L6258E View Datasheet(PDF) - STMicroelectronics
Part Name
Description
MFG CO.
'L6258E' PDF : 24 Pages View PDF
L6258E
In order to cancel the pole of the load, the zero of the
Bx block must be located at the same frequency of
163Hz; so now we have to find a compromise be-
tween the resistor and the capacitor of the compen-
sation network.
Considering that the resistor value defines the gain of
the Bx block at the zero frequency, it is clear that this
parameter will influence the total bandwidth of the
system because, annulling the load pole with the er-
ror amplifier zero, the slope of the total transfer func-
tion is -20dB/decade.
So the resistor value must be chosen in order to have
an error amplifier gain enough to guarantee a desired
total bandwidth .
In our example we fix at 35dB the gain of the Bx block
at zero frequency, so from the formula:
Bx_gain@ zero freq. = 20 ⋅ log R-R----bc--
where: Rb = 20kΩ
we have: Rc = 1.1MΩ
Therefore we have the zero with a 163Hz the capac-
itor value :
Cc = 2----π-----⋅---F----z---1-e---r---o-----⋅---R-----c- = -6---.-2----8----⋅----1---6---3---1--⋅---1---.--1-----⋅---1---0----–--6-- = 880pF
Now we have to analyse how the new Aloop transfer
function with a compensation network on the error
amplifier is.
The following bode diagram shows :
– the Ax function showing the position of the load
pole
– the open loop transfer function of the Bx block
– the transfer function of the Bx with the RC com-
pensation network on the error amplifier
– the total Aloop transfer function that is the sum
of the Ax function plus the transfer function of
the compensated Bx block.
We can see that the effect of the load pole is can-
celled by the zero of the Bx block ; the total Aloop
cross a the 0dB axis with a slope of -20dB/decade,
having in this way a stable system with an high gain
at low frequency and a bandwidth of around 8KHz.
To increase the bandwidth of the system, we should
increase the gain of the Bx block, keeping the zero in
the same position. In this way the result is a shift of
the total Aloop transfer function up to a greater value.
Effect of the Bemf of the stepper motor on the
current control loop stability
In order to evaluate what is the effect of the Bemf
voltage of the stepper motor we have to look at the
load block :
OU T+
Bemf
RL
LL
RS
to Sense
Amplifier
OU T-
The schematic now shows the equivalent circuit of
the stepper motor including a sine wave voltage gen-
erator of the Bemf. The Bemf voltage of the motor is
not constant, its value changes depending on the
speed of the motor.
Increasing the motor speed the Bemf voltage in-
creases :
Bemf = Kt · ω
where:
Kt is the motor constant
ω is the motor speed in radiant per second
The formula defining the gain of the load considering
the Bemf of the stepper motor becomes:
ACload = V-----Vs---e-o---n-u---s-t--e-- = (---V----S-----–----B-----e---m---V---f-S-)----⋅----R--------L-----R----+-----S----R----------S---
Acload
=
-V----S----–-----B----e----m------f
VS
⋅
-------R-----S--------
RL + RS
14/20
Share Link: 
