Optimisation of Marine Boilers using Model-based Multivariable ...

10 1. INTRODUCTION
of water level and pressure variations which naturally leads to MPC.
Model predictive control
Model predictive control is a widely applied advanced control strategy for industrial
applications [Qin and Badgwell, 1997, 2003]. In relation to boiler control, examples are
documented in [Kothare et al., 2000; Lee et al., 2000; Rossiter et al., 2002]. MPC refers
to the control algorithms that explicitly make use of a process model to predict future
responses. The algorithm implementation is also known as receding horizon control.
At each controller update the predictions are based on current measurements gathered
from the plant. They are used to evaluate a performance function and an optimisation
problem is solved to find the input sequence which optimises the predicted performance
over a chosen horizon. Now the first input in the sequence is applied to the plant, and
the same procedure is repeated at the next controller update.
Motivation The model used in the predictions can be both linear and nonlinear. In
this thesis we will look at MPC using linear models and a special kind of nonlinear
models called hybrid models, which we will treat later. For an overview of linear MPC
see e.g. [Maciejowski, 2001; Rossiter, 2003]. MPC has a number of advantages over
other advanced control strategies. First of all, as finding the optimal input consists
of solving an optimisation problem, it is possible to incorporate constraints on both
inputs, rate of change of inputs, outputs and internal state variables into the controller.
This obviously means that even though we refer to it as linear MPC, the controller is
not linear. The MPC controller is also pro-active, meaning that future trajectories of
setpoints and disturbances can be handled in the control setup. Further, MPC naturally
handles MIMO processes and has the advantages over linear controllers that it allows
for moving the setpoints closer to the constraints without increasing the number of
constraint violations.
The process control hierarchy In relation to the process control hierarchy discussed in
the previous section, the MPC controller can be found at the middle level. The reason
for this is mostly computational complexity and complexity of implementation, which
means that it is difficult to apply MPC at the lower level where the SISO PID controllers
are most popular. However, lately results have shown that even in the SISO case MPC
should be considered over PID as the computational demands of the SISO MPC controller
are similar to those of PID control, and further the MPC controller in general
outperforms the PID controller regarding setpoint changes, disturbance rejection and
constraint handling – see [Pannocchia et al., 2005].
Computational aspects The optimisation problem arising in linear MPC using a quadratic
performance function is a convex quadratic programming problem. Such problems
are the topic of [Boyd and Vandenberghe, 2004]. It is possible to exploit the struc-