The Development of Neural Network Based System Identification ...

160 CHAPTER 6 NEURAL NETWORK BASED PREDICTIVE CONTROL SYSTEM
respectively. The predicted output vector Ŷ and control trajectory ∆U for the MIMO
case are defined as:
Ŷ = [y 1 (k + 1|k) y 1 (k + 2|k) y 2 (k + 1|k) y 2 (k + 2|k) · · · y q (k + N p |k)] T
∆U = [∆u 1 (k) ∆u 1 (k + 1) ∆u 2 (k) ∆u 2 (k + 1) · · · ∆u m (k + N c )] T (6.2)
The data vector R s that contains qN p set-points is defined by:
⎡
⎤
1 1 1 1 · · · 1
1 1 1 1 · · · 1
R s =
. ⎢.
. . . .. . ⎥
⎣
⎦
1
}
1 1 1
{{
· · · 1
}
qN p
⎤
r 1 (k)
r 2 (k)
= ¯R s r(k) (6.3)
⎢ . ⎥
⎣ ⎦
r q (k)
T ⎡
The first term of the objective function in Equation (6.1) is related to the minimisation
of error between predicted output variables and predefined set-point. Subsequently,
the second term in the objective function indicates the treatment of ∆U when minimising
the objective function J(k). In Equation (6.1), the variable matrix R represents a
diagonal matrix in the form of R = r w I mNc×mN c
(r w ≥ 0). The constant r w is used
as a tuning parameter for the desired closed-loop performance. The closer r w value to
zero would cause the optimisation to prioritise the minimisation of error between the
predicted output variables and the predefined set-points to the smallest value possible,
without considering the magnitude and the smoothness of the control trajectory ∆U.
In general, the implementation principle of NNAPC control shown in Figure 6.2
can be summarised as follows:
1. The internal dynamic model of the system is used to predict the future output
response of the system. This model can be obtained and implemented either from
off-line or on-line system identification algorithms.
2. Using instantaneous linearisation principle, a linear model is extracted from the
NNARX model and converted to corresponding state space model. This state