Civil Engineering Reference
In-Depth Information
adaptive control strategy, process variation, and predictive power of the parametric model greatly influ-
ence the stability of the total system, and thus the degree of success.
An approach taken in adaptive force control effort for grinding is different from that of Tonshoff
et al. (1986), discussed earlier. Tonshoff applied a fixed-gain controller to regulate the grinding force
for an internal diameter grinder. In that work a deadbeat controller design is implemented for a third
order recursive model between feedrate and normal force. Tonshoff used a separate off-line model
estimation routine to determined the fixed-gains of the controller. In contrast, the work undertaken by
Jenkins and Kurfess (1996) performs real-time estimation of the grinding process and uses a pole-zero
cancellation approach to remove the process variation continuously in real-time.
Adaptive Controller Development
The development of an adaptive force controller for the grinding process can proceed directly from the
plant model, Eq. (3.16), rewritten in Eq. (3.25).
F
N
()
x
e
s
s
s
--------------
-------------
G
TPW
s
()
K
s
(3.25)
()
s
where
K
P
K
S
V/A
. Combining Eqs. (3.11) and (3.12) yields the following continuous plant transfer
function.
F
N
s
()
x
d
s
s
1
G
PC
s
()
G
TWP
s
()
-------------
203
K
s
--------------
-----------------------.
(3.26)
()
s
(
s
224
)
224. Thus, variations in the process can dominate
the system response. A fixed-gain controller can lead to poor performance as well as instabilities. Thus,
an adaptive controller is desired to mitigate the effects of changing process dynamics and maintain a
high MRR and a stable controller. From Eq. (3.26) it can be seen that the process dynamics can be
eliminated by a pole-zero cancellation using a PI-type controller. The controlled system would then be
of the form
From the earlier work, it has been shown that
F
N
s
()
E
F
s
K
PROP
s
(
)
s
-------------
--------------
--------------------------------
.
G
FC
()
s
G
PC
()
s
G
TWP
s
()
203
K
S
(3.27)
()
s
ss
(
224
)
, then the entire process
grinding dynamics can be eliminated from the resulting equation. This reduces Eq. (3.27) to that of the
previous situation of only a contact stiffness with a position loop, represented by Eq. (3.28).
In this scheme if the
(or
K
I
/
K
PROP
) of the PI controller in Eq. (3.27) is set to
F
N
s
()
E
F
s
203
K
S
K
PROP
s
G
FC
()
s
G
PC
()
s
G
TWP
s
()
-------------
----------------------------
(3.28)
()
(
224
)
where
. Since a discrete equivalent system is needed for the sampled plant in order to implement
such a scheme on the PMAC controller, a ZOH (zero order hold) equivalent discrete system is used.
F
N
z
()
X
d
z
z
z
1
1
-- 203
K
S
s
1
Z
1
-------------
-------------
--------------
-----------------------
G
PC
G
TWP
z
()
(3.29)
s
(
s
224
)
()
203
K
s
224
z
1
--------------------
e
T
224
T
-------------------------------------------------------
G
PC
G
TWP
()
z
(
e
)
(3.30)
ze
T
ze
224
T
(
)
(
)
