State Feedback Control Solutions for a Mechatronics System with

Variable Moment of Inertia

Alexandra-Iulia Szedlak-Stinean

1

, Radu-Emil Precup

1

, Stefan Preitl

1

, Emil M. Petriu

2

and Claudia-Adina Bojan-Dragos

1

1

Department of Automation and Applied Informatics, Politehnica University of Timisoara,

Bd. V. Parvan 2, 300223, Timisoara, Romania

2

School of Electrical Engineering and Computer Science, University of Ottawa,

800 King Edward, K1N 6N5, Ottawa, ON, Canada

Keywords: Experimental Results, Flexible Drive Dynamics, Mechatronics Application, PID Controllers, Position

Control, Rigid Body Dynamics, Variable Moment of Inertia.

Abstract: This paper presents details regarding the design of two state feedback control (SFC) solutions for the

position control of a mechatronics application represented by the Model 220 Industrial Plant Emulator.

Since SFC is not effective in terms of zero steady-state control error, the SFC structure of both solutions is

inserted in a control loop that contains a PID controller with or without low-pass filter. This leads to the two

SFC solutions proposed in this paper and dedicated to mechatronics applications with variable moment of

inertia. The PID controllers are tuned by the Modulus Optimum method to ensure high control system

performance expressed as increased phase margins and improved tracking performance. The performance of

the proposed SFC solutions is illustrated by case studies that deal with experimentally identified parameters

in two situations, rigid body dynamics and flexible drive dynamics. Simulation and experimental results

obtained for the three significant values of the moment of inertia of the load disk are given.

1 INTRODUCTION

Mechatronics systems are successfully used in many

industrial and non-industrial applications because of

their initial simple and robust structure. The design

steps of control structures for mechatronics

applications are (Isermann, 2005; Bishop, 2007): 1.

accept a simplified system representation, 2. set the

control system performance, 3. design the

measurement instrumentation including state

estimation. 4. generate dynamic behaviours in special

situations, 5. develop convenient control algorithms,

and 6. perform the fault diagnosis.

The mechatronics application considered in this

paper is the Model 220 Industrial Plant Emulator

(M220IPE) laboratory equipment, which is a

complex and nonlinear device that illustrates and

models industrial processes with variable inertia

(ECP, 2010; Stinean et al., 2013a, 2013b). The main

advantages of M220IPE are the possibility to adjust

the dynamic parameters and the ability to introduce

and remove non-ideal proprieties in a controlled

manner. M220IPE is also advantageous from the

experimental testing point of view: it does not allow

a continuous variation (during operation) of the

moment of inertia, which in turn determines the

validation at important operating points, and a

reduced flexibility to modifications of the control

algorithms.

Some well acknowledged control solutions for

M22OIPE will be briefly analyzed as follows. The

disturbances are estimated in (Gao et al., 2001) using

an extended state observer and compensated at each

sampling period. Three state observer design

techniques including high-gain observers, sliding

mode observers and extended state observers are

discussed in (Wang and Gao, 2003). The design of a

static anti-windup compensator is suggested in

(Takamatsu et al., 2010) on the basis of the circle

criterion that leads to numerically solved linear

matrix inequalities. A data-driven design method of

a PID controller and a robust feedback control

designed for mechanisms with backlash are given in

(Saeki and Kishil, 2011). Fuzzy and neuro-fuzzy

control solutions are investigated in (Stinean et al.,

2013a, 2013b, 2015).

This paper gives details on the design and

implementation of two state feedback control (SFC)

458

Szedlak-Stinean, A-I., Precup, R-E., Preitl, S., Petriu, E. and Bojan-Dragos, C-A.

State Feedback Control Solutions for a Mechatronics System with Variable Moment of Inertia.

DOI: 10.5220/0005988904580465

In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2016) - Volume 2, pages 458-465

ISBN: 978-989-758-198-4

Copyright

c

2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

solutions for M220IPE. These solutions include a

PID controller with a low-pass filter in case of rigid

body dynamics and a PID without filter in case of

flexible drive dynamics.

