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DE LA FACULTAD DE INGENIERÍA
REVIST
A TÉCNICAREVISTA TÉCNICA
“Buscar la verdad y aanzar
los valores transcendentales”,
misión de las universidades en
su artículo primero, inspirado
en los principios humanísticos.
Ley de Universidades 8 de
septiembre de 1970.
“Buscar la verdad y aanzar
los valores transcendentales”,
misión de las universidades en
su artículo primero, inspirado
en los principios humanísticos.
Ley de Universidades 8 de
septiembre de 1970.
VOLUME 43
SEPTEMBER - DECEMBER 2020
NUMBER 3
Rev. Téc. Ing. Univ. Zulia. Vol. 43, No. 3, 2020, September-December, pp. 114 - 176
Design and construction of an analogue control module lead-
lag type as a learning tool in control theory
Jormany Quintero-Rojas
1
* , Cecilia Bermúdez
1
, María Coronel
2
1
Departamento de Sistemas de Control, Escuela Ingeniería de Sistemas, Facultad de Ingeniería, Universidad de
Los Andes, Apartado 5101, Mérida, Venezuela.
2
Escuela de Ingeniería Eléctrica, Facultad de Ingeniería, Universidad de Los Andes, Apartado 5101, Mérida,
Venezuela.
*Autor de correspondencia: jormany@ula.ve
https://doi.org/10.22209/rt.v43n3a05
Received: 09/10/2019 | Accepted: 06/07/2020 | Available:: 01/09/2020
Abstract
Lead-lag compensators are still used for the control of various real systems, therefore, they are an indispensable
topic in the study of automatic process control. In the teaching of control theory, the need for didactic systems is evident
to offer the possibility of experimenting with analog controllers, this way the theoretical knowledge is strengthened with
practice. The object of this work is to describe the design and implementation of a control module based on lead-lag
controllers as a physical tool in teaching the theoretical principles of automatic control. The control module was built with
easy use and low cost elements in Venezuela. This module features four independent sub-modules: two controllers and two
electrical systems to be controlled, which can be connected to each other. The results obtained with the control module
slightly differ from the simulations. This designed module allows the user to develop analysis skills in control systems by
single, friendly and safe interaction when varying controller parameters.
Keywords: control systems; control teaching module; lead-lag controller; analogue control.
Diseño y construcción de un módulo de control analógico
tipo adelanto-atraso como herramienta de aprendizaje en la
teoría de control
Resumen
Los compensadores de adelanto y atraso aún son utilizados para el control de diversos sistemas reales, por lo cual
es un tema indispensable en las cátedras de control automático de procesos. En la enseñanza de la teoría de control es cada
vez más necesario contar con sistemas didácticos que ofrezcan la posibilidad de fortalecer los conocimientos teóricos con
la práctica. El presente trabajo tiene por objetivo describir el diseño e implementación de un módulo de control basado
automático. El módulo de control fue construido con elementos de fácil uso y bajo costo en Venezuela. Este presenta cuatro
sub-módulos independientes: dos controladores y dos sistemas eléctricos a controlar, que pueden conectarse entre si.
al usuario desarrollar habilidades de análisis en los sistemas de control por la interacción amigable, sencilla y segura al
momento de variar los parámetros del controlador.
Palabras clave: sistemas de control; módulo didáctico de control; controlador adelanto-atraso; control analógico.
Rev. Téc. Ing. Univ. Zulia. Vol. 43, No. 3, 2020, 150-158
Rev. Téc. Ing. Univ. Zulia. Vol. 43, No. 3, 2020, September-December, pp. 114 - 176
151
Design and construction of a lead-lag analog control module
Introduction
Control theory involves the study of a set of
strategies or laws that allow processes to be regulated
in the desired way. These laws include PID and Sliding
Mode Control [1], anti-windup compensation [2], in
addition to other classic control laws. For this purpose,
a device that allows regulating variables under these
control lawsis needed, device known as the controller. An
analog controller is a system that implements a control
law, which is made up of a set of basic electronic elements
such as resistors, capacitors, and integrated circuits. There
are different types of analog control laws, such as PID, full
state feedback, lead-lag compensators, among others [3].
