1. Analysis of Robustness for Industrial Motion
Control using Extended State Observer with
Experimental Validation
Kaliprasad A. Mahapatro∗, Ashitosh D. Chavan, Prasheel V. Suryawanshi, Member, IEEE
MIT Academy of Engineering, Alandi (D), Pune, Maharashtra, INDIA
∗ Email: kamahapatro@entc.mitaoe.ac.in
Abstract—This paper proposes a robust control strategy for
industrial motion control using Extended State Observer (ESO).
The proposed control enforces robustness without having the
information of uncertainties and disturbances. The ESO is used
to estimate the lumped uncertainties and guarantee robust perfor-
mance. The robustness is analyzed for different uncertainties like
backlash, friction and disturbances; induced practically on the
plant. The effectiveness of the proposed strategy is experimentally
validated on industry relevant hardware for trajectory tracking.
Keywords—Extended State Observer, Motion Control, Backlash,
Coulomb Friction and Disturbances
I. INTRODUCTION
MOTION control is a vital requirement in many appli-
cations. The same has been successfully implemented
in industrial, military and space applications [1]–[4]. The
critical requirement in motion control is robustness; which
is concerned with tracking performance in the presence of
uncertainties and disturbance. The control is expected to ensure
trajectory tracking, with fast convergence.
A two axis motion control using sliding mode control and
neural network is reported in [5], [6]. A variety of other strate-
gies like adaptive back-stepping [7], extended state observer
[8], feed-forward friction compensation [9], adaptive friction
compensation [10] have been proposed for robust motion
control. The robustness is a major concern in motion control on
account of backlash, coulomb friction, uneven distribution of
load [11]–[13]. The control law in most cases is dependent on
plant model and sensor signals. ESO is a model independent
strategy [14] that can be used for robustness. Some other
designs like sliding mode observer [15], high gain observer
[16] disturbance observer [17] are also available, which poses
some concerns for model independent design and high degree
of uncertainties.
ESO estimates the states as well as uncertainties, with
minimal information of plant. The uncertainty in plant pa-
rameters and unknown disturbances are lumped together as
an additional state [18]. ESO has been applied in various
applications like motion control [19], robotics [20], automo-
tive [21], vibration [22]. The efficacy of ESO for estimating
states and uncertainty is validated in [23]. It is proved that ESO
performs better than sliding mode observer (SMO) and high
gain observer (HGO). Additionally ESO is able to estimate
even when maximum information of plant is unknown and
exact calibration of sensor is not required [24].
A control strategy for robust motion control based on ESO
is proposed in this paper. The strategy proposed is experimen-
tally validated on an industrial motion control test-bed (ECP
220) from ECP US [25]. The design is experimentally tested
for variable backlash, friction and disturbance adjusted through
hardware. The technique gives stable, convergent response in
steady state. The main contributions of this paper as follows:
• The type of uncertainties considered is significantly
larger and is correlated to practical applications
• No information of uncertainty and disturbance is re-
quired
• The estimation error (˜e) and tracking error ( ˜et) are
within limits
• The control strategy is tested and validated for prac-
tical variations on an actual hardware
The paper is organized as follows: Section II introduces ECP-
220 motion control setup and mathematical model. Section III
describes the concept of extended state observer (ESO) and
explains the robust control law. The results on hardware along
with related discussions are illustrated in Section IV. Finally
the paper is concluded in Section V.
II. PLANT DYNAMICS
An industrial motion control test set-up is used to exper-
imentally validate the designed algorithm. The set-up: Model
220 [25] includes a DC brushless servo system with a PC based
control platform. The system consists of two motors, one as a
drive, and other as a source of disturbance, a power amplifier
and an encoder for position feedback. The inertia, friction and
backlash are all adjustable. A schematic is shown in Fig. 1.
The drive motor is coupled via a timing belt to a drive
disk with variable inertia. Another timing belt connects the
drive disk to the speed reduction (SR) assembly while a third
belt completes the drive train to the load disk. The load and
drive disks have variable inertia which may be adjusted by
moving or removing brass weights. Speed reduction is adjusted
by interchangeable belt pulleys in the SR assembly. Backlash
may be introduced through a mechanism incorporated in the
SR assembly. A disturbance motor connects to the load disk via
a 4:1 speed reduction and is used to emulate viscous friction
and disturbances at the plant output. A brake below the load
disk may be used to introduce coulomb friction.
2015 International Conference on Industrial Instrumentation and Control (ICIC)
College of Engineering Pune, India. May 28-30, 2015
978-1-4799-7165-7/15/$31.00 ©2015 IEEE 29

2. In this paper, a typical case is considered in which 4 brass
weight, each of 500 gm is added on disturbance motor and no
weight on drive motor. The gear ratio is chosen by selecting
top and bottom pulley in SR assembly. In the present case
the pulleys selected are with npl as 18 and npd as 72 (Refer
Table I for detailed description of all related parameters).
(a) Top View
(b) Front View
Fig. 1: ECP220 Actual Plant
The dynamics of industrial motion control test-bed can be
written as in [25],
Jr
¨θ + Cr
˙θ = Td (1)
where Jr is reflected inertia at drive and Cr is reflected
damping to drive. The parameter Td is the desired torque
which can be achieved suitably by selecting appropriate control
voltage (u) and hardware gain (khw).
Therefore (1) can be rewritten as,
Jr
¨θ + Cr
˙θ = khw u (2)
The plant dynamics can be modeled in state space notation as,
˙x1
˙x2
=
0 1
0 −Cr
Jr
α
x1
x2
+
0
khw
Jr
β
u (3)
y = 1 0
x1
x2
(4)
where, [x1 x2]T
are the states - position (θ) and velocity ( ˙θ),
u is the control signal in volts and y is the output position in
degrees.
The other parameters in (3) and (4) are,
Cr = C1 + C2 (gr)−2
(5)
gr = 6
npd
npl
(6)
Jr = Jd + Jp (grprime)
−2
+ Jl (gr)−2
(7)
Jd = Jdd + mwd (rwd)
2
+ Jwd0 (8)
Jp = Jpd + Jpl + Jpbl (9)
grprime =
npd
12
(10)
Jl = Jdl + mwl (rwl)
2
+ Jwl0
(11)
Jwl0
=
1
2
mwl (rwl0
)
2
(12)
The details of various plant parameters are stated in Table I.
III. EXTENDED STATE OBSERVER BASED CONTROL
ESO was originally proposed by Han [14], in which the
plant model and bound uncertainty model is combined to sup-
plement the control signal with estimate of lumped uncertainty.
The tuning of ESO is well reported in [26].
A. Overview of ESO
A general nth
order plant is mathematically represented as,
⎧
⎪⎪⎪⎨
⎪⎪⎪⎩
˙x1 = x2
˙x2 = x3
...
˙xn = xn+1 + b u
(13)
The plant in (13) is augmented with an additional state to
include lumped uncertainty and disturbance. An ESO for the
augmented plant can be represented as,
⎧
⎪⎪⎪⎨
⎪⎪⎪⎩
˙ˆz1 = ˆz2 + β1g1(e)
...
˙ˆzn = ˆzn+1 + βngn(e) + b0u
˙ˆzn+1 = βn+1gn+1(e)
(14)
The equation (14) depicts ˆz1, ˆz2 . . . ˆzn as the estimate of plant
states and ˆzn+1 as the extended state, which gives the estimate
of uncertainties in plant. This estimate of uncertainty adds
robustness in the control design. Additionally, e = y−ˆz1 is the
error and gi(.) is suitably constructed nonlinear gain functions
satisfying e × gi > 0 ∀ e = 0.
30

3. TABLE I: Notations
Symbol Meaning Value Change in Variable due to Uncertainty
( )
Cr Reflected damping to drive 4.08 × 10−3
C1 Rotary damping at the load disk 0.004
C2 Rotary damping at the drive disk 0.005
gr Drive train gear ratio 24
Jr Reflected inertia at drive 4.63 × 10−4
kg − m2
Jd Drive inertia 4 × 10−4
kg − m2
Jp Inertia associated with the idler pulley in SR-assembly 5.84 × 10−4
kg − m2
Jl Load inertia 0.027125kg − m2
grprime Drive to SR pulley gear ratio 6
Jdd Inertia of the bare drive disk plus the drive motor, encoder, 4 × 10−4
kg − m2
drive disk/ motor belt and pulleys
mwd Weight on drive inertia 0 kg
rwd Radius of weight from middle axis of drive disk 0 m
Jwd0
Inertia associated with the brass weights at the drive disk 0kg − m2
Jpd Drive pulley inertia 5.5 × 10−4
kg − m2
Jpl Load pulley inertia 0.03 × 10−4
kg − m2
Jpbl Inertia associated with backlash 0.31 × 10−4
kg − m2
npd Number of teeth on bottom pulley of SR-assembly 72
npl Number of teeth on top pulley of SR-assembly 18
Jdl Inertia of the bare load disk plus the disturbance motor, 65 × 10−4
kg − m2
encoder, load disk/ motor belt and pulleys
mwl Weight on load inertia 2 kg
rwl Radius of weight from middle axis of load disk 0.1 m
Jwl0
Inertia associated with the brass weights at the load disk 6.25 × 10−4
kg − m2
rwl0
Radius of larger brass weight 0.025 m
khw Hardware gain 5.81
If one chooses the nonlinear function gi(.) and their
related parameters properly, the estimated state variable ˆzi are
expected to converge to the respective state of the system xi,
i.e. ˆzi → xi. The choice of gi is heuristically given in [23]
gi(e, αi, δ) =
| e |αi
, | e |> δ
e
δ1−αi
, | e |≤ δ
(15)
where δ is the small number(δ > 0) used to limit the gain, β
is the observer gain determined by the pole-placement method.
α is chosen between 0 and 1 for nonlinear ESO (NESO) and
is considered unity for linear ESO (LESO). The present case
is concerned with LESO.
The LESO for any system is given by (14) with gains
g(e) = e. The state-space model, of the LESO dynamics can
be written as,
˙ˆz = Aˆz + Bu + LC(x − ˆz) (16)
where
L = β1 β2 · · · βn βn+1
T
(17)
is the observer gain vector.
B. Design of Robust Control Law
A control law for the second order plant in (3) and (4) is
designed using ESO as in (14). A schematic block diagram of
the robust control configuration is shown in Fig. 2.
Fig. 2: Feedback control with ESO
The equation (14) is reconfigured for a 2nd
order plant as,
⎧
⎪⎪⎪⎨
⎪⎪⎪⎩
˙ˆz1 = ˆz2 + β1e
˙ˆz2 = ˆz3 + β2e + b0u
˙ˆz3 = β3e
y = z1
(18)
31

4. A robust control for an industrial motion plant is designed
with integration of ESO and feedback linearization (FL). As
stated in [27], smooth vector f(x) and g(x) on n
is said
to be input state linearizable if there exist a region Ω in n
a diffeomorphism Φ = Ω → n
and a non linear feedback
control law as,
υ = α + βu (19)
where, α and β are information about the plant, u is the control
voltage Vm such that z = φ(x) and the new input υ satisfy a
linear time invariant relation.
The detail FL design and simulation verification of
ECP 220 can be found in [24]. The control law for 2nd
order
system can be stated as,
u =
1
β
[ ¨θc + k1(θc − x1) + k2( ˙θc − x2) − α] (20)
where θc is the command position and x1, x2 are plant states.
In the proposed design, the estimated states ˆz1 and ˆz2 are
used instead of actual states x1 and x2. The parameters α and
β in (20) are concerned with plant information; all of which
may not be known. As such the unknowns are estimated by
extended state ˆz3. Therefore, the control effort u takes the form
as,
u =
1
b0
[ ¨θc + k1(θc − ˆz1) + k2( ˙θc − ˆz2) − ˆz3] (21)
where b0 is the best available value of β
IV. RESULTS AND DISCUSSION
The validity of the proposed algorithm is demonstrated
in real-time on ECP-220 [25] motion control setup. The
set-up is an electromechanical plant, which consists of the
emulator mechanism, its actuator and sensors, brushless DC
servo motors for both drive and disturbance generation, high
resolution encoders. The real-time controller unit contains
the digital signal processor (DSP) based realtime controller,
servo/actuator interfaces, servo amplifiers, and auxiliary power
supplies. The DSP is capable of executing control laws at high
sampling rates allowing the implementation to be modeled as
continuous or discrete time.
In the present study, the control strategy is tested for
tracking performance with different trajectories θc as step,
ramp and parabola with different amplitude and cycles. The
different cases such as backlash, coulomb friction, multiple
disturbances are considered. The controller and observer gains
are determined using pole-placement method. The constants
used in experimentation are stated in Table-II.
TABLE II: Constant Parameters
Sampling frequency 1 KHz
b0 1254
k [13.5 4.3]
β [30 900 2500]
The uncertainty is highlighted as ( ) in Table-I.
A. Case 1: Nominal plant
The nominal plant is as described in Section II with the
parameters as in Table-I. The plant is evaluated for tracking
different trajectories. Fig. 3 shows the performance for a
representative trajectory of ramp type, with 30◦
amplitude,
velocity of 20 deg/sec. Fig. 3a shows good tracking with
control effort as shown in Fig. 3b. The uncertainty estimation
can be seen in Fig. 3c and estimation error for position in
Fig. 3d. The performance is also tested for step and parabolic
trajectories and the results are as desired.
(a) command position (-) encoder po-
sition (- -)
(b) control effort
(c) Estimation of uncertainty (d) estimation error for position
Fig. 3: Control performance for nominal plant
B. Case 2: Addition of backlash
The nominal plant is modified to include backlash, which
is introduced by loosening backlash adjustment screw (Refer
Fig. 1a). The results for a ramp trajectory of 30◦
with velocity
20 deg/sec is shown in Fig. 4. The tracking accuracy as shown
in Fig. 4a is good with minimum control effort as in Fig. 4b.
Similar results are observed for step and parabolic inputs
(a) command position (-) encoder po-
sition (- -)
(b) control effort
Fig. 4: Control performance for plant with backlash
32

5. C. Case 3: Addition of coulomb friction
The plant in case 2 is modified to include coulomb friction,
which is introduced by applying friction brake (Refer Fig. 1b).
The results for ramp trajectory tracking is shown in Fig. 5. The
tracking shown in Fig. 5a is good with minimum control effort
as in Fig. 5b.
(a) command position (-) encoder po-
sition (- -)
(b) control effort
Fig. 5: Control performance with backlash & coulomb friction
D. Case 4: Uneven load on drive motor
The drive motor is loaded with a weight of 500 gm and the
same is placed unevenly (Refer Fig. 1a). This case pertains to
a practical condition where the uncertain load may act in an
uncertain manner. The results for a ramp trajectory are shown
in Fig. 6.
(a) command position (-) encoder po-
sition (- -)
(b) control effort
Fig. 6: Control performance with uneven load on drive disk
The results for Case 2, Case 3 and Case 4 are intentionally
illustrated for ramp input to depict a comparative analysis.
The tracking performance in Fig. 4a, 5a, and 6a illustrate
robustness for varying uncertainties. The magnitude of control
effort required is within limits, but the variations for increased
complexity can be observed in Fig. 4b, 5b, and 6b.
E. Case 5: Disturbance
A sinusoidal disturbance of frequency 1Hz is introduced
on drive disk by disturbance motor (Refer Fig. 1b). The drive
disk is commanded for a ramp input of 30◦
with velocity 20
deg/sec. The results can be seen in Fig. 7. The ESO is able to
efficiently compensate this disturbance, as seen in Fig. 7a and
Fig. 7b. The system is also tested for an undefined disturbance
added at t = 5 sec and the robust performance is observed as
shown in Fig. 8.
(a) command position (-) encoder po-
sition (- -)
(b) control effort
Fig. 7: Sine Disturbance on drive disk
(a) estimation uncertainty (b) control effort
Fig. 8: Undefined Disturbance on drive disk
The tracking performance for Case 1 to Case 5 is tested
for three different trajectories- step, ramp, parabola. The cu-
mulative results for estimation error (˜e) and tracking error ( ˜et)
for all the cases is tabulated in Table-III and Table-IV.
TABLE III: RMS Values of ˜e
Case RMS value of ˜e = x1 − ˆz1
Step Ramp Parabola
1 0.784499055 0.739372596 0.732273398
2 0.725796085 0.699083097 0.612963648
3 0.778998503 0.720673513 0.711772117
4 0.465284041 0.395106480 0.516703946
5 0.65448456 0.134132503 0.070988748
TABLE IV: RMS Values of ˜et
Case RMS value of ˜et = r − x1
Step Ramp Parabola
1 2.019099267 1.412762107 1.488130996
2 1.634166452 1.051554938 1.306133183
3 1.47556471 1.130936895 1.401211971
4 1.84840051 1.299338336 1.551514183
5 0.821117525 0.850783359 0.903242758
The error for step type disturbance is marginally higher as
compared to ramp and parabolic type. This is on account of
sudden change in case of step as compared to the gradual or
smooth variations in case of ramp and parabola. The error can
be reduced further by increasing the band-width of controller.
33

6. The robustness analysis in terms of estimation error (˜e)
and tracking error ( ˜et) can be seen in Table-III and Table-IV.
The RMS values of both; estimation error (˜e) and tracking
error ( ˜et) are within acceptable bounds. The bounds can be
further lowered by redesigning β. The estimation error (˜e) and
tracking error ( ˜et) can be further lowered if some nominal
values of plant parameters are available. However the present
work is concerned with control design with no knowledge
of plant parameters. The results demonstrate the efficacy of
ESO for robust performance in varying types and degrees of
uncertainty and disturbance.
V. CONCLUSION
In this paper a ESO based robust control law is proposed
for motion control and the same is experimentally validated on
industry relevant hardware. The proposed control is enforced
by keeping the observer and controller gains constant, for
different hardware induced uncertainties like backlash, friction
and disturbances. The ESO is able to effectively compensate
the effect of uncertainties and guarantee robust performance.
It is experimentally proved that, estimation error and tracking
error are ultimately bounded. The control effort required is
minimal for tracking of different trajectories.
ACKNOWLEDGMENT
This work is supported by Board of Research in Nuclear
Science, Department of Atomic Energy, Government of India,
vide Ref. No. 2012/34/55/BRNS
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