This paper offers four new contributions: 1. the

mathematical modelling of the servo system

M220IPE and the interpretation of these models as

benchmark type mathematical models (MMs), 2. the

design of two SFC solutions, 3. the experimental and

simulated validation of the SFC structures with PID

controllers in nine case studies dedicated to the

position control of M220IPE with rigid body

dynamics and three case studies with flexible drive

dynamics, and 4. the comparative analysis of all

control structures.

This paper is structured as follows: an overview

on the numerical values of the system parameters is

given in the next section. The MMs in case of rigid

body dynamics and flexible drive dynamics are also

defined. The design and implementation of the SFC

solutions are discussed in Section 3. The simulation

and experimental results are presented in Section 4.

A comparison of the control systems performance is

included. The conclusions are offered in Section 5.

2 MODEL 220 INDUSTRIAL

PLANT EMULATOR

2.1 Numerical Values of System

Parameters

Since the laboratory setup built around M220IPE

can only provide discontinuous changes of the

moment of inertia, three case studies described

briefly in (Stinean et al., 2015) have been

implemented, tested by simulation and experiments

and analyzed. The proposed control solutions will be

designed for three significant values of the moment

of inertia of the load disk, J

load

: the initial value

J

load,init

=0.0065kgm

2

(without weights on the load

disk), the average value J

load,avg

=0.01474kgm

2

(four

brass weights of 0.2 kg each), and the maximum

value J

load,max

=0.0271kgm

2

(four brass weights of 0.5

kg each). Based on past experience (Stinean et al.,

2013a, 2013b, 2015) nine combinations between

process parameters and controller parameters are

possible. The following notations were used to

analyze and develop the proposed control solutions:

,12/,/6

, ,

,

'

____

___

pdplpd

backlashploadpdrivepploadw

loaddloaddrivewdriveddrive

ngrnngr

JJJJJ

JJJJJ

(1)

where: J

drive

– the inertia of the drive disk, J

d_drive

–

the inertia of the bare drive disk, drive motor,

encoder, drive disk/motor belt and pulleys, J

w_drive

–

the inertia associated with the brass weights at the

drive disk, J

load

– the inertia of the load disk, J

d_load

– the inertia of the bare load disk, disturbance motor,

encoder, load disk/motor belt and pulleys, J

w_load

–

the inertia associated with the brass weights at the

load disk, J

p

– the pulley inertia, J

p_drive

, J

p_load

– the

inertia associated with the pulleys in the masses

assembly, J

p_backlash

– the inertia of the backlash

mechanism, gr – the drive train gear ratio, gr

’

– the

partial gear ratio between the idler pulley assembly

and the drive disk, n

pd

– the number of teeth on

bottom pulley, n

pl

– the number of teeth on top

pulley, c

1

,c

2

– the drive and load friction (modelled

as viscous), c

12

– the coupled friction, and k – the

rotary (torsional) spring constant. The parameters of

the servo system M220IPE used in the SFC design

are (ECP, 2010; Stinean et al., 2013a)

Nm/rad. 45.8 ,Nm/rad/ 017.0

Nm/rad/s, 05.0 Nm/rad/s, 004.0

36),=n(n kgm 000039.0J J

24),=n(n kgm 000008.0J J

,m) 0.1rat kg 0.5 (4 kgm 0206.0

,m) 0.1rat kg 0.2 (4 kgm 00824.0

,m) 0.05rat kg 0.5 (4

kgm 00561.0

,m) 0.05rat kg 0.2 (4 kgm 0021.0

,kgm 000031.0

,kgm 0065.0 ,kgm 00040.0

2

plpd

2

__

plpd

2

__

wl

2

_

wl

2

_

wd

2

_

wd

2

_

2

_

2

_

2

_

ksc

cc

J

J

J

J

J

JJ

12

1

loadpdrivep

loadpdrivep

loadw

loadw

drivew

drivew

backlashp

loadddrived

(2)

2.2 Mathematical Models of M220IPE

This sub-section presents the dynamic equations

used in the process MM in two situations, rigid body

dynamics and flexible drive dynamics.

2.2.1 Rigid Body Dynamics

The MM of M220IPE with rigid body dynamics

(ECP, 2010; Stinean et al., 2013a) is obtained from

the balance equation in matrix form

.

