The Development of Neural Network Based System Identification ...

2.4 AUTOMATIC FLIGHT CONTROL SYSTEM 49
results from the flight tests provide further justification of the proposed controller.
However due to demanding computation of the non-linear optimisation of the proposed
method, only SISO based controller was implemented in flight. Further simplification
is made to the optimisation problem where only soft constraints are considered in the
work. The hard constraints on the amplitude and the rate of the control inputs are
considered only as saturation and rate limiter blocks. The limitations due to the high
demanding computation of the non-linear optimisation should be addressed, in order to
enable us to fully utilise the capability of the MPC technique.
The implementation of the NNARX model with MPC algorithm involves high
computation effort since the non-linear optimisation problem needs to be solved at each
sampling time. This causes the control implementation to be only feasible with slow
dynamic processes [Allgower, 2000, Norgaard, 2000]. Several alternatives to solve the
non-linear optimisation problem is reported in Lawrynczuk [2007a]. Lawrynczuk [2007a]
proposes that the straightforward and simple solution to the non-linear optimisation
problem can be achieved by using the approximation of the non-linear model used in
the MPC to resemble linear form that nearly matches the system under consideration.
The idea to use approximation to the non-linear model such as NN to mimic the
simpler linear model form has been proposed in Kuure-Kinsey et al. [2006a], Kuure-
Kinsey and Bequette [2008] and Norgaard [2000]. In these published work, a novel
MPC approach is developed to control the ‘van de Russe’ reactor using the feed-forward
NNARX or RNN model. The approximation to the non-linear feed-forward NN model
is obtained by decoupling the standard feed-forward NNARX network inputs into
separated groups of inputs as shown in Figure 2.14(a). The modification to the standard
NNARX network produces a NN model with a 3-layer architecture. Similarly, the
same arrangement can also be made with the RNN architecture as shown in Figure
2.14(b) which results in a 2-layer network. As can be seen in the figure, the RNN
network is comprises two recurrent layer connections from the output, y k+1 to the
input of layer 1 and from the output of layer 1 back to the input of layer 1. The
calculation of the predicted outputs from the feed-forward NNARX and RNN model
results in non-linear state space model representations. The linear state space models