L6258 datasheet(12/18 Pages) STMICROELECTRONICS

12 / 18 page

In order to cancel the pole of the load, the zero of

the Bx block must be located at the same fre-

quency of 163Hz; so now we have to find a com-

promise between the resistor and the capacitor of

the compensation 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 error amplifier zero, the slope

of the total transfer function 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

where: Rb = 20K

Ω

we have : Rc = 1.1M

Ω

Therefore we have the zero with a 163Hz the ca-

pacitor value :

π ⋅ Fzero ⋅ Rc

6.28

⋅ 163 ⋅ 1.1 ⋅ 10

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/dec-

ade, 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 re-

sult 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 :

The schematic now shows the equivalent circuit

of the stepper motor including a sine wave volt-

age generator of the Bemf. The Bemf voltage of

the motor is not constant, its value changes de-

pending 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 consid-

ering the Bemf of the stepper motor becomes:

ACload

Vsense

Vout

(VS

− Bemf) ⋅

+ RS

ACload

− Bemf

⋅

+ RS

OUT+

Bemf

OUT-

to Sense

Amplifier

L6258

12/18

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