,

0

0

,

0

0

,,

*

*

*

*

2

1

D

D

load

drive

load

drive

Tgr

T

c

c

J

J

Tc

JθTθcθJ

(3)

with θ

1

=grθ

2

or θ

1

=gr

’

θ

p

, where:

θ

1

– the drive disk

position, θ

2

– the load disk position, θ

p

– the idler

State Feedback Control Solutions for a Mechatronics System with Variable Moment of Inertia

459

pulleys position, J

drive

*

– the total inertia reflected to

the drive disk, J

load

*

– the total inertia reflected to the

load disk, c

drive

*

, c

load

*

– the total reflected friction

constants, and T

D

– drive torque, and the expressions

of the parameters in (3)

. ,)(

,)/(

,)()(

2

2

1

*2

21

*

2'2*

22'*

cgrccgrccc

JgrgrJgrJJ

grJgrJJJ

loaddrive

loadpdriveload

loadpdrivedrive

(4)

The state-space MM of M220IPE with rigid body

dynamics with θ

1

as the process output is

,,

1

1

x

xC

TBxAx

y

(5)

with the matrix expressions

].0 1[,

/1

0

,

/0

10

***

CBA

drivedrivedrive

JJc

(6)

Applying the Laplace transform to (3) and accepting

zero initial conditions, the process transfer function

(t.f.) is

)]./(/[)/1()(/)(

***

1 drivedrivedriveD

JcssJsTs

(7)

2.2.2 Flexible Drive Dynamics

The balance equation in matrix form enables the

derivation of the MM of M220IPE with flexible

drive dynamics (ECP, 2010; Zheng et al., 2012):

.

1

,

0

,

,

0

0

, ,

1

1

2

122

1

12

1

12

2

121

*

2

1

gr

gr

gr

k

T

ccgrc

grcgrcc

J

J

D

load

drive

K

Tc

JθTKθθcθJ

(8)

Considering θ

1

as the process output, the state-space

MM of M220IPE with flexible drive dynamics is

given in (5), with the matrices

],0 0 0 1[ ,][

,][ ,] [

4...11

4...1,2211

CB

Ax

ii

jiij

T

b

a

(9)

with the matrix elements

.0 ,0 ,/1 ,0 ,/)

( ,/ ,/

,/ 1, 0, 0,

,0,/ ,/

,/)( ,/

0, 0, 1, ,0

4131

*

211112

24443

1

1242

1

41343332

31

*1

1224

*1

23

*2

12122

*2

21

14131211

bbJbbJc

caJkaJgrca

Jkgraaaa

aJgrcaJkgra

JgrccaJkgra

aaaa

driveload

loadload

load

drivedrive

drivedrive

(10)

Applying the Laplace transform to (8) and accepting

zero initial conditions, the process t.f. is

.0

,)/( ,)/(

)/( )],/(

[)( ,

,)(

),(/])([)(/)(

0

2

211

2

212121

21

2*

2

2

12

1122

*

3

*

4

01

2

2

3

3

4

4

122

2

1

n

grkckcngrcccc

ccgrkJkJngrc

cJccJnJJn

nsnsnsnsnsD

sDksccsJsTs

loaddrive

loaddriveloaddrive

loadD

(11)

The t.f.s given in (7) and (11) and the matrix

coefficients for three significant values of the

moment of inertia of the load disk are given in

Tables 1 and 2.

3 STATE FEEDBACK CONTROL

SOLUTIONS

3.1 Classical SFC Solutions

The SFC structure is illustrated as the internal

control loop in Figure 1. It is next extended and

included in a control loop with a PID controller in

order to ensure a zero steady-state control error as

discussed in sub-section 3.2. The state feedback gain

matrix k

c

T

in both situations is of proportional type.

The state feedback controller includes an

additional amplifier with the gain set to k

AS

=1.

