Siemens PCS 7 manual

Stabilization of Unstable Control Loops
MPC Level
V 1.0, Beitrags-ID: 42200753 13
Copyright  Siemens AG 2010 All rights reserved
The behaviour of an integrating process  
1
1
sts
k
sg i
i can be described by
two parameters:
 The maximal gradient ki of the response to a unit-step (of height one)
 The delay time t1 needed by the process to reach its maximal gradient after a
step in the manipulated variable (intersection point of the tangent with the base
line in Figure 3-1)
The transfer function of the closed loop including a proportional-only controller

p
ksk  (kp is the proportional gain) is
 

1
1
1
12
1



s
kk
s
kk
t
sksg
sksg
sg
ipip
i
i
cl
Thus the closed control loop has unity gain (the actual process value is equal to
the set point in steady state, if no disturbance at the input occurs) and two poles at
ipipip kk
t
kkkk
s1
2
2/1 4
11 








 .
Both poles are real, if the (absolute value of) gain kp of the controller is chosen
such that
i
pkt
k
1
4
1
.
Hence, an asymptotic stable control loop is ensured. A considerably smaller value
is a good starting point for a stable controller parameterization and a following
computer-based PID tuning, even if the specific values of the process are not
known exactly.
If the process is uncritical, an adequately small gain can be chosen arbitrarily and
used as starting point. You can increase this starting value iteratively until first indi-
cations of oscillations in the control loop become visible.
NOTE The sign of the controller gain must be negative, if the sign of the controlled
process ki is negative too (open drain valve -> level decreases)!