### VOLTAGE ORIENTED CONTROL – SIMULATION

# 3.6 Stability analysis

We decided to do a small stability analysis with the current controller only, voltage controller, then both voltage and current controller together. Furthermore, the analysis is done for

three different voltage controller. First, only a proportional controller is taking in account (

). In a

second time, the integration part is added (

## ). And finally, the active damping coefficient

is added.

# 3.6.1 Current controller

## If the cross coupling cancellation is ideal, that is,

, we saw in section “3.4.3 Design of

the synchronous PI controller” (and see Figure 3.8) that the system transfer function becomes

1 (3.7)

## If we see

as a disturbance that we neglect, we obtain the following diagram

Figure 3.28 : stability analysis of current control

## Now, following the IMC, we saw that the controller is calculated with

## The open and closed loop transfer function are noted respectively

and

(3.38) (3.39)

## Furthermore, if

and

, we can obtain the open and closed loop transfer function

(3.40)

(3.41)

is a first order system, low pass filter, with a cut off frequency

rad/s.

There is only one pole for means stability).

and it’s located at

(negative Real part of the Imaginary domain

3.6.2 Voltage controller PROPORTIONAL CONTROL ONLY

We consider again the Figure 3.16 without load disturbance following diagram. The system transfer function is (equation (3.26))

and we obtain the

41