Siemens PCS 7 manual t 1s

Copyright  Siemens AG 2010 All rights reserved

Stabilization of Unstable Control Loops

The behaviour of an integrating process gi s 	ki		can be described by
	st1s	 1
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 k s  k p (kp is the proportional gain) is

gcl s 		gi sk s					1
	1	 gi sk s		t1	s	2	1		s  1
				k p ki				k p ki

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

		1			1		2	t
s	 						 4	1	.
1/ 2		k p ki						k p ki
				 k p ki 

Both poles are real, if the (absolute value of) gain kp of the controller is chosen such that

k p 	1	.
	4t1ki

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)!

MPC Level	13
V 1.0, Beitrags-ID: 42200753