Fluid delivery systems PID autotuning
A method for calculating PID parameters of a fluid system including a motor driving a pump, a compressor or a fan, including further a feedback sensor providing a feedback signal on the system and a PID regulation controlling the motor speed. The method includes: after an initial approximation of the fluid system by a first order transfer function with delay where three parameters of the transfer function of the process to be identified are: K Static gain, θ Delay, τ Time constant, one or more sequences of: a—bypassing the PID regulation and implementing the following processes: a periodic relay process providing a first point (ω −180 ; G −180 ) at −180° of phase named critical point, a periodic relay with integration process providing a second point (ω −90 ; G −90 ) at −90° of phase and, a step injection providing a third point G 0 at ω=0° of phase and at null frequency, b—resolving the relevant equations in equation systems according to the points obtained through the processes to calculate the transfer function parameters available among K = G 0 , τ = 1 ω - 1 8 0 ( K G - 1 8 0 ) 2 - 1 , θ = ( tan - 1 ( ω - 1 8 0 · τ ) + π ) · 1 ω - 1 8 0 c—applying the transfer function parameters obtained to calculate PID parameters for the system regulation { K p = τ K · ( λ + θ ) T i = τ T d = θ
1 . A method for calculating PID parameters of a fluid system comprising a motor driving a pump, a compressor or a fan, the fluid system further comprising a feedback sensor providing a feedback signal on the system and a PID regulation controlling a speed of the motor, wherein the method comprises:
after an initial approximation of the fluid system by a first order transfer function with delay of a form of
P
estim
(
S
)
=
K
·
e
-
θ
·
s
1
+
τ
·
s
where three parameters of the transfer function of a process to be identified are K Static gain, θ Delay, τ Time constant,
performing one or more sequences of:
bypassing the PID regulation controlling the speed of the motor; implementing each of:
a periodic relay process providing a first point (ω −180 ;G −180 ) at −180° of phase named critical point,
a periodic relay with integration process providing a second point (ω −90 ;G −90 ) at −90° of phase and,
a step injection process providing a third point G 0 at ω=0° of phase and at null frequency;
resolving:
G
0
=
K
G
-
90
=
K
1
+
(
τ
·
ω
-
90
)
2
cos
(
ω
-
90
·
θ
)
-
ω
-
90
·
τ
·
sin
(
ω
-
90
·
θ
)
=
0
G
-
180
=
K
1
+
(
τ
·
ω
-
180
)
2
sin
(
ω
-
180
·
θ
)
-
ω
-
180
·
τ
·
cos
(
ω
-
180
·
θ
)
=
0
according to the first point, the second point, and the third point to calculate the transfer function parameters available among:
K
=
G
0
τ
=
1
ω
-
1
8
0
(
K
G
-
1
8
0
)
2
-
1
θ
=
(
tan
-
1
(
ω
-
1
8
0
·
τ
)
+
π
)
·
1
ω
-
1
8
0
;
applying the transfer function parameters obtained to calculate PID parameters for the system regulation:
{
K
p
=
τ
K
·
(
λ
+
θ
)
T
i
=
τ
T
d
=
θ
where λ=α·max(τ,θ) and α is between 0.1 to 2; and
then reestablishing the PID regulation controlling the speed of the motor.
2 . The method according to claim 1 , wherein T d is approximated to zero.
3 . The method according to claim 1 , wherein said step injection process comprises, inputting a step having an amplitude Δu to a current speed command of the motor, waiting for process feedback convergence, measuring a feedback signal value Δv, and calculating said static gain K as Δv/Δu.
4 . The method according to claim 3 , wherein having the amplitude Δu is limited in order not to exceed an upper limit s h of the motor speed.
5 . The method according to claim 3 , wherein the waiting for process feedback convergence includes detecting the convergence, the detecting convergence comprises periodically providing measures of a feedback signal sample and comparing the measures of the feedback signal sample to a mean value of the measures of the feedback signal sample based on a dedicated number of samples, comparing an absolute difference between said measures and said mean value, confirming achievement of the convergence when said absolute difference remains under a defined limit for a specified period of time.