Lead-lag compensators allow reference tracking,
in addition to improving the response of the controlled
system. The lag compensation manages to increase the
closed-loop gain, which allows improving the steady-
state errorwithout modifying the transient state of the
system; while the lead compensation creates a phase
lead in the system adjusting the response of the transient
lag controllers are one of the frequently used analog
controllers, designed to improve steady-state and the
transient state of the system to be controlled. Among its
uses are the control of double rotor systems to overcome
speed in three-machine systems [8], control of the
fractional-order system using Matsuda’s fourth-order
integer approximation [9], in addition to others.
Technological advances in the teaching of
control theory exhort today’s student to master theory
equipment and physical components to develop such
practices. For this reason, the practice activities are being
replaced by simulations for the study and interaction
of control systems [6,11,13-15]. Therefore, the control
engineering teaching process needs to have physical
didactic platforms that allow experimentation with
variations in the parameters of an analog controller [12,16].
Currently, there are several proposals for academic and
commercial didactic modules in the study of control
theory. Particularly some modules implement the PID
control [16-20] and academic modules with controllers
access [10,20-23]. Among the commercial options that use
lead-lag compensators, high-cost laboratory equipment
stands out, this presents a disadvantage for the acquisition
[13]. Therefore, it is desiderable to have
equipment for similar purposes, but at a low cost. For the
aforementioned, the purpose of this work is to describe
the design and implementation of a control module based
on the lead-lag compensator as a physical tool in teaching
the theoretical principles of automatic control.
Experimental
LCBox control module design
The control module design (Lead-Lag Control
the classic closed-loop system scheme. It consists of two
lag and lead-lag) and the second block contains two linear
electronic systems, one second-order and another third
order. Both controllers and systems, allow the exchange
of physical parameters, capacitors or resistors, through
connectors.
submodules that constitute the LCBox is illustrated in
Figure 1. The dotted lines represent interchangeable
connections. The lines to the left of the systems represent
the control signals of the different controllers and the line
to the right represents the connection to the out point.
Figure 1.Block diagram of the LCBox control module.
As it is a closed-loop control system, it is
necessary to incorporate a unitary subtraction element
and another –12V Power sources were selected to
adjust the allowed voltage range supply for operational
For the choice of linear systems, a second-order
system and another third-order system were used. The
selected second-order system is shown in Figure 3. The
mathematical model that describes the dynamics of this
system is given by equation1 and equation 2:
Figure 2. Differentialamplifierconfiguration
Rev. Téc. Ing. Univ. Zulia. Vol. 43, No. 3, 2020, September-December, pp. 114 - 176
152
Quintero-Rojas et al.
Figure 3.Second-ordercircuit
zeros in the transfer function. The appearance of zero can
with the output of the system. The transfer function for
this case corresponds to equation 3.
The selected third-order system is shown in
Figure 4. Equations 4 and 5 describe the mathematical
model in the system state space.
capacitor C3 (VC3), for the reasons explained in the case
of the second-order system.
Figure 4. Third-ordercircuit.
Considering equation 5, the equivalent transfer
function is described in equation 6
Where the parameters of the polynomial are described in
equation 7.
Lead or lag controller design
as illustrated in Figure 5. The transfer function of the
circuit is given by equation 8.
(8)
Figure 5.Schematic design of a lead or lag compensator
The relationship betweenthe controller
parameters to the physical components is described in
equation 9.
(1)
(2)
(3)
(5)
(6)
(7)
(8)
(4)
(9)
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Design and construction of a lead-lag analog control module
To reduce the number of parameters, C = C1 =
C2. So equation 8 is rewritten as equation 10.
The equivalence between the controller
parameters and the physical components are given by
equation 11.
The transfer function, equation 10, represents
a phase lag controller, provided that
phase lead if the inequality 0 <
Lead-lag controller design
This controller combines both networks (lead
and lag) into a single control element. The design of
the compensators is carried out separately, equation
12 represents the classic transfer function for the
aforementioned.
The inequalities 0 <1 <1 and 2> 1 must be
met, for this the adjustment of the lead network and then
the lag network is carried out. Figure 6 representsthe
equivalent circuit to the transfer function described in
equation 13.