Figure 1 leads to

. ,

xASxxx

ekuywe

(12)

The pole placement method is applied to compute

k

c

T

using three sets of poles imposed, each for the

three significant values of the moment of inertia of

the load disk, i.e., J

load,init

, J

load,avg

, J

load,max

. The

notation y

x

= k

c

T

x is used in Figure 1. This leads to

the state-space MM of the SFC structure

, ,

AS

AS

x

k

y

wk

T

cx

x

kBAA

xC

BxAx

(13)

where A

x

is the matrix of the inner SFC loop. The

state feedback gain matrix of M220IPE with rigid

body dynamics is according to Table 3, columns 4

and 5 and the state feedback gain matrix of

M220IPE with flexible drive dynamics is according

to Table 3, columns 10, 11, 12 and 13. The closed-

loop system poles (i.e., the inner SFC loop) are

given Table 3, columns 2 and 3 for rigid body

dynamics and in columns 6, 7, 8 and 9 for flexible

drive dynamics. The t.f. of the inner SFC loop is

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

460

,

)1)(1)(1)(1(

)21(

)1)(1(

)()(

4321

22

21

1

sTsTsTsT

sTsTk

or

sTsT

k

ssH

bbbSFC

SFC

xSFC

BAIC

(14)

where I is the second-order (or fourth-order) identity

matrix, k

SFC

is the inner SFC loop gain, T

1

(or T

1

, T

2

)

is (are) the large time constant, and T

2

(or T

3

, T

4

) is

(are) the small time constant (s).

3.2 Design and Implementation of PID

Controllers

The first SFC solution uses a PID controller with a

low-pass filter with the generic t.f. and parameters

,9.0,,

),2/(1),1/(

)1)(1)(/()(

22211

2

21

cfcc

SFCcf

cccc

TTTTTT

TkksT

sTsTsksH

(15)

where k

c

is the controller gain, T

c1

and T

c2

are the

controller time constants, and T

f

is the filter time

constant. The control algorithm is designed and tuned

in terms of Kessler’s Modulus Optimum method

(MO-m) referred in (Åström and Hägglund, 1995).

Using the backwards difference method, the

continuous-time PID controller with the continuous-

time t.f. H

c

(s) is discretized resulting in the discrete-

time t.f. H

c

(z

-1

)

,),2(,

)],()([

,),)((

,)(

210

12211

212210

2

2

1

10

2

2

1

10

1

fsfsf

sccsccc

cccscscc

c

TpTTpTTp

TTTTTTkq

TTkqTTTTkq

zpzpp

zqzqq

zH

(16)

where T

s

=0.004s is the sampling period. The

numerical values related to SFC structure and the

PID controllers for three significant operating points

are given in Table 4.

Table 1: State-space MM matrices and transfer functions expressions of M220IPE with rigid body dynamics.

Moment of inertia Matrices A, B and C Process transfer function θ

1

(s)/T

D

(s)

J

load,init

01,

7036

0

,

8.630

10

CBA

)63.8(

7036

ss

J

load,avg

01,

4362

0

,

5.350

10

CBA

)35.5(

4362

ss

J

load,max

01,

2741

0

,

37.30

10

CBA

)37.3(

2741

ss

Table 2: State-space MM matrices and transfer functions expressions for M220IPE with flexible drive dynamics.

Moment of

inertia

Matrices A, B and C Process transfer function θ

1

(s)/T

D

(s)

J

load,init

]0001[,

0

0

13850

0

,

307.10

1

13.10

0

1300

0

5036

0

654.0

0

068.12

1

325

0

1259

0

CBA

)220782.267737.22(

)1300307.10(13850

23

2

ssss

ss

J

load,avg

]0001[,

0

0

13850

0

,

59.4

1

13.10

0

579

0

5036

0

3.0

0

068.12

1

145

0

1259

0

CBA

)4.98277.189365.16(

)57959.4(13850

23

2

ssss

ss

J

load,max

]0001[,

0

0

13850

0

,

47.2

1

13.10

0

312

0

5036

0

157.0

0

068.12

1

9.77

0

1259

0

CBA

)4.52904.159953.14(

)31247.2(13850

23

2

ssss

ss

State Feedback Control Solutions for a Mechatronics System with Variable Moment of Inertia

461

Figure 1: Control structure of M220IPE with rigid body dynamics and flexible drive dynamics.

Table 3: Selected poles and state feedback gain matrix numerical values.

