rate) and d2 (cold water
addition in main tank). Manipulated variable, u,
is cold water flow rate. In the main tank there
is a loop where the water is circulated with a
pump. y is measured in this loop, and therefore
we get a delay. The circulation loop also gives
mixing. The levels are controlled with an
overflow drain (in the mixing tank) and an on-off
drainage valve (in the main tank).

• Conclusions
• Experiment temperature control in a process
  with two tanks in series
• Model predictive control, MPC
• Non-square case two measurements, one
  manipulated variable
• Offset-free steady state obtained by input
  disturbance estimates for the determination of
  the manipulated variable steady-state
• Simulation indicates that estimation of one
  disturbance is sufficient
• The experiment shows that two disturbance
  estimates are needed, i.e., the number of
  disturbance estimates must equal the number of
  measurements (in accordance with Pannocchia and
  Rawlings (2003) and Faanes and Skogestad (2003))
• Offset free steady state in the simulation is an
  apparent effect of perfect feedforward control
• Estimates of input disturbances have been
  described in the literature as efficient for a
  quick response back to the desired steady state.
  The present work confirms this (provided that it
  is correctly done).
• Acknowledgements
• The experimental equipment has been set up at
  Norsk Hydro Research Centre, and was originally
  designed by Jostein Toft, Arne Henriksen and
  Terje Karstang. Norsk Hydro ASA has financed the
  experiments.
• References
• Faanes, A. (2003). Controllability Analysis for
  Process and Control Structure Design. PhD thesis.
  Department of Chemical Engineering, Norwegian
  University of Science and Technology.
• Faanes, A. and Skogestad, S. (2003). On MPC
  without active constraints. Submitted to
  Modeling, Identification and Control, MIC.
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  State-space interpretation of model predictive
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• Lundström, P., J. H. Lee, M. Morari and S.
  Skogestad (1995). Limitations of dynamic matrix
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• Muske, K. R. and Badgewell, T. A. (2002).
  Disturbance modeling for offset-free linear model
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  12, 617-632
• Muske, K. R. and J. B. Rawlings (1993). Model
  predictive control with linear models. AIChE
  Journal. 39(2), 262-287.
• Pannocchia, G. and J. B. Rawlings (2003).
  Disturbance Models for Offset-Free
  Model-Predictive Control. AIChE Journal. 49(2),
  426-437.