6 . The method according to claim 5 , wherein any one of said step injection process, said periodic relay process, and said periodic relay process with integration is aborted and the PID regulation is reestablished if the convergence is not achieved within a stipulated time limit or if the feedback signal exceeds a stipulated amplitude limit.
7 . The method according to claim 6 , wherein in case the convergence is not achieved, recovery of missing elements is done with:
If (ω −90 ;G −90 ) AND (ω −180 ;G −180 ) are known:
If G 0 is known:
K=G 0
Else:
K
=
G
-
9
0
·
G
-
180
·
ω
-
90
2
-
ω
-
180
2
(
ω
-
90
·
G
90
)
2
-
(
ω
-
180
·
G
180
)
2
Or
K
=
G
-
9
0
·
2
in
case
ω
-
90
2
-
ω
-
180
2
(
ω
-
90
·
G
90
)
2
-
(
ω
-
1
·
G
180
)
2
is negative
τ
=
1
ω
-
9
(
K
G
-
9
0
)
2
-
1
θ
=
tan
-
1
(
1
ω
-
9
0
·
τ
)
·
1
ω
-
9
If (ω −90 ;G −90 ) is known:
If G 0 is known:
K=G 0
Else:
K=G −90 ·√{square root over (2)}
τ
=
1
ω
-
9
0
(
K
G
-
9
0
)
2
-
1
θ
=
tan
-
1
(
1
ω
-
9
0
·
τ
)
·
1
ω
-
9
0
If (ω −180 ;G −180 ) is known:
If G 0 is known:
K=G 0
Else:
K=G −180 √{square root over (2)}
τ
=
1
ω
-
18
(
K
G
-
180
)
2
-
1
θ
=
(
tan
-
1
(
ω
-
180
·
τ
)
+
π
)
·
1
ω
-
180
.
8 . The method according to claim 1 , wherein said periodic relay process comprises:
providing a series of relay switching on sign changes of the feedback signal,
waiting for convergence of the feedback signal, and
measuring a relay period T, a feedback amplitude A and a relay amplitude d thus providing a critical period T u =T and a critical gain
K
u
=
4
·
d
π
·
A
/
2
,
9 . The method according to claim 8 , wherein the relay amplitude d is limited in order that the speed of the motor does not to exceed defined upper and lower limits s h , s i .
10 . The method according to claim 1 , wherein said periodic relay with integration process comprises:
applying a series of ramps or relay switching with integration around a last PID output wherein the relay switches on sign change of the feedback signal;
analyzing convergence of the feedback signal and when convergence is achieved recording a point at 90° of phase at a relay period T and calculating:
Input
amplitude
:
D
=
2
·
d
=
G
·
T
2
,
Process
period
@
-
90
°
phase
:
T
90
=
T
,
Process
gain
@
-
90
°
phase
:
K
-
90
=
π
2
8
·
A
2
d
=
π
2
·
a
8
·
d
,
and
where A is a peak-to-peak amplitude of the feedback signal, D=2·d is the peak-to-peak amplitude of the relay signal, G is a slope of relay triangle waves.
11 . The method according to claim 1 , wherein said one or more sequences are repeated from time to time during an operational life of the fluid system to calculate the PID parameters adapted to ageing of the fluid system.
12 . A method for calculating PID parameters of a fluid system comprising a motor driving a pump, a compressor or a fan, the fluid system further comprising a feedback sensor on the system to provide a PID regulation controlling the speed of the motor, the method comprising:
choosing settings between settings based on the method of claim 1 and settings based on Ziegler Nichols method or choosing settings based minimal proportional gain, maximal integral time constant and minimal derivative time constant
K
p
=
min
(
0.4
·
K
cr
;
τ
K
·
(
λ
+
θ
)
)
;
T
i
=
max
(
0.8
·
T
cr
;
τ
)
;
T
d
=
0
between the method of claim 1 and the Ziegler Nichols method; where
Critical gain
K
cr
=
4
·
d
π
·
A
/
2
,
A is feedback amplitude, d is relay amplitude, Critical period T cr =T, and T is relay period.
