Abstract
In this paper the application of model predictive control (MPC) to a two-mode model of the dynamics of the combustion process is considered. It is shown that the MPC by itself does not stabilize the combustor and the control gains obtained by applying the MPC algorithms need to be optimized further to ensure that the phase difference between the two modes is also stable. The results of applying the algorithm are compared with the open loop model amplitude responses and to the closed loop responses obtained by the application of a direct adaptive control algorithm. It is shown that the MPC coupled with the cost parameter optimisation proposed in the paper, always guarantees the closed loop stability, a feature that may not always be possible with an adaptive implementations.
Present address: I. Yazar, Department of Mechatronics, Eskisehir Osmangazi University, Eskisehir Vocational School, Industrial Zone Campus, Eskisehir, Turkey
Funding statement: This study was supported from Eskisehir Osmangazi University fund of scientific research project No. 2015-975.
Nomenclature
speed of sound
state distribution matrix
control distribution matrix
exchange of momentum
cost function
subscript index
differential gain
proportional gain
- K
gain
- L
length of combustion chamber
pressure fluctuation
local pressure
exchange of energy
scaling factor in the cost function
terminal state weighting matrix in cost function
terminal state weighting matrix in cost function
block diagonal matrix of weighting matrices
scaling factors in the cost function
modal amplitudes
control input weighting matrix in cost function
block diagonal matrix of weighting matrices
time
scalar control input
control input vector in dynamic model
- U
control input vector in prediction model
local velocity of the gas phase
exchange of mass
- x
state vector
- y
output vector
scalar output
model parameters
model parameter
model parameters
mean ratio of specific heats
model parameters
model parameters
local density of the two phase mixture
model parameters
derivative
phase angle
gradient
References
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