Introduction to Digital Power Conversion
XMC4000/1000 Family
Application Software
Application Guide
90
V1.0, 2015-01
8.7
Digital Switch Mode Control by New Feed-Forward Techniques
With computer technology the feed-forward terms can anticipate system changes before they impact
the output state of the power converter; i.e. the control loop does not have to be simply reactive in a
traditional way, but may add commands for the desired output state upon given calculation models.
These models are based on the expected PWM duty-cycles for a given set of input / output variables,
such as voltages, currents, circuit topology properties and overall conditions.
8.8
Non-linear Slope Compensation
Since the damping factor in the duty-cycle-(D)-to-output voltage frequency function is dependent on
the duty-cycle D, there should be a new slope compensation ramp (
s
C
) calculated by software for
every new input voltage
(V
IN
)
, in order to keep the damping factor invariable, by a desired constant
(
const
).
Buck Converter example
If the operating point for the steady state duty-cycle-to-output transfer function is
V
OUT
= D
1
V
IN1
and
s
C1
is chosen for a desired damping influence by a chosen constant =
const
1
– then, if the input
voltage is changed to V
IN2
, then the slope compensation should be
s
C2
= ((const
1
- 0.5)V
IN2
+ V
OUT
) / L,
to keep the same damping and same output voltage
V
OUT
on an input voltage change to
V
IN2
.
Taking the following expressions:
Q = 1 / (
*const)
where
const = (1 - D)(1 + s
C
/
s
A
) - 0.5 > 0
and
s
A
= (V
IN
– V
OUT
) / L
and
DV
IN
= (1
– D)V
OUT
These give a stability condition that includes a desired damping factor (Q) to stay constant upon the
V
IN
variations, by the following slope compensation function -
s
C
(D)
with variable D, described as:
–s
C
(D) =
– ((const – 0,5)/D
+
1)V
OUT
/ L
By regarding
-
s
C
(D)
as a differential function with variable D, there is a primitive function -
S
C
that is
associated to this differential function, satisfying a non-linear negative slope compensation curve:
S
C
(D)
/
D
=
– ((const – 0,5)/D
+
1)V
OUT
/ L
Without any further details, this expression says that there is an advanced solution for maintaining
slope compensation, by a negative ramp that is a non-linear curve, which offers a steady state duty-
cycle-to-output transfer function with an inherently constant damping, within a certain operating range.
