Download Calculated Industries 6250 User guide

most controls textbooks. The second-order system is of
the form:
H(S) =
ξ
Where,
S2 +
ω n2
2 ξ ω nS
Equating this with our system,
KP2πKAa =
(a + KPKV2πKAa) = 2ξωn
ω n2
+
KP =
= damping ratio
ωn
= natural frequency
The time constant of this system is
1
ωn
KV =
.
The damped frequency is ωd = ωn
√
1 -
ξ2.
For the output to settle to within 2% of its stead state value
when a step input is applied, it will take four time constants,
4
or TS =
, to settle to within 2%.
ξωη
Equating our transfer function to the second-order
equation, we find:
KP
K PK V
KDKT
=
J
ωn2
K DK T
= 2ξωn
J
If we select a settling time of 30 ms and a damping ratio of
0.9, we can then determine KP and KV.
TS = 0.03 sec =
KV =
ω n2 ∗ J
1000 ∗ 2π
ERES
SGV = KV *
106 ∗ 2π
ERES
(ERES is the encoder resolution)
SGP = KP *
1000 ∗ 2π
ERES
SGV = KV *
106 ∗ 2π
ERES
If we now add an integral term to our control system, you will
find that the order is increased to 3.
The polynomials will now be added for the control algorithm:
K S +K P K I
P
= P
L
S
N = KPKVS
F = KAFFSS2 + KVFFS
Note that we have set KAFFS(acceleration feedforward
gain) and KVFF (velocity feedforward gain) to zero.
The block diagram for the control algorithm is as follows:
KAFFS2 + KVFFS
θc
After you have calculated KP and KV, then you must use
the following scale factor to put it in the units of SGP
(proportional feedback gain) and SGV (velocity feedback
gain) for the 6250:
SGP = KP *
[2 ξω n - a]
KP2πKAa
P I V S y s te m G ai n C al c u l ati o n s
KDK T
2 ξω n ∗ J
K PK DK T
2πKAa
"KA" and "a" can be measured using Motion Architect's
drive tuning module. In this module, you will issue a step
command to the drive system and then obtain a value for
"KA" and "a" for the calculations above.
The values of KD, KT, and T can be found from the
motor/drive's user documentation.
KP =
ω n2
(ERES is the encoder resolution)
4
rad
= > ωn = 148.15
sec
0.9 ( ω n )
It then follows that:
ω n2
KP
θa
A
B
I
θa
KI
S
KP KV S
Substituting this into our transfer function yields the
following:
θa
A [K P S + K P K I ]
=
B
S
+
[
K
S
+
K P K I] A + K V K P S ∗ S ∗ A
P
θc
PIV System — Torque Drive Gain Calculations
PV System — Velocity Drive Gain Calculations
For a velocity drive system, the transfer function is:
θa
K P ∗ 2πK A a
=
S(S+a) + K P 2πK A a + K P K V S2πK A a
θc
θa
K P ∗ 2πK A a
= 2
S + (a + K P K V 2πK A a)S + K P 2πK A a
θc
122
6250 Servo Controller User Guide
For the torque drive system under PIV control, the position
loop transfer function is as follows:
K D K T [K P S + K P K I]
θa
= 2
θc
S K D K T K V K P + JS 2 ∗ S + K D K T K P S + K D K T K P K I
θa
=
θc
K DK T KPS + KDK TK PK I
K
KDKT
KDKT
K
D T
S3 +
KVK PS 2 +
KPS +
KPK I
J
J
J