The relation between the parameters and
physical components is given by equation 14.
1
<1 and
2
> 1 [24].
Figure 6.Lead-lag controller circuit.
Selection of components for implementation
The used elements show easy use, adquisition
and low cost in Venezuela as characteristics. The LM741
used in several analog applications related to control. It
was chosen for its wide gain andvaried operating voltage
ranges, allowing it to achieve exceptional performance
(10)
(11)
(12)
(13)
other more economic integrated circuits, however, forthis
investigation sakeand availability of acquisition, the
integrated LM741 was choosen.
in the implementation of the control loop subtractor, to
ensure the unit gain of the control loop. The user selects
the desired controller employing a dip switch. A (150x90)
mm copper faced bakelite board was used for circuit
printing. The connections between the controllers, the
systems, and the interchangeable electronic components
are made using header bases. Banana plugs were used
LCBox, and the output of the control module. Connectors
components in case of failure.
Input protection
The system reference input and the power inputs of the
A 0.1A fuse is included for overload or short circuit
protection, the acceptable nominal current range is 0.1A,
are protected using two voltage regulators: An LM7812
1 summarizes the components used to make the LCBox
control module and their prices in US dollars.
Figure 7.Application of the LM7812 Voltage Regulator.
Figure 8.Application of the LM7912 Voltage Regulator.
(14)
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Table 1. Components used in the implementation of the LCBox control module
Schematic symbol Value Componentdescription Quantity Unitprice (USD)
U1, U2, U3, U4, U5, U6, U7, U8 --- OperationalAmplier 8 0.99
R1, R3, R4, R5 1000Ω Resistor 4 0.004
C10, C11 0.33µF y 0.1µF Electrolytic capacitor 2 0.0193
C12, C13 2.2µF y 1µF Tantalum capacitor 2 0.0398
--- --- Bakelite PCB (10x15)cm 1 2.28
--- --- 6PIN Headersconnector 14 0.0955
--- --- Male Banana Plugs 5 0.1995
--- --- DIP-8 IC DIP Sockets 8 0.138
--- 0.1 A European Fuse 1 0.498
--- --- European Fuse Holder 1 0.663
--- 12V VoltageRegulator LM7812 1 0.127
--- -12V VoltageRegulator LM7912 1 0.246
Total cost 15.307
LCBox control module construction
The schematic design of the LCBox control
module made in the ISIS software is illustrated in Figure
9. Once the design was made, the ARES software was
used to create the tracks or connections between the
components of the printed circuit, as shown in Figure 10.
For the printed circuit, the bakelite printing technique
was used, the result is shown in Figure 11. The upper part
of the LCBox contains a user guide connection diagram,
which is illustrated in Figure 12. The upper part of the
ground, 12V, -12V) and one output terminal (to display the
system’s output), as well as header connectors.
Figure 9.Schematic diagram obtained with Proteus’ ISIS
for the LCBox control module
Figure 10.Design obtained in ARES by Proteus to make
the printed circuit board (PCB) of the LCBox.
Figure 11.Upperside of the printed circuit board
Rev. Téc. Ing. Univ. Zulia. Vol. 43, No. 3, 2020, September-December, pp. 114 - 176
155
Design and construction of a lead-lag analog control module
Figure 12. Top of the LCBox module
Unlike the upper part, the rest of the module is
made of steel. Inside the module, insulating bases were
built for the plate, which protects the components and
lines against short circuits. The cover of the LCBox and the
of the construction of the LCBox is shown in Figure 13.
Figure 13.View of the lead-lag analog control module
Operating range of the LCBox module
Table 2 and Figure 12 describe the operating
limits and location of each component to be connected to
the module. The maximum and minimum voltage that the
reference input can withstand is given by the capacity of
in the datasheet of the LM741 package [25]. The minimum
and maximum values of the capacitors and resistors
represent the range of values with which the LCBox was
successfully tested.
Table 2.Operating range of the LCBox control module.
