RX62T

Position Control of PMSM with Encoder

R01AN0899EU0200 Rev. 2.00

Page 13 of 22

Jan. 31, 2014

An encoder coupled directly to the motor shaft measures the actual motor position θ(s). External shaft torque

disturbances Td are added to the torque generated by the motor's current to give the torque available to accelerate the

total inertia J.

Around the current regulator, motor block is the servo position controller that closes the position loop. The basic servo

position controller provides both a trajectory generator and a PID controller. The trajectory generator provides only

position set-point commands labeled in Figure 9 as θ*(s). The PID controller operates on the position error and outputs

a current command.

There are three gains to adjust in the PID controller, Kp, Ki and Kd. These gains all act on the position error defined as:

)

(

)

(

*

s

s

θ

θ

θ

−

=

∆

Note the superscript “*” refers to a commanded value.

The output of the PID is given mathematically in the time domain as:

)

(

)

(

)

(

)

(

*

t

dt

d

K

dt

t

K

t

K

t

iq

d

i

p

θ

θ

θ

∆

+

∆

−

∆

=

∫

Loosely speaking, the proportional term affects the overall response of the system to a position error. The integral term is

needed to force the steady state position error to zero for a constant position command and the derivative term is needed

to provide a damping action, as the response becomes oscillatory. Unfortunately all three parameters are inter-related so

that by adjusting one parameter will affect any of a previous parameter adjustment.

Tuning the PID controller can be done if the motor and load parameters are known and the desired frequency response

are known. They are adjusted using the following parameters in the header file of “customize.h”.

6.3 Current Control Loop

The current loop is a standard PI type based on the standard Park-Clarke stationary reference frame to rotary reference

transformations. The initial rotor position is determined by use of the Hall sensors. Once a Hall transition occurs, the

rotor position is then determined by reading the incremental encoder. The basic block diagram for the current vector

control is shown in Figure 12.

Figure 12 Block diagram of current vector control

Neglecting motor saliency, the commanded q axis current, iq* is linearly related to the commanded torque. The “d” axis

current command, id* is set to zero as field weakening is not required. The transformation takes two steps. First, the

stationary currents are transformed to an arbitrary stationary pair of orthogonal axes α, β and second, the axes are then

rotated to the rotor axes for control purposes.