The Development of Neural Network Based System Identification ...

172 CHAPTER 6 NEURAL NETWORK BASED PREDICTIVE CONTROL SYSTEM
6.8 MODEL PREDICTIVE CONTROL WITH CONSTRAINTS
The performance of a control system can significantly deteriorate when the control
signals from the original control design meet the operating constraints [Wang, 2009d].
The performance degradation due to this problem can be reduced to a certain degree if
the operational constraints can be introduced in the optimal control formulation.
The main idea in constrained control design is to modify the control variable ∆U to
satisfy condition when the constraints become active. This could be done systematically
in MPC control design through the optimisation process. Obviously, the unconstrained
optimisation previously described in the previous section needs to be reformulated to
incorporate constraints in the optimisation calculation.
There are three types of constraint variations typically used in control application:
(1) constraints based on the incremental control variable, ∆u min ≤ ∆u(k) ≤ ∆u max (2)
constraints based on the amplitude of control variable, u min ≤ u(k) ≤ u max , and (3)
constraints based on output variable, y min ≤ y(k) ≤ y max . For a plant with multiple
inputs and outputs, the constraints are specified for each input and output independently.
For example:
∆u min
1 ≤ ∆u 1 (k) ≤ ∆u max
1
∆u min
2 ≤ ∆u 2 (k) ≤ ∆u max
2
∆u min
3 ≤ ∆u 3 (k) ≤ ∆u max
3
∆u min
m
.
≤ ∆u m (k) ≤ ∆u max
m
Since predictive control problem is formulated and solved in the framework of receding
horizon, the constraints are taken into consideration for all future sampling instants.
By taking example of constraints on incremental control variation, all constraints are
expressed in the form of parameter vector ∆U as follows:
∆U = [∆u(k) ∆u(k + 1) ∆u(k + 2) · · · ∆u(k + N c )] T