13 . A process for tuning a PID regulated process comprising calculating PID parameters with the method as claimed in claim 1 , and reestablishing the PID regulation with the calculated PID parameters.
14 . A control device to calculate PID parameters of a fluid system comprising a motor driving a pump, a compressor or a fan, the fluid system further comprising a feedback sensor providing a feedback signal on the system and a PID regulation controlling a speed of the motor, wherein the control device is configured to:
after an initial approximation of the fluid system by a first order transfer function with delay of a form of
P
e
s
t
i
m
(
S
)
=
K
·
e
-
θ
·
s
1
+
τ
·
s
where three parameters of the transfer function of a process to be identified are K Static gain, θ Delay, τ Time constant,
perform one or more sequences of:
bypassing the PID regulation controlling the speed of the motor;
implementing each of:
a periodic relay process providing a first point (ω −180 ;G −180 ) at −180° of phase named critical point,
a periodic relay with integration process providing a second point (ω −90 ;G −9 ) at −90° of phase and,
a step injection process providing a third point G 0 at ω=0° of phase and at null frequency;
resolve:
G
0
=
K
G
-
9
0
=
K
1
+
(
τ
·
ω
-
90
)
2
cos
(
ω
-
9
0
)
-
ω
-
9
·
τ
·
sin
(
ω
-
90
·
θ
)
=
0
G
-
180
=
K
1
+
(
τ
·
ω
-
180
)
2
sin
(
ω
-
1
8
·
θ
)
-
ω
-
1
8
0
·
τ
·
cos
(
ω
-
1
8
0
·
θ
)
=
0
according to the first point, the second point, and the third point to calculate the transfer function parameters available among:
K
=
G
0
τ
=
1
ω
-
1
8
0
(
K
G
-
1
8
0
)
2
-
1
θ
=
(
tan
-
1
(
ω
-
18
·
τ
)
+
π
)
·
1
ω
-
1
8
0
;
apply the transfer function parameters obtained to calculate PID parameters for the system regulation:
{
K
p
=
τ
K
·
(
λ
+
θ
)
T
i
=
τ
T
d
=
θ
where λ=π·max(τ,θ) and α is between 0.1 to 2; and
then reestablish the PID regulation controlling the speed of the motor.
15 . The control device according to claim 14 , wherein T d is approximated to zero.
16 . The control device according to claim 14 , wherein said step injection process comprises inputting a step having an amplitude Δu to a current speed command of the motor, waiting for process feedback convergence, measuring a feedback signal value Δv, and calculating said static gain K as Δv/Δu.
17 . The control device to claim 16 , wherein having the amplitude Δu is limited in order not to exceed an upper limit s h of the motor speed.
18 . The control device according to claim 14 , wherein said periodic relay process comprises:
providing a series of relay switching on sign changes of the feedback signal,
waiting for convergence of the feedback signal, and
measuring a relay period T, a feedback amplitude A and a relay amplitude d thus providing a critical period T u =T and a critical gain
K
u
=
4
·
d
π
·
A
/
2
.
19 . The control device according to claim 18 , wherein the relay amplitude d is limited in order that the speed of the motor does not to exceed defined upper and lower limits s h , s i .
20 . The control device according to claim 14 , wherein said periodic relay with integration process comprises:
applying a series of ramps or relay switching with integration around a last PID output wherein the relay switches on sign change of the feedback signal;
analyzing convergence of the feedback signal and when convergence is achieved recording a point at 90° of phase at a relay period T and calculating:
Input
amplitude
:
D
=
2
·
d
=
G
·
T
2
,
Process
period
@
-
90
°
phase
:
T
90
=
T
,
Process
gain
@
-
90
°
phase
:
K
-
90
=
π
2
8
·
A
2
d
=
π
2
·
a
8
·
d
,
and
where A is a peak-to-peak amplitude of the feedback signal, D=2·d is the peak-to-peak amplitude of the relay signal, G is a slope of relay triangle waves.