Moment

of inertia

Rigid body dynamics Flexible drive dynamics

Selected poles

State feedback gain

matrix

Selected poles State feedback gain matrix

1

2 3 4 5 6 7 8 9 10 11 12 13

p

1

*

p

2

*

k

c1

k

c2

p

1

*

p

2

*

p

3

*

p

4

*

k

c1

k

c2

k

c3

k

c4

J

load,init

-20 -11

0.0313 0.0032 -20 -11 -105 -110 0.9735 0.0161 -3.3304 -0.0036

J

load,avg

-20 -7

0.0321 0.0050 -20 -7 -50 -55 0.2385 0.0083 -0.7600 0.0002

J

load,max

-20 -5

0.0365 0.0079 -20 -5 -30 -35 0.0712 0.0054 -0.1873 0.0018

Table 4: SFC structure t.f.s and numerical values of PID controllers’ parameters for rigid body dynamics.

Moment of

inertia

SFC structure t.f. H

SFC

(s)

Parameters of PID controllers

q

0

q

1

q

2

p

0

p

1

p

2

J

load,init

)05.01)(0909.01(

9818.31

ss

0.0016 -0.0030 0.0014 0.0490 -0.0940 0.0450

J

load,avg

)05.01)(1429.01(

1571.31

ss

0.0025 -0.0048 0.0023 0.0490 -0.0940 0.0450

J

load,max

)05.01)(2.01(

41.27

ss

0.0040 -0.0077 0.0036 0.0490 -0.0940 0.0450

Since the M220IPE with flexible drive dynamics

is a fourth-order system, the second SFC solution

uses a PID controller to compensate two large time

constants. The generic continuous-time t.f. of the

PID controller is given in (15). The requirement to

ensure zero steady-state control error is fulfilled by

the I component of the PID controller. The MO-m is

also applied to tune the three PID controllers with

fixed parameter values. Setting the value of the

sampling period to T

s

=0.004s, the continuous-time

PID controller is discretized using the backwards

difference method and the discrete-time parameters

q

0

, q

1

and q

2

are according to relation (16), the only

differences are in p

0

and p

1

(p

0

=T

s

and p

1

=-T

s

)

parameters. The numerical values of the parameters

of the PID controllers used in simulations and

experiments are presented in Table 5.

4 SIMULATION AND

EXPERIMENTAL RESULTS

The two SFC solutions described in Section 3 have

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

462

Table 5: SFC structure t.f.s and numerical values of PID controllers’ parameters for flexible drive dynamics.

Moment of

inertia

SFC structure t.f. H

SFC

(s)

Parameters of PID controllers

q

0

q

1

q

2

p

0

p

1

J

load,init

)0091.01)(0095.01)(05.01)(0909.01(

)00077.00079.01(0838.7

2

ssss

ss

0.0038 -0.0072 0.0034 0.0040 -0.0040

J

load,avg

)0182.01)(02.01)(05.01)(1429.01(

)0017.00079.01(8286.20

2

ssss

ss

0.0040 -0.0075 0.0036 0.0040 -0.0040

J

load,max

)0286.01)(0333.01)(05.01)(2.01(

)0032.00079.01(0952.41

2

ssss

ss

0.0028 -0.0053 0.0025 0.0040 -0.0040

Table 6: Performance indices achieved by the control systems with PID controllers.

Case study 1.1 Case study 1.2 Case study 1.3

σ

1

t

1

t

s

σ

1

t

1

t

s

σ

1

t

1

t

s

5.05% 0.2209 0.4928 18.75% 0.266 0.7717 20.625% 0.3281 0.8898

Case study 2.1 Case study 2.2 Case study 2.3

σ

1

t

1

t

s

σ

1

t

1

t

s

σ

1

t

1

t

s

1% 0.1867 1.3021 12.5% 0.2306 0.6901 15% 0.2806 0.7202

Case study 3.1 Case study 3.2 Case study 3.3

σ

1

t

1

t

s

σ

1

t

1

t

s

σ

1

t

1

t

s

17.1% 0.1236 1.4997 16.99% 0.1707 1.2411 13% 0.2428 0.7625

Figure 2: Simulation (a) and experimental (b) results regarding the behaviour of SFC structures with PID controllers

designed for M220IPE with rigid body dynamics: case studies 1.1-1.3, 2.1-2.3 and 3.1-3.3.

