Abstract
The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steadystates. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.
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Abbreviations
- A:
-
dynamic matrix of controlled variable step response coefficients
- CT:
-
composition transmitter
- e(k+1):
-
controlled variable projected setpoint error vector
- ei(k+1):
-
ith controlled variable projected setpoint error vector
- I(k):
-
system manipulated variable at time k
- ΔI(k):
-
move of manipulated variable at time k
- k:
-
discrete time
- k:
-
present time
- K:
-
gain matrix
- l :
-
control horizon
- O r :
-
Or-th controlled variable
- Ors :
-
r-th controlled variable setpoint
- Os:
-
controlled variable setpoint
- Q:
-
weighting matrix of controlled variables
- R:
-
weighting matrix of manipulated variables
- Ra :
-
universal gas constant
- r:
-
number of manipulated variables
- s:
-
number of controlled variables
- TT:
-
temperature transmitter
- u(k):
-
vector of present and future moves of manipulated variables, ΔI(k)
- u,(k):
-
ith manipulated variable moves
- x:
-
state variables
- x r :
-
uncontrolled variables
- ym :
-
measured output variables
- y:
-
selected controlled variables
- z:
-
augmented variables
- *:
-
projection based on moves up to present time k
- m:
-
feedback measurement
- max:
-
maximum
- min:
-
minimum
- r:
-
index for uncontrolled variables
- y:
-
index for controlled variables
- z:
-
index for augmented variables
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Lee, J.K., Park, S.W. Model predictive control for multivariable unstable processes with constraints on manipulated variables. Korean J. Chem. Eng. 8, 195–202 (1991). https://doi.org/10.1007/BF02706682
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DOI: https://doi.org/10.1007/BF02706682