Parallel PI Voltage-H Current Control of a Neutral Leg - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 212

avoid a large control action and a weighting factor is introduced so that the impact of the

measurement noise n can be tuned during the process of controller design. The weighting
factors

ξ

can be used to adjust the relative importance of the disturbances i N and n
in the H ∞ norm. The H ∞ control problem, as shown in Figure 13.4, is then formulated
to minimise the H ∞ norm of the transfer function from

ξ and μ

[ n N ] T z 2 ] T , w = to z = [ z 1

denoted T z w = F l ( P , C ). The closed-loop system can be represented as

z
y

P u

= ,

u = C y ,

where P is the generalised plant that includes the original control plant and weighting functions,
C is the controller to be designed and y is the measured current i C that contains the effect of
the measurement noise n , which is an imaginary variable introduced to facilitate the design of
the controller so that the impact of the measurement noise n in the current i C is reflected and
minimised. When the controller is implemented, as shown in Figure 13.3, the feedback signal
to the controller C is the measured current i C , which contains the effect of the measurement
noise, so there is no need to determine or calculate the value of the measurement noise n .
It is worth noting that the controlled variables z in the previous chapter are the neutral-point
voltage shift and the neutral line inductor voltage but the controlled variables here are chosen
as the current flowing through the split DC capacitors and the duty cycle for the switches.
Moreover, a two-input-one-output controller is adopted in Chapter 12 but a single-input-single-
output controller is adopted here, with the add-on of a voltage controller to be discussed later.

13.2.3 State-space Realisation of the Plant P

= i L V c T . The The inductor current i L and the voltage V c are chosen as state variables x

output signal from the plant P is the capacitor current i C = i L , i.e., the difference between

the neutral current and the current through the inductor. The plant P can then be described by
the state equation

i N −

x = Ax + B 1 i N + B 2 u (13.2)

and the output equation

y = e = C 1 x + D 1 i N + D 2 u (13.3)

with

⎡ ⎤

R N
L N

1
L N

−

⎣ ⎦ ,

A =

1
C N + +

− 0

C N −

⎡ ⎤ ⎡ ⎤

V DC
2 L N
0

0
1
C N + +

⎣ ⎦ , ⎣ ⎦ ,

B 1 = B 2 =

C N −

C 1 = − 10 , D 1 = 1 , D 2 = 0 .