State Feedback Control Solutions for a Mechatronics System with Variable Moment of Inertia

463

Figure 3: Simulation (q) and experimental (b) results regarding the behaviour of SFC structures with PID controllers

developed for M220IPE with flexible drive dynamics: case study 1.1, 2.2 and 3.3.

been implemented and tested on M220IPE laboratory

as position control systems. The results obtained on

the M220IPE laboratory equipment with rigid body

dynamics are presented in Figure 2. Three SFC

structures – each for every moment of inertia of the

load disk – have been tested on the nonlinear system

and validated by simulation and real-time

experiments. Analyzing the comparative results

illustrated in Figure 2 and the performance

synthesized in Table 6 for the experimental results, it

can be concluded that the best reference tracking and

control system performance has been obtained in the

case studies 1.1, 2.2 and 3.3.

The three most favourable case studies were

tested for M220IPE with flexible drive dynamics, and

the results are presented in Figure 3. Both simulation

and experimental results show similar performance

indices in terms of the settling time values, the first

settling time values and the overshoot values as

follows: case study 1.1: σ

1

≈0%, t

1

≈0.934s, t

s

≈1s;

case study 2.2: σ

1

≈11.25%, t

1

≈0.252s, t

s

≈1.2308s;

case study 3.3: σ

1

≈15.5%, t

1

≈0.267s, t

s

≈1.3916s. The

analysis of the set of results presented for the two

SFC solutions points out that all tested control

solutions provide relatively good reference tracking.

The comparative results given in Figures 2 and 3

prove that the PID controllers contribute in average

to both good dynamic performance and robustness

with respect to at least one process parameter.

5 CONCLUSIONS

This paper has given design and implementation

details on two SFC solutions for a mechatronics

application with rigid body dynamics and flexible

drive dynamics for three significant values of the

moment of inertia on the load disk. The simulation

and real-time experimental results show that our

SFC structures exhibit good control system

performance indices that should be improved in

critical applications. The main advantages of the

new results given in this paper are the simplicity of

the SFC structure with a reduced number of

parameters and the transparency of the design

approach.

Our SFC solutions can be viewed as a support

for other control solutions including fuzzy, neural,

sliding mode and adaptive control (Blažič et al.,

2010; Precup et al., 2009, 2012; Ruano et al., 2002).

The performance can be improved by inserting

sensitivity, robustness objectives and constraints

(Casavola et al., 2014; Gutiérrez-Carvajal et al.,

2016). The pole placement method applied in this

paper can be replaced by the optimal design and

tuning by means of classical or modern optimization

algorithms (Bandarabadi et al., 2015; Johanyák,

2015; Menchaca-Mendez and Coello Coello, 2016).

This has not been investigated, but it represents a

subject of future research. Future research will also

be focused on applications to other illustrative

nonlinear processes.

ACKNOWLEDGEMENTS

This work was supported by grants from the

Partnerships in priority areas – PN II program of the

ICINCO 2016 - 13th International Conference on Informatics in Control, Automation and Robotics

464

Romanian Ministry of National Education and

Scientific Research – the Executive Agency for

Higher Education, Research, Development and

Innovation Funding (UEFISCDI), project numbers

PN-II-PT-PCCA-2013-4-0544 and PN-II-PT-PCCA-

2013-4-0070, the Partnerships in priority areas – PN

II program of the Romanian National Authority for

Scientific Research ANCS, CNDI – UEFISCDI,

project number PN-II-PT-PCCA-2011-3.2-0732, the

Romanian National Authority for Scientific

Research, CNCS – UEFISCDI, project numbers PN-

II-ID-PCE-2011-3-0109 and PN-II-RU-TE-2014-4-

0207, and from the NSERC of Canada.

REFERENCES

Åström, K. J., Hägglund, T., 1995. PID Controllers

Theory: Design and Tuning. Research Triangle Park,

NC: Instrument Society of America.

Bandarabadi, M., Rasekhi, J., Teixeira, C. A., Netoff, T. I.,

Parhi, K. K., Dourado, A., 2015. Early seizure detection

using neuronal potential similarity: a generalized low-

complexity and robust measure. International Journal

of Neural Systems. 25, 1-18.

Bishop, R. H., 2007. The Mechatronics Handbook. Boca

Raton, FL: CRC Press, 2

nd

edition.

Blažič, S., Matko, D., Škrjanc, I., 2010. Adaptive law with a

new leakage term. IET Control Theory & Applications.

4, 1533-1542.

