The Development of Neural Network Based System Identification ...

2.4 AUTOMATIC FLIGHT CONTROL SYSTEM 47
transfer function models is applicable for both stable and unstable plants. Typically,
the state space model is preferred over other models in the MPC controller design
because of its simplicity and effectiveness in handling multi-variable processes. The
linear models are widely used with MPC due to relatively simple procedure to identify
the plant dynamic through system identification methods. They generally give good
results whenever the plant is operating within or near the operating flight condition.
Moreover, the application of linear models with MPC objective function results in a
quadratic and convex optimisation problem which is much easier to solve compared
with the usage of non-linear dynamic models with MPC. Unique solution of MPC
optimisation with linear models enables direct implementation of the control law to
meet real-time requirements.
In many control applications, the dynamics of the system under consideration is
non-linear with frequent changes from one condition to another. Therefore, a linear
model of the system is inadequate to represent the broad range of operating conditions
and this motivates the application of non-linear dynamic model with MPC to achieve
better control performance. The application of non-linear model for prediction process
in MPC leads to non-convex and non-quadratic optimisation problems [Lawrynczuk,
2007b]. Subsequently, the nature of the optimisation problem can lead to solution with
multiple local minima in the objective criterion as shown in Figure 2.13. Lawrynczuk
[2007b] further argues that for a non-linear optimisation problem, there are currently
no reliable and fast optimisation algorithms that are able to determine the global
optimal solution at each time step within a prescribed time limit. The gradient based
optimisation algorithms such as those suggested in Norgaard [2000], Wilamowski [2011a],
Haykin [2009] may trap in local minimum and give no guarantee that a global optimal
solution is found.
Another way to represent the broad range of flight operating conditions is by using
different multiple linear models for different flight modes as suggested in Joelianto
et al. [2011] and Gopinathan et al. [1998]. The multiple linear models are obtained by
linearising the non-linear dynamic model from first principle modelling for each trim
condition of the helicopter flight mode. The design parameters of the MPC controllers