Control Techniques M'Ax, Руководство для продвинутых пользователей

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M’Ax Advanced User Guide
22
Issue Number: 4 www.controltechniques.com
Parameter 3.16 may be changed when the drive is enabled or disabled. It is necessary to update the SLM with the required PID set by setting
PID buffer update bit i.e. Pr 11.67 to 1. Any of the available 3 buffers can be selected "on the fly".
Proportional gain (Kp)
If Kp has a value and Ki is set to zero the controller will only have a proportional term, and there must be a speed error to produce a torque
reference. Therefore as the motor load increases there will be a difference between the reference and actual speeds. This effect, called
regulation, depends on the level of the proportional gain, the higher the gain the smaller the speed error for a given load. If the proportional
gain is too high then the closed-loop stability limit is reached.
Integral gain (Ki)
The integral gain is provided to prevent speed regulation. The error is accumulated over a period of time and used to produce the necessary
torque demand without any speed error. Increasing the integral gain reduces the time taken for the speed to reach the correct level and
increases the stiffness of the system, i.e. it reduces the positional displacement produced by applying a load torque to the motor.
Unfortunately increasing the integral gain also reduces the system damping giving overshoot after a transient. For a given integral gain the
damping can be improved by increasing the proportional gain. A compromise must be reached where the system response, stiffness and
damping are all adequate for the application. The integral term is implemented in the form of
Σ
(Ki x error), and so the integral gain can be
changed when the controller is active without causing large torque demand transients.
Differential gain (Kd)
The differential gain is provided in the feedback of the speed controller to give additional damping. The differential term is implemented in a
way that does not introduce excessive noise normally associated with this type of function. Increasing the differential term reduces the
overshoot produced by under-damping, however, for most applications the proportional and integral gains alone are sufficient.
To analyse the performance of the speed controller it may be represented as an s-domain model as shown below.
Where:
Kc is the conversion between torque reference and torque producing current. A value of unity at the input to this block gives a torque
producing current equivalent to the full scale current of the drive. The drive automatically compensates the torque producing current for flux
variations in field weakening, and so Kc can be assumed to have a constant value. Drive rated current is equivalent to 0.5 x full scale (see
Menu 4 for details of current scaling), and so
Kc = Drive rated current / 0.5
Kt is the torque constant of the motor (i.e. torque in Nm per amp of torque producing current).
L(s) is the transfer function of the load.
The s-domain system above may be used to determine the performance of systems with a relatively low bandwidth. However, the real drive
system also includes non-ideal delays due to the torque controller response, and speed measurement and control delays. These delays,
which can be approximated with a simple unity gain transport delay (T
delay
) as shown below, should be taken into account for more accurate
results.
Kp
Ki
Kd
Speed
reference
(wr*)
Speed
feedback
(wr)
Torque
reference
(Te*)
-
+
+
+
+
+
1
s
s
Kp
Ki 1/s
Kd
Ke
Kc Kt L(s)
Ke
+
_
+
+
+
w*(s)
(rs
-1
)
w(s)
(rs
-1
)
+
s