38 Scientific Journals 28(100) z. 1
Scientific Journals
Zeszyty Naukowe
Maritime University of Szczecin
Akademia Morska w Szczecinie
2011, 28(100) z. 1 pp. 38–40 2011, 28(100) z. 1 s. 38–40
Linear positioning system using programmable controller
and optical displacement sensor
Układ pozycjonowania liniowego z wykorzystaniem sterownika
programowalnego oraz optycznego czujnika przemieszczenia
Leszek Kaszycki, Lech Dorobczyński
Maritime University of Szczecin, Institut of Marine Electrical Engineering and Vessel Automation
Akademia Morska w Szczecinie, Instytut Elektrotechniki i Automatyki Okrętowej, Zakład Automatyki i Robotyki 70-500 Szczecin, Wały Chrobrego 1–2, e-mail: l.kaszycki@am.szczecin.pl, l.dorobczynski@am.szczecin.pl
Key words: linear displacement, automatic control, robotics, approximation Abstract
The paper presents a concept of application of optical displacement sensor type Sharp GP2Y0A02 in the linear positioning system containing rodless pneumatic actuator and programmable controller. The coupling circuit between sensor and controller, containing voltage controlled current source was proposed. The properties of measuring system were investigated, and some mathematical models of its static characteristic were found using the less squares method. The analysis of residual errors, and sum of squared residual errors were performed. