10417
FACTA UNIVERSITATIS
Series: Mechanical Engineering Vol. 20, No 1, 2022, pp. 21 - 36
https://doi.org/10.22190/FUME220111005P
© 2022 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND
Original scientific paper
A LOW-COST APPROACH TO DATA-DRIVEN FUZZY
CONTROL OF SERVO SYSTEMS
Radu-Emil Precup1, Stefan Preitl1, Claudia-Adina Bojan-Dragos1,
Elena-Lorena Hedrea1, Raul-Cristian Roman1, Emil M. Petriu2
1Politehnica University of Timisoara, Dept. Automation and Applied Informatics, Romania
2University of Ottawa, School of Electrical Engineering and Computer Science, Canada
Abstract. Servo systems become more and more important in control systems
applications in various fields as both separate control systems and actuators. Ensuring
very good control system performance using few information on the servo system model
(viewed as a controlled process) is a challenging task. Starting with authors’ results on
data-driven model-free control, fuzzy control and the indirect model-free tuning of fuzzy
controllers, this paper suggests a low-cost approach to the data-driven fuzzy control of
servo systems. The data-driven fuzzy control approach consists of six steps: (i) open-
loop data-driven system identification to produce the process model from input-output
data expressed as the system step response, (ii) Proportional-Integral (PI) controller
tuning using the Extended Symmetrical Optimum (ESO) method, (iii) PI controller
parameters mapping onto parameters of Takagi-Sugeno PI-fuzzy controller in terms of
the modal equivalence principle, (iv) closed-loop data-driven system identification, (v)
PI controller tuning using the ESO method, (vi) PI controller parameters mapping onto
parameters of Takagi-Sugeno PI-fuzzy controller. The steps (iv), (v) and (vi) are
optional. The approach is applied to the position control of a nonlinear servo system.
The experimental results obtained on laboratory equipment validate the approach.
Key words: Closed-loop data-driven system identification, Data-driven fuzzy control,
Extended Symmetrical Optimum method, Servo systems
1. INTRODUCTION
As specified in the project [1], in contrast to model-based control, data-driven control
avoids the system (process) identification by constructing controllers directly from data.
That is the reason why data-driven control is also referred to as model-free control (i.e. no
Received: January 11, 2022 / Accepted February 13, 2022
Corresponding author: Radu-Emil Precup
Politehnica University of Timisoara, Department of Automation and Applied Informatics, Bd. V. Parvan 2,
300223 Timisoara, Romania
E-mail: radu.precup@aut.upt.ro
22 R.-E. PRECUP, S. PREITL, C.-A. BOJAN-DRAGOS, ET AL.
model in controller tuning), justifying the high interest in nonlinear controllers whose
parameters are tuned using process input-output data after conducting few experiments,
or, more generally, data-driven model-free control [2]. Instead, one or more experiments
are conducted in order to use the information in controller tuning, and non-parametric
system or process models) can be employed in this regard.
A concise discussion on the popular data-driven control techniques is given in Precup
et al. [3] pointing out the following ones that ensure the iterative experiment-based
update of controller parameters: Iterative Feedback Tuning (IFT) [4], [5], Model-free
Adaptive Control (MFAC) [6], [7], Simultaneous Perturbation Stochastic Approximation
[8], [9], Correlation-based Tuning [10], [11], Frequency Domain Tuning [12], [13],
Iterative Regression Tuning [14], and adaptive online IFT [15]. A review on data-driven
control [16] offers classifications and highlights the role of observers and estimation in
control, also leading to non-iterative data-driven control techniques: Model-Free Control
(MFC) [17], [18], Virtual Reference Feedback Tuning (VRFT) [19], [20], Active
Disturbance Rejection Control (ADRC) [21], [22], data-driven predictive control [23],
[24], unfalsified control [25], [26], Data-Driven Inversion Based Control [27], [28], and
the investigation of equivalent conditions on the given data under which different
analysis and control problems can be solved [29]. Other representative techniques are
emphasized in book [2]. It is suggestively stated in [3] and [30] that MFC is an efficient
tool for Machine Learning; moreover, as specified earlier in [25], unfalsified control is
also an efficient tool for Machine Learning.
As pointed out in the studies conducted in [1] and [31], fuzzy control is an important
subject in the area of nonlinear control as the fuzzy controllers are relatively easily
understandable and also offer very good control system performance indices. However,
the heuristic approach to design and tune fuzzy controllers is compensated by the
systematic design of fuzzy controllers that can employ the stable design of fuzzy control
systems, the optimal and robust controller design and tuning. Classical and recent
applications of fuzzy control deal with Popov-type stability analysis [32], embedded
fuzzy control system for machining processes [33], tire slip control [34], predictive
functional control based on fuzzy models [35], stability and sensitivity analysis of fuzzy
control systems [36], stability analysis dedicated to the fuzzy control of nonlinear
processes [37], robust evolving cloud-based control [38], power control of series hybrid
electric vehicles [39], vehicle navigation by fuzzy cognitive maps [40], fuzzy control for
the iron ore sintering process [41], type-2 fuzzy control for line following [42], and
Singularity-free fixed-time fuzzy control for robotic systems [43].
The model-free tuning of fuzzy controllers is an alternative approach to the model-
based design resulting in data-driven fuzzy control [1] to benefit from the advantages of
data-driven control and fuzzy control and to mitigate their drawbacks. The combinations
of data-driven model-free and fuzzy control include H∞ fuzzy control [44], fault tolerant
fuzzy control [45], parameterized data-driven fuzzy control [46], data-driven interpretable
fuzzy control [47], MFC merged with Proportional-Derivative (PD) Takagi-Sugeno fuzzy
control [48], [49], MFAC merged with PD Takagi-Sugeno fuzzy control [50], [51],
ADRC mixed with PD Takagi-Sugeno fuzzy control [52] and tuned by VRFT [22] as
well, fuzzy logic-based adaptive ADRC [53], data-driven arithmetic fuzzy control using
the distending function [54], and data-driven MFC developed around continuous-time
intelligent Proportional-Integral (PI) control [31]. The indirect model-free tuning of fuzzy
controllers has initially been proposed in authors’ papers [55] and [56], and continued in
A Low-Cost Approach to data-Driven Fuzzy Control of Servo Systems 23
[48] and [50] by controller structures that combine data-driven control and fuzzy control
in order to incorporate model-free features in fuzzy control system structures.
According to the studies carried out in [57]–[59], several auto-tuning approaches,
using a single relay, a sequential array of relays or decentralized relays, are available in
the literature. Relay identification can achieve fine tuning of controllers including fuzzy
controllers. Since experiments are conducted with the control system, it is justified to
consider auto-tuning as an approach to data-driven fuzzy control. Some recent approaches to
the auto-tuning of fuzzy controllers include the auto-tuning of PI-fuzzy controllers for variable
speed wind turbines [60], the PI-fuzzy logic-based tuning of controllers for hybrid wind &
photovoltaic power systems [61], the auto-tuning of Proportional-Integral-Derivative (PID)-
fuzzy controllers for pitch angle control of wind turbines [62], telescope tracking systems
[63], and indoor control for renewable air-conditioning [64].
Building upon authors’ results on the indirect model-free tuning on fuzzy controllers
[55], [56] and the auto-tuning of PI controllers [65], [66], this paper suggests a low-cost
approach to data-driven fuzzy control of servo systems focusing on servo systems that
can be modeled by second-order systems with an integral (I) component and a small time
constant. These servo systems are controlled by Takagi-Sugeno PI-fuzzy controllers. The
data-driven fuzzy control approach consists of six steps which include open-loop and
closed-loop data-driven system identification to produce the process model from input-
output data expressed as system step responses (i.e. non-parametric models), tuning the
linear PI controller using the Extended Symmetrical Optimum (ESO) method [67], [68],
and mapping the parameters of the PI controller onto the parameters of the Takagi-
Sugeno PI-fuzzy controller in terms of the modal equivalence principle [69]. The approach
is important with respect to the state-of-the-art because it is relatively simple as far as both
the theoretical support and the implementation are concerned. Nevertheless, only few of the
steps must be proceeded, depending on the interests of the control systems designers, who
do not need to possess strong knowledge on the control systems and the controlled processes.
Concluding, this work presents a low-cost approach to data-driven fuzzy control. This
approach is novel and feasible in practical applications.
The rest of the paper treats the following topics: the tuning approach is presented in
the next section. Section 3 is dedicated to the validation in the illustrative example of
position control of a nonlinear servo system using a Takagi-Sugeno PI-fuzzy controller.
Experimental results obtained on laboratory equipment [70] are included. The conclusions are
pointed out in Section 4.
2. THE TUNING APPROACH
It is assumed that the servo system as a controlled process can be modeled by the
transfer function P(s):
,
)1(
)(
sTs
k
sP P
+
= (1)
where kp is the process gain and T > 0 is the process small time constant or parasitic time
constant. The transfer function in (1) includes the actuator dynamics and the measurement
instrumentation dynamics.
24 R.-E. PRECUP, S. PREITL, C.-A. BOJAN-DRAGOS, ET AL.
The presence of the I component in the transfer function (1) increases the difficulty of
system identification, namely the computation of the two parameters such that (1) to
approximate with an acceptable accuracy the behavior of the real-world servo system.
Two data-driven identification approaches, (i) and (ii) discussed as follows, are considered
to be adequate for the process with the transfer function given in (1).
(i) The open-loop approach. A step signal input is applied to the servo system around
the operating point of interest on a time horizon of approximately
T10 .
If the step signal u(t) of magnitude u:
)()( tutu =
(2)
is applied to the input of the servo system, as shown in Fig. 1, then a system response
expressed in Fig. 1 is illustrated, where y(t) is the servo system (or process) output and
also the controlled system output, (t) is the unit step signal, and the subscript
indicates the steady-state value of a certain variable. The step signal u(t) is also the
control signal if the servo system is included in a control system structure, and u, which
is used in the controller is assumed to be known, and matches one of the operating
regimes that are important for the servo control system.
Fig. 1 Input step signal applied as control signal and servo system response. This figure is
adapted from Preitl et al. [66]
Fig. 1 highlights that it is not necessarily impose to the servo system to evolve starting
with zero initial conditions. The initial conditions are stated by means of the pair of input-
output data values (u0, y0), which define the initial operating point. Therefore, nonzero
initial conditions can be accepted, which is the usual situation in servo control systems
operation.
The expression of the system response is:
).()]1([)(
/
0
tueTTtkyty
Tt
P
−−+=
−
(3)
A Low-Cost Approach to data-Driven Fuzzy Control of Servo Systems 25
For large values of time, i.e. t >> T, the exponential component is vanishing because
0lim
/
=
−
→
Tt
t
e , so the steady-state response can be approximated by:
.)()(
0
−+ uTtkyty
P
(4)
As shown in [65] and [66], the time constant Td = T, where the asymptote to the system
response cuts the t axis in Fig. 1, plays the role of a pure time delay for which:
.368.0)(
0
+= uTkyTy
Pd
(5)
The data-driven identification approach (i) is carried out in terms of the steps (i1), (i2)
and (i2) described as follows:
Step (i1). A unit step signal defined in (2) is applied as a control signal to the servo
system viewed as a controlled output and the system response is recorded.
Step (i2). Considering two time moments t1 and t2, the corresponding output values
y(t1) and y(t2) are measured on the basis of Fig. 1. The expression of the process small
time constant is [65], [66]:
.
)()(
)()(
12
1221
tyty
tyttyt
TT
d
−
−
==
(6)
Step (i3). The expression of the process gain results after the manipulation of (5):
.
368.0
)(
0
−
=
uT
yTy
k d
P
(7)
Using (4), another (approximate) way to compute
P
k is:
.
)(
)(
1
01
−
−
uTt
yty
k
P
(8)
(ii) The closed-loop approach. A Proportional (P) controller with the transfer function C(s):
C
ksC =)( (9)
is included in a control loop that represents the control system for the servo system (Fig.
2), where kc is the controller gain.
Fig. 2 Servo system control system structure as a control loop
The variables and blocks in Fig. 2 are: r – reference input or set-point, r~ – filtered
reference input, FR – reference input filter, d – disturbance input, which can be applied to
the process input, the process output or, as shown in Fig. 2, in a certain (informational)
place in the process structure, C – controller (a P controller in the framework of the
26 R.-E. PRECUP, S. PREITL, C.-A. BOJAN-DRAGOS, ET AL.
approach (ii)), P – controlled process, i.e. the servo system, which can be modeled using
(1), yre −= ~ – control error.
Using the control system structure illustrated in Fig. 2, the transfer functions of the
blocks in (1) and (9), assuming the absence of the block Fr, the closed-loop control
system transfer function with respect to the reference input (assuming a zero disturbance
input) is expressed as:
,
2
)(
2
00
2
2
0
++
=
ss
sH
r
(10)
with the parameters
0
– natural frequency [65], [66]:
,
0
=
T
kk
PC (11)
and – damping factor [65], [66]:
.
5.0
=
Tkk
PC
(12)
For an adequately chosen value of kC the control system can be brought in the situation to
have two complex conjugated poles and the system response with respect to a step reference
input of magnitude r, which is also supposed to be known as u in relation with (2):
),()( trtr =
(13)
to exhibit the oscillatory behavior illustrated in Fig. 3.
The expression of the control system response is:
).()]arccos1sin(
1
1[)(
2
0
2
0
0
trt
e
yty
t
+−
−
−+=
−
(14)
The following notations are introduced:
2
0
2
0
1
11
,1
−
=
=−=
n
nn
T (15)
for the damped natural frequency
n
and the period of oscillations
n
T of the response.
Fig. 3 highlights, similar to the approach (i), that it is not necessarily imposed to the
control system to evolve starting with zero initial conditions. In this context, the initial
conditions are stated by means of the pair of input-output data values (r0, y0), which
define the initial operating point, and nonzero initial conditions can be accepted as well.
The considered situation is normal because this approach is applied only if the control
systems designer considers that it is of interest to apply it for possible re-tuning the
controller.
A Low-Cost Approach to data-Driven Fuzzy Control of Servo Systems 27
Fig. 3 Reference input step signal (without Fr) and control system response. This figure is
adapted from Preitl et al. [66] and it assumes that all sub-systems of the control
systems are implemented accurately
The expressions of the time moments specific to the response and illustrated in Fig. 3
are as follows [65], [66]:
},2,1{ ,
1
,
212
2
0
2
0
21
−
=
=
−
=
m
n t
T
t (16)
and the relationship between the system response (output) values in Fig. 3, which also gives
the overshoot 1, is [65], [66]:
.
1
1/1
2
==
− −−
e
y
yy
m (17)
Aiming an as accurate as possible data-driven identification, the control system must be
brought in the situation 0.25 < < 0.707 (it is recommended in [65] and [66] to set = 0.5)
by the appropriate modification of kC. This “ideal” value = 0.5 is convenient in order to
measure relatively easily the specific numerical values on both axes in Fig. 3.
The relationships (16) and (17) are equivalent to the following reversed relationships
[65], [66]:
.
121
1
,
2
,
)
ln
(1
1
2
21
2
0
21
2
1
−
=
−
=
=
+
=
tT
t
T
n
n
(18)
In the conditions of known kC, measured 1 and Tn, and computed and 0, the
expressions of the two parameters in (1) are [65], [66]:
28 R.-E. PRECUP, S. PREITL, C.-A. BOJAN-DRAGOS, ET AL.
. ,
4
1 2
0
2
=
−
=
C
P
n
k
T
k
T
T (19)
The data-driven identification approach (ii) is carried out in terms of the steps (ii1),
(ii2) and (ii2) described as follows:
Step (ii1). A unit step signal defined in (13) is applied as a reference input to the
control system and the system response is recorded.
Step (ii2). The controller gain kC is set such that to obtain a system response with
0.25 < < 0.707. If the system response fulfils this condition, the approach continues with
the step (ii3). Otherwise, the step (ii1) is repeated.
Step (ii3). The values of ym1, y and t21 are measured. Relationships in (18) are next
applied to obtain the values of and 0. Finally, relationships in (19) are applied to
compute the values of T and next kp.
PI controllers can cope with the process modeled in (1). The transfer function of a PI
controller is C(S):
, ),
1
1(
)1(
)(
icC
i
C
ic
Tkk
sT
k
s
sTk
sC =+=
+
= (20)
where kC > 0 or kc > 0 are two expressions of the controller gain, with their relation
specified in (20), and Ti > 0 is the integral time constant. The ESO method [67], [68] is
successfully applied to tune the PI controller parameters in (20) as it guarantees a trade-
off to the empirical control system performance specifications (expressed as maximum
values of percent overshoot, settling time and rise time) of the linear control system
making use of a single design parameter within the largest recommended domain
1 < 20. The PI tuning conditions specific to the ESO method are as follows [67], [68]:
. ,
1
,
1
2
=
=
= TT
Tk
k
Tk
k
i
P
C
P
c
(21)
The transfer function of the simplest reference input filter out of the two ones
recommended in the papers [67] and [68] is:
.
1
1
)(
sT
sFr
+
= (22)
The Takagi-Sugeno fuzzy controller is designed and tuned in terms of transferring in a
fuzzy logic-like interpretation the knowledge from the PI controller structure. The structure
and the input membership functions of a the low-cost Takagi-Sugeno fuzzy controller are
presented in Fig. 4, where q−1 indicates the backward shift operator, td indicates the discrete
time index, TISO-FC is the Two Inputs-Single Output fuzzy controller, e(td) is the
increment of control error, and u(td) is the increment of control signal.
A Low-Cost Approach to data-Driven Fuzzy Control of Servo Systems 29
A B
Fig. 4 Structure (A) and input membership functions (B) of low-cost Takagi-Sugeno
fuzzy controller. This figure is adapted from Precup et al. [71]
Discretizing the continuous-time PI controller by Tustin’s method, the recurrent
equation of the incremental discrete-time PI controller is as follows [71]:
)],( )([)(
ddPd
teteKtu += (23)
where [71]: ,
2
2
),
2
(
si
ss
icP
TT
TT
TkK
−
=−= (24)
and Ts > 0 is the sampling period.
The TISO-FC block employs the weighted average method for defuzzification, and
the SUM and PROD operators in the inference engine. The complete rule base of the
TISO-FC block is expressed as [71]:
)].( )([)( THEN
)P IS )( AND P IS )(( OR ) ZEIS )( AND
P IS )(( OR )P IS )( AND N IS )((
OR ) ZEIS )( AND N IS )(( OR ) ZEIS )(( F
)],( )([ )( THEN )P IS )( AND
P IS )(( OR )N IS )( AND N IS )(( IF
ddPd
ddd
ddd
ddd
ddPdd
ddd
teteKtu
tetete
tetete
tetete
teteKtute
tetete
+=
+=
(25)
The role of the additional parameter , with the largest domain 0 < < 1, is to reduce
the overshoot of the control system. Therefore, (25) and the fuzzy controller structure
make this low-cost fuzzy controller behaves as a bumpless interpolator between two
linear PI controllers.
The modal equivalence principle [69] applied to this Takagi-Sugeno PI-fuzzy controller
leads to the tuning equation:
,
ee
BB =
(26)
where the parameter Be should be chosen according to the experience of the control
systems designer. The parameter is chosen in a similar way. The optimal tuning can be
performed with very good results [71] to get the values of these parameters.
Summarizing all aspects presented in this section, the low-cost data-driven fuzzy
control approach consists of the six steps (dd1) to (dd6):
30 R.-E. PRECUP, S. PREITL, C.-A. BOJAN-DRAGOS, ET AL.
Step (dd1). The open-loop data-driven system identification approach (i) is applied to
produce the process model in (1) using the input-output data of the controlled process
(the servo system) expressed as the servo system step response shown in Fig. 1.
Step (dd2). The linear PI controller is tuned using the ESO method such that to meet
the performance specifications imposed to the control system.
Step (dd3). The parameters of the PI controller are mapped onto the parameters of the
Takagi-Sugeno PI-fuzzy controller using (26).
Step (dd4). This step is optional and conducted only if the control systems designer
considers that it is relevant. For example, such situations occur if the control system
performance indices are deteriorated in time. The closed-loop data-driven system
identification approach (ii) is applied to produce the process model in (1) using the input-
output data of the control system expressed as the (closed-loop) control system step
response shown in Fig. 3.
Step (dd5). This step is also optional in the context of the step (dd4). The linear PI
controller is tuned using the ESO method such that to meet again the performance
specifications imposed to the control system.
Step (dd6). This step is also optional in the context of the step (dd4) and it is identical
to the step (dd3). The parameters of the PI controller are mapped onto the parameters of
the Takagi-Sugeno PI-fuzzy controller using (26).
Since the step (dd4) is applied in terms of the real-world operation of the control
system, a special attention should be paid to the transfer from the Takagi-Sugeno PI-
fuzzy controller to the P controller and vice-versa. Bumpless transfers should be ensured
in this regard, meaning that the history of the “old” digital control algorithm requires to
be modified in order to avoid big modifications of the control system, which might affect
negatively the actuators and finally the control system behavior. A simple solution in the
linear case is presented in the references [65] and [66].
3. EXPERIMENTAL RESULTS
The tuning approach presented in the previous section is validated as follows by
applying it to the design and tuning of a Takagi-Sugeno PI-fuzzy controller to the angular
position of a nonlinear servo system laboratory equipment [70]. Some details on the steps
are given as follows. The state-space model of the servo system is expressed as [71]:
,])()([ ]01[)(
),(
0
)(
)(
10
10
)(
)(
,)( if,1
,)( if,
)(
,|)(| if,0
,)( if,
)(
,)( if,1
)(
21
2
1
2
1
T
P
b
ba
ab
a
ac
cb
cb
c
b
txtxty
tm
T
k
tx
tx
T
tx
tx
utu
utuu
uu
utu
utuu
utuu
uu
utu
utu
tm
=
+
−=
−
−
−
−−
−
+
−−
=
(27)
A Low-Cost Approach to data-Driven Fuzzy Control of Servo Systems 31
where the control signal u(t) applied to the Direct Current (DC) motor is a pulse width
modulated duty cycle, x1(t) = (t) (rad) is the angular position, x2(t) = (t) (rad/s) is the
angular speed, and the superscript T indicates matrix transposition. The variable m(t) is
the output of the saturation and dead zone static nonlinearity, modeled in the first part in
(27), with the parameters ua = 0.15, ub = 0.1 and uc = 0.15. The application of the step (dd1)
leads to the values of the servo system (i.e. process) parameters kP = 140 and T = 0.92 s.
The first steps (dd1) and (dd2) of the approach presented in the previous section are
applied. These two steps are applied simultaneously in terms of the optimal tuning [71] of the
Takagi-Sugeno PI-fuzzy controller parameters such that to ensure a reduced parametric
sensitivity with respect to one of the two parameters in (1). One set of linear PI controller and
Takagi-Sugeno PI-fuzzy controller parameter values, which ensures the strongest mitigation
of the parametric sensitivity with respect to T is recommended in [71]: β = 16.9763, kc =
0.001884, Ti = 15.618 s, Be = 20, BΔe = 0.01281, and η = 0.287. Three optimization algorithms
were applied in [71], however other ones could be of interest because of the nonlinearity of
the process and the controller as, for example, parameterized genetic algorithms [72], [73],
various algorithms adapted from their general formulation for community detection in
networks [74], metaheuristic algorithms with information feedback models [75], MOEA/D
[76], slime mould algorithms [77], grey wolf optimizers [78], and algorithms specific to
neuro-fuzzy model training [79]. The optimization problems in this context should be defined
with great care accounting for various constraints, which may be caused by man-computer
symbiosis [80], stochastic demands [81], fault detection and isolation and recovery [82], trade-
off to approximation accuracy and complexity [83], and specific structures of fuzzy systems
[84], [85], requiring appropriate handling and the modification of the optimization algorithms.
Using the above parameter values and implementing the low-cost Takagi-Sugeno
fuzzy controller according to the details given in the previous section, Fig. 5 offers a
sample of experimental results for the fuzzy control system. Fig. 5 illustrates that the
Fig. 5 Real-time experimental results expressed as fuzzy control system responses y and
u (PWM indicates Pulse Width Modulation)
32 R.-E. PRECUP, S. PREITL, C.-A. BOJAN-DRAGOS, ET AL.
fuzzy control system exhibits good control system dynamics performance with respect to
the 40 rad step modifications of the reference input. Fig. 5 also outlines the effects of the
nonlinearity in (27).
The results considered in this section help the reader to understand the effectiveness
and the efficacy of the proposed approach. More effective metrics and performance indices
could be exploited to assess the advantages of the developed controllers.
5. CONCLUSIONS
Starting with a control structure with auto-tuning Proportional-Integral controller, which
was previously developed by the authors, and two open-loop data-driven system identification
approaches, this paper gave a low-cost approach to data-driven fuzzy control of servo systems
focusing on Takagi-Sugeno Proportional-Integral-fuzzy controllers.
Using well stated tuning relations, which can ensure good control system performance
indices, which are selectable according to the needs / application, the Extended Symmetrical
Optimum method is initially used to tune the linear Proportional-Integral controllers. The
modal equivalence principle is next involved in mapping the parameters of the linear
controller onto the parameters of the fuzzy one. The paper also presented two identification
approaches (i) and (ii) of a certain category of servo systems together with the relations for the
computation of the parameters based on dynamic regime measurements, which are relatively
easily performed and implemented. The authors helped the reader to understand the novelty
issues of the developed scheme.
The approach suggested in this paper is advantageous as it can be generalized to
processes of integral type and several dynamics and delays. The approach can be
implemented automatically by the computer-aided computation of the process parameters
in the two identification approaches instead of actually representing the system responses.
The data-driven approach presented in the paper proves the potential of auto-tuning
approaches in data-driven control. The applications had in view belong to the field of
electrical driving systems with fast / slow variable parameters as function of the process
operation.
Section 2 should have addressed more details regarding the considered models and
tools; in particular, it does not consider the robustness and reliability issues, due for
example to uncertainty and disturbance effects, as well as the model-reality mismatch.
This point is fundamental when the reliability and robustness features of the proposed
solutions have to be verified and validated with respect to real engineering and safety
critical systems. Therefore, the effectiveness of the methodology proposed in Section 2 is
a suggested open problem and future issue that could require further investigations.
Another direction of open research direction is the combination of this data-driven
technique with other data-driven techniques in order to reduce the heuristics in the steps
(dd2) and (dd3). The optimal tuning of fuzzy controllers will be carried out accounting
for stability constraints but with great care to preserve the data-driven feature of the
future novel approaches. All these open problems and future issues will contribute to
make data-driven fuzzy control clear and non-questionable.
Acknowledgement: This work was supported by grants of the Romanian Ministry of Education
and Research, CNCS - UEFISCDI, project numbers PN-III-P4-ID-PCE-2020-0269, PN-III-P1-1.1-
TE-2019-1117, PN-III-P1-1.1-PD-2019-0637, within PNCDI III, by the CNFIS-FDI-2021-0582
project of the Politehnica University of Timisoara, Romania, and by the NSERC of Canada.
A Low-Cost Approach to data-Driven Fuzzy Control of Servo Systems 33
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