The document discusses the equivalence between PD+DOB (proportional derivative plus disturbance observer) control and weighted PID control for servo drives. It shows that when a PD+DOB controller is designed for a servo drive with velocity feedback, it is equivalent to a weighted PID controller. This provides a tuning rule for the weighted PID gains called the DOB tuning, where the gains are expressed in terms of the cutoff frequency of the filter used in the disturbance observer. The document supports this with mathematical analysis and presents experimental results demonstrating the performance of PD+DOB and weighted PID controllers on a servo drive testbed.

1. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
1
3rd IFAC Conference on Advances in
Proportional-Integral-Derivative Control
On the equivalence between PD+DOB and PID
controllers applied to servo drives
J. Luis Luna
Rubén Garrido
CINVESTAV-Departamento de Control Automático, México
Ghent, Belgium May, 2018

2. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
2
Outline
1 Introduction
2 Preliminaries on Disturbance Observers
3 Disturbance Observer (DOB) applied to a servo drive
4 Equivalence between PD+DOB and weighted PID controllers
The weighted PID controller under the DOB tuning.
5 Experiments
Experimental setup
Comparative study using the weighted PID and PD+DOB con-
trollers
Experimental results with the weighted PID controller
6 Conclusions
7 References

3. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
3
The aim of this work is to show that:
• When a PD+DOB controller is designed for a servo drive
under velocity feedback, it is equivalent to a weighted PID
controller.
• The equivalence provides a tuning rule for the weighted PID
controller called the DOB tuning.
• The tuning rule is expressed in terms of the cutoff frequency
of the filter used for building the DOB.

4. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
4
PID controller
• It is one of the most employed algorithms for regulating
industrial processes [Åström, 1995],[Visioli, 2006].
• It is also employed for controlling:
• Servo drives [Ellis, 2012].
• Robot manipulators [Spong, 1989].
• Quadrotors [Pounds et al., 2012].

5. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
5
Disturbance Observer (DOB)-based control
• Disturbance Observer is employed for rejecting internal and
external disturbances acting on a plant.
• It relies on input and output measurements on a nominal
model of a perturbed plant to estimate the disturbances
[Ohishi et al., 1988, Ohnishi et al., 1996].
• The disturbance estimate is injected to the plant input to
counteract the effects of the real disturbance.

6. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
6
Disturbance Observer
! "
m
P s
!
u
d
y
!
P s
!
d
!"#$%&'()*+
,&"*%-*%
r
!"#$!%%&$
!
e
!
F s
v
!
C s
Figure 1: Disturbance Observer-based controller block diagram.
The output of the plant with a perturbation is given by
y = P(s)(u + d) (1)
To reconstruct the disturbance we use measurements of the plant
input and output
d = P−1
(s)y − u (2)

7. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
7
Problem: The plant inverse P−1
(s) is not proper.
• To avoid this problem the disturbance estimation is performed
as follows
ˆ
d =
P−1
m (s)y − u
F(s)
• F(s) is a strictly proper stable filter guaranteeing a proper or
strictly proper transfer function P−1
m (s)F(s)

8. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
8
Disturbance observer applied to a servo drive
Servo drive model
Jq̈(t) + F(q̇) = ku + ¯
dm
Alternative writing
q̈(t) = −f(q̇) + bu + ¯
d
where b =
k
J
, f(q̇) =
F(q̇)
J
and ¯
d =
¯
dm
J
.
If the friction torques f(q̇) are unknown, these can be grouped
together with the disturbance ¯
d as follows
q̈(t) = bu + d
and d = ¯
d − f(q̇).

9. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
9
The Laplace transform of the servo drive model is given by:
L {q̈(t) = bu + d} ⇔ s2
Q(s) = bU(s) + D(s)
DOB filter
F(s) =
β
s + β
with cutoff frequency β 0.
+
u
d
q
1
s
b
1
s
b
s
b
b
+
s
s
b
b
+
+
-
d̂
SERVOMOTOR
-
DISTURBANCE OBSERVER
-
+
r
PD CONTROLLER
WITH WEIGHTED
DERIVATIVE ACTION
+
-
e q
1
b
p
K
d
K
+
Figure 2: PD+DOB controller applied to a servo drive.

10. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
10
Equivalence between PD+DOB and weighted PID controllers
Fig. 2 defines the PD+DOB control law and error equation:
e = r − q
u =
1
b
h
Kpe − Kdq̇ − ˆ
d
i
(3)
Applying the Laplace transform to (3) leads to:
U(s) =
1
b
h
KpE(s) − KdsQ(s) − D̂(s)
i
(4)
The disturbance D̂(s) can be expressed in terms of β, Kp and Kd
as follows:
D̂(s) = βKdQ(s) − βKp
1
s
E(s) + βsQ(s) (5)

11. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
11
Substituting (5) into (4) boils down to
U(s) =
1
b
[KpR(s) − KpQ(s) − βKdQ(s)
+βKp
1
s
E(s) − (Kd + β)sQ(s)]
u
d
q
s
b
s
p
K
s
E
^ZsKDKdKZ
r
W/KEdZKZ
e q
b
p
K
d
K E
p d
K K
E
Figure 3: Weighted PID controller applied to a servo drive.

12. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
12
Alternative writing in terms of weighted errors
Weighted PID
U(s) =
1
b
K̄pEp(s) + K̄i
1
s
E(s) + K̄dsEd(s)
(6)
where
Ep(s) = b̄R(s) − Q(s)
E(s) = R(s) − Q(s)
Ed(s) = c̄R(s) − Q(s)
weights: b̄ =
Kp
Kp + βKd
, c̄ = 0

13. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
13
On the other hand, the gains in (6) have the following expressions
DOB Tunning
K̄p = Kp + βKd
K̄i = βKp (7)
K̄d = Kd + β
Figure 4: From PD+DOB controller to Weighted PID controller.

14. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
14
Procedure for DOB tuning:
• Set β equal zero.
• Apply some tuning criterion for Kp and Kd.
• If the stationary state error is non zero, increase the
value of β until the error is close or equal to zero.

15. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
15
The PID controller under the DOB tuning and close-loop
stability.
The next equation corresponds to the transfer function of the plant
without disturbances
s2
Q(s) = bU(s)
in closed loop with the controller
U(s) =
1
b
[KpE(s) − βKdQ(s) + βKp
1
s
E(s) − (Kd + β)sQ(s)]
G(s) =
Q(s)
U(s)
=
N(s)
R(s)
(8)
The characteristic polynomial in (8) is defined as:
R(s) = (s + β)(s2
+ Kds + Kp) (9)
The fact that Kp, Kd and β are positive constants guarantees that
the poles of G(s) are stable.

16. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
16
Experimental setup
Control
Computer
DC Motor Position
sensor
Isolation
box
Control
Signal ± 10 V
Power
amplifier
Connection
panel for the
data acquisition
card
Figure 5: Experimental setup.

17. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
17
Experimental setup
• The reference is a filtered step of 0.5 servomotor shaft
revolutions.
• The value of the input gain in the next servo drive model is
b = 51.49
q̈(t) = bu + d
• In order to evaluate large position errors and excessive
oscillatory responses, the performance is measured using the
Integral Squared Error (ISE), which is evaluated at T = 2s.
ISE =
Z T
0
100 [e(t)]
2
dt (10)

18. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
18
Experiments
PD+DOB control law
U(S) =
1
b
h
KpE(s) − KdsQ(s) − D̂(s)
i
(11)
D̂(s) = sY (s)
sβ
s + β
− U(s)
bβ
s + β
(12)
Weighted PID
U(s) =
1
b
K̄pEp(s) + K̄i
1
s
E(s) + K̄dsEd(s)
(13)
• The servomotor angular velocity q̇ is estimated from position
measurements through the next filter:
Gv(s) =
300s
s + 300
400
s + 400
(14)

19. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
19
PD+DOB and weighted PID
0 1 2 3 4
−0.5
0
0.5
Time (s)
Position
Reference
PD+DOB
PID
Figure 6: Responses of the weighted PID and PD+DOB controllers.
0 0.5 1 1.5 2
−0.5
−0.4
−0.3
−0.2
−0.1
0
Time (s)
Position
Reference
PD+DOB
PID
Figure 7: Closer look to the responses of the weighted PID and
PD+DOB controllers.

20. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
20
0 1 2 3 4
−0.4
−0.2
0
0.2
0.4
0.6
Time(s)
Position
error
PD+DOB
PID
(a) Error signals for the weighted PID and
PD+DOB controllers.
0 1 2 3 4
−2
0
2 PD+DOB
0 1 2 3 4
−2
0
2
Time (s)
Control
signal
(V)
PID
(b) Control signals for the weighted PID and
PD+DOB controllers.

21. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
21
Table 1: Experimental results for the weighted PID and PD+DOB
controllers.
Experiment Kp Kd β ISE
1 Weighted PID 400 80 20 101.7836
2 PD+DOB 400 80 20 96.7817
• The dynamics of the filter Gv(s) used to estimate the
servomotor angular velocity seems to affect in a different way
the behavior of both controllers:
• In the case of the PD+DOB controller the velocity estimate
produced by the filter is used to compute the disturbance
estimate.
• On the other hand the weighted PID controller the velocity
estimate only feeds the Derivative action.
Remark: Numerical simulations do not exhibit differences in
the response in both controllers when they are simulated with-
out velocity estimators.

22. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
22
Weighted PID controller response using
different values of the parameter β
0 1 2 3 4
−0.5
0
0.5
Time (s)
Position
Reference
PID β=0
PID β=10
PID β=20
PID β=30
Figure 8: Step response for the weighted PID controller.

23. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
23
0 1 2 3 4
−2
−1
0
1
2
3
Time (s)
Control
signal
(V)
PID β=0
PID β=10
PID β=20
PID β=30
Figure 9: Control signals for the weighted PID controller under the
DOB tuning.

24. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
24
Table 2: Experimental Results for the weighted PID controller using the
DOB tuning Kp = 400 and Kd = 80.
β −ess +ess ISE IAVC IAC
0 0.0051 0.002 100.9910 6.2421 0.1566
10 1.72×10−15
1.72×10−15
101.632 8.5889 0.1185
20 1.72×10−15
1.72×10−15
101.80848 9.1970 0.1354
30 1.72×10−15
1.72×10−15
101.9634 9.8852 0.140
• Integral of the Absolute value of the Control (IAC) index
defined as
IAC =
Z T
0
|u(t)| dt (15)
• Integral of the Absolute value of the Control Variation (IACV)
index defined as:
IACV =
Z T
0
du(t)
dt
dt (16)

25. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
25
Conclusions
• Both controllers produce smooth responses without overshoot
and display essentially the same performance in terms of the
Integral Squared Error (ISE) index, and slight discrepancies
exist due to the effect of the filter used to estimate the
servomotor angular velocity.

26. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
25
Conclusions
• Both controllers produce smooth responses without overshoot
and display essentially the same performance in terms of the
Integral Squared Error (ISE) index, and slight discrepancies
exist due to the effect of the filter used to estimate the
servomotor angular velocity.
• Large values of the β term used in the DOB tuning, which
corresponds to the cutoff frequency of the DOB in the
PD+DOB controller, does not significantly improves
closed-loop performance.

27. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
25
Conclusions
• Both controllers produce smooth responses without overshoot
and display essentially the same performance in terms of the
Integral Squared Error (ISE) index, and slight discrepancies
exist due to the effect of the filter used to estimate the
servomotor angular velocity.
• Large values of the β term used in the DOB tuning, which
corresponds to the cutoff frequency of the DOB in the
PD+DOB controller, does not significantly improves
closed-loop performance.
• Therefore, large values of weighted PID controller gains are
not necessary to obtain reasonable performance.

28. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
25
Conclusions
• Both controllers produce smooth responses without overshoot
and display essentially the same performance in terms of the
Integral Squared Error (ISE) index, and slight discrepancies
exist due to the effect of the filter used to estimate the
servomotor angular velocity.
• Large values of the β term used in the DOB tuning, which
corresponds to the cutoff frequency of the DOB in the
PD+DOB controller, does not significantly improves
closed-loop performance.
• Therefore, large values of weighted PID controller gains are
not necessary to obtain reasonable performance.
• Future work includes using the PID controller under the DOB
tuning when the servomotor is affected by more complex
disturbances.

29. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
25
Conclusions
• Both controllers produce smooth responses without overshoot
and display essentially the same performance in terms of the
Integral Squared Error (ISE) index, and slight discrepancies
exist due to the effect of the filter used to estimate the
servomotor angular velocity.
• Large values of the β term used in the DOB tuning, which
corresponds to the cutoff frequency of the DOB in the
PD+DOB controller, does not significantly improves
closed-loop performance.
• Therefore, large values of weighted PID controller gains are
not necessary to obtain reasonable performance.
• Future work includes using the PID controller under the DOB
tuning when the servomotor is affected by more complex
disturbances.
• The effect on closed-loop performance using other velocity
estimators would be worth studying.

30. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
26
[Åström, 1995] Åström, Karl Johan Hägglund, T. (1995).
PID controllers: theory, design, and tuning, volume 2.
Isa Research Triangle Park, NC.
[Ellis, 2012] Ellis, G. (2012).
Control system design guide: using your computer to
understand and diagnose feedback controllers.
Butterworth-Heinemann.
[Ohishi et al., 1988] Ohishi, K., Ohnishi, K., and Miyachi, K.
(1988).
Adaptive dc servo drive control taking force disturbance
suppression into account.
IEEE Transactions on Industry Applications, 24(1):171–176.
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(1996).
Motion control for advanced mechatronics.
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31. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
27
[Pounds et al., 2012] Pounds, P. E., Bersak, D. R., and Dollar,
A. M. (2012).
Stability of small-scale uav helicopters and quadrotors with
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[Spong, 1989] Spong, M. W. Vidyasagar, M. (1989).
Robot Dynamics and Control.
Wiley, New York.
[Visioli, 2006] Visioli, A. (2006).
Practical PID control.
Springer Science Business Media.

32. Introduction
Preliminaries on
Disturbance Observers
Disturbance Observer
(DOB) applied to a
servo drive
Equivalence between
PD+DOB and
weighted PID
controllers
The weighted PID controller
under the DOB tuning.
Experiments
Experimental setup
Comparative study using
the weighted PID and
PD+DOB controllers
Experimental results with
the weighted PID controller
Conclusions
References
28
Thanks!