Symbol onthecover MinValue MaxValue
Reference -15V 15V
12 Volts 7.5V 35V
-12 Volts -35V -6.1V
C1, C2, C5, C6 0.1 µF 100 µF
R1, R2, R3, R4, R7, R8, R9,
R10, R11, R12
39Ω 180KΩ
Results and Discussion
To check the performance of the control module,
different tests were carried out. A square wave from a
signal generator was used as a reference signal and the
output signal of the controlled system was recorded in a
closed loop with the help of an oscilloscope.
Lead compensation in the second-order system
For the system to be controlled, the following
In this case, we set upthe closed-loop system to meet the
following requirements: error
p
6% (position error) and
10%<%SD<20% (variation of the oveshoot). Applying the
desing algorithm in the lead controller, andthrough the
c
= 22.6659,
= 0.7059, and T = 5.7499x10
-4
were obtained. The
transfer function of the advance compensator (equation
8) is then turn into equation 15.
The values for the implementation of the controller were
calculated using equation 11 and the parameters used
were: R
1
2
3
=
4
1
= 0.1µF y C
2
= 0.47 µF.
The data of the real output of the closed-loop system was
stored and compared with the simulations performed in
the PSIM and MATLAB software, as shown in Figure 14.
The curves were plotted in MATLAB for comparison. The
output plots provide a very good approximation of the real
data with the simulated data in the PSIM software. It can be
seen how it reaches the desired maximum overshootand
follows the reference within the established range,
this behavior is due to the good choice of the controller
parameters.
Figure 14.LCBox output signal for the closed-loop lead
compensator
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156
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Lag compensator in the second-order system
For this case, the following parameters were
used: C
3
= 0.1µF, C
4
= 0.22µF, R
5
6
which an open-loop overdamping dynamics is obtained in
a second order system. The system is to be built to meet
the following control requirements: error
p
< 3% and %SD
= 0%. As in the previous case, the parameters for the
c
= 1.2136, = 28.8403 and T = 0.022
were calculated and its transfer function is described in
equation 16.
The following real parameters were calculated
for the implementation of the controller: R
1
2
3
4
1
= 10µF y C
2
= 10µF. The response of the system
is shown in Figure 15, it is seen how the real curve
corresponds to the curve simulated by the PSIM software,
complying with the value of the reference set and the
simulated dynamics.
Figure 15. LCBox output curve for lag compensator.
Lead- Lag compensator in the third-order system
For this system, a lead-lag controller was used.
The system parameters were as follows: C
7
= 0.1µF, C
8
=
0.22µF, C
9
= 0.33µF, R
13
14
15
corresponding to a third-order system with overdamped
dynamics.
The closed-loop system must comply with:
errorp< 2% and %SD < 10%. The controller design
algorithm was applied by lead-lag motion under the
frequency method and the following parameters were
c
= 48.07168,
1
= 0.2169,
2
= 5.7544, T
1
=
(16)
3.4633x10
-4
, T
2
= 0.0028, the transfer function for the
controller described in equation 17 was obtained.
Taking into account the equivalencies of
equation 14, the most suitable physical parameters for the
controller were determined. The values used were: R
7
=
8
9
R
10
11
12
5
= 0.10829 µF y C
6
= 6.8 µF. Figure 16 shows how
the real output of the system controlled by the lead-lag
compensator approaches with good accuracy the curve
simulated in the PSIM and MATLAB software achieving the
Figure 16.LCBox output curve for the lead-lag
compensator
Conclusions
The LCBox is a platform of great potential
designed to be used in the teaching of control theory,
because of its simplicity in its construction, use, and
handling. It allows the user to implement lead, lag, or
lead-lag compensators designed in theory and set up with
basic electronic elements to control electrical systems,
of different engineering specialties to develop analytical
skills in the control systems by the friendly and safe
interaction when changing the controller parameters.
It should be noted that the construction of the
module was done with electronic elements and devices
of easy acquisition and low cost, so it makes the LCBox a
controller simple, powerful, robust, and easy construction.
The control module only contains two types ofcontrollers,
however, this presents a disadvantage for the study of
other different analog control strategies.
(17)
Rev. Téc. Ing. Univ. Zulia. Vol. 43, No. 3, 2020, September-December, pp. 114 - 176
157
Design and construction of a lead-lag analog control module
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OF THE FACULTY OF ENGINEERING
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