Casavola, A., Garone, E., Tedesco, F., 2014. Improved feed-

forward command governor strategies for constrained

discrete-time linear systems. IEEE Transactions on

Automatic Control. 59, 216-223.

ECP (2010). Industrial Emulator/Servo Trainer Model

220 System, Testbed for Practical Control Training.

Bell Canyon, CA: Educational Control Products.

Gao, Z., Hu, S., Jiang, F., 2001. A novel motion control

design approach based on active disturbance rejection.

In Proceedings of 40

th

IEEE Conference on Decision

and Control. Orlando, FL, USA, 5, 4877-4882.

Gutiérrez-Carvajal, R. E., de Melo, L. F., Rosário, J. M.,

Tenreiro Machado, J. A., 2016. Condition-based

diagnosis of mechatronic systems using a fractional

calculus approach. International Journal of Systems

Science. 47, 2169-2177.

Isermann, R., 2005. Mechatronic Systems: Fundamentals.

Berlin, Heidelberg, New York: Springer-Verlag.

Johanyák, Z. C., 2015. A simple fuzzy logic based power

control for a series hybrid electric vehicle. In

Proceedings of 9

th

IEEE European Modelling

Symposium on Mathematical Modelling and Computer

Simulation. Madrid, Spain, 207-212.

Menchaca-Mendez, A., Coello Coello, C. A., 2016.

Selection mechanisms based on the maximin fitness

function to solve multi-objective optimization problems.

Information Sciences. 332, 131-152.

Precup, R.-E., Dragos, C.-A., Preitl, S., Radac, M.-B.,

Petriu, E. M., 2012. Novel tensor product models for

automatic transmission system control. IEEE Systems

Journal. 6, 488–498.

Precup, R.-E., Tomescu, M. L., Preitl, S., 2009. Fuzzy logic

control system stability analysis based on Lyapunov’s

direct method. International Journal of Computers,

Communication & Control. 4, 415–426.

Ruano, A. E. B., Cabrita, C., Oliveira, J. V., Kóczy, L. T.,

2002. Supervised training algorithms for B-Spline

neural networks and neuro-fuzzy systems.

International Journal of Systems Science. 33, 689-711.

Saeki, M., Kishi, R., 2011. A data-driven PID control

design by linear programming for stable plants. In

Proceedings of 18

th

IFAC World Congress. Milano,

Italy, 7420-7425.

Stinean, A.-I., Bojan-Dragos, C.-A., Precup, R.-E., Preitl,

S., Petriu, E. M., 2015. Takagi-Sugeno PD+I fuzzy

control of processes with variable moment of inertia.

In Proceedings of 2015 International Symposium on

Innovations in Intelligent Systems and Applications.

Madrid, Spain, 1-8.

Stinean, A.-I., Preitl, S., Precup, R.-E., Dragos, C.-A.,

Radac, M.-B., Petriu, E. M., 2013a. Modeling and

control of an electric drive system with continuously

variable reference, moment of inertia and load

disturbance. In Proceedings of 9

th

Asian Control

Conference. Istanbul, Turkey, 1-6.

Stinean, A.-I., Preitl, S., Precup, R.-E., Dragos, C.-A.,

Radac, M.-B., Petriu, E. M., 2013b. Low-cost neuro-

fuzzy control solution for servo systems with variable

parameters. In Proceedings of 2013 IEEE

International Conference on Computational

Intelligence and Virtual Environments for

Measurement Systems and Applications. Milano, Italy,

156-161.

Takamatsu, S., Wasiwitono, U., Saeki, M., Wada, N.,

2010. Anti-windup compensator design considering

behavior of controller state. In Proceedings of 2010

IEEE International Conference on Control

Applications. Yokohoma, Japan, 1963-1968.

Wang, W., Gao, Z., 2003. A comparison study of

advanced state observer design techniques. In

Proceedings of 2003 American Control Conference.

Denver, CO, USA, 6, 4754-4759.

Zheng, Q., Gao, L. Q., Gao, Z., 2012. On validation of

extended state observer through analysis and

experimentation. Journal of Dynamic Systems,

Measurement, and Control. 134, 024505.1–024505.6.

State Feedback Control Solutions for a Mechatronics System with Variable Moment of Inertia

465