  This thesis is concerned with the rejection of time-varying disturbances in
linear model predictive control of discrete-time systems. In the literature,
disturbances are widely rejected by using velocity models, disturbance model
with observer approach or a scheme that combines the compensation of a
disturbance observer and the feedback regulation of MPC. Contrary to the widely
used methods, the technique proposed in this research utilises the increment
model of plants, with the assumption of fast-changing disturbances, to
formulate a control law to reject the varying-disturbances. The uniqueness of
the method stems from the compensation of the disturbance magnitude and rate of
change. By proposing a cost function where the increment form of the system
disturbance is taken as an optimisation variable, a control signal that is a
function of a computed optimal disturbance increment is formulated to ensure
that the plant is driven according to the minimisation of the cost function.
The degree of freedom introduced by using the optimal disturbance in the
control law was exploited to introduce the estimated disturbance increment into
the control signal such that it is always in opposition to the external
disturbance increment. Moreover, the proposed cost function provides a
weighting matrix that can be used to manipulate the impacts of the exogenous
disturbances on the response of the system. To estimate the unmeasurable
disturbances, a combined state and disturbance observer is designed based on a
convex optimisation stated in terms of an H2-minimisation problem. Simulations
of three different systems are used to show the benefits of the proposed
algorithm when compared with conventional offset-free MPC techniques. The
results demonstrated that the proposed scheme can give significantly improved
output tracking and regulation.
