The Development of Neural Network Based System Identification ...

166 CHAPTER 6 NEURAL NETWORK BASED PREDICTIVE CONTROL SYSTEM
6.5 GENERAL FORMULATION OF AUGMENTED MODEL
The design of predictive control is based on the dynamic model of the system. The state
space model approach is used in this work to design the predictive controller for the
system under consideration. By using a state-space model representation, the current
state variable information is used to predict the future response of the system. The
MPC controller design used in this work is adapted from Wang [2009a], which requires
an integrator term to be embedded into the state space model of the plant. The general
formulation of the model is described in the following.
Assuming a MIMO plant has m inputs, n 1 states and q outputs, the basic formulation
of the state space model is given in Equation (6.20). By taking difference operation on
both sides of Equation (6.20), we obtain:
x m (k + 1) − x m (k) = A m (x m (k) − x m (k − 1)) + B m (u(k) − u(k − 1))
+ B d (ɛ(k) − ɛ(k − 1)) (6.22)
Introducing ∆x m (k + 1) = x m (k + 1) − x m (k), ∆x(k) = x m (k) − x m (k − 1), ∆u(k) =
u(k) − u(k − 1) and w(k) = ɛ(k) − ɛ(k − 1), the difference of the state-space equation is:
∆x m (k + 1) = A m ∆x m (k) + B m ∆u m (k) + B d w(k) (6.23)
To relate the state variable ∆x m (k) with the output y(k), the following formulation is
introduced:
∆y(k + 1) = C m ∆x m (k + 1)
= C m A m ∆x m (k) + C m B m ∆u(k) + C m B d w(k) (6.24)
where ∆y(k + 1) = y(k + 1) − y(k).
If x(k) = [ ∆x m (k) T
y(k) T ] T is introduced as a new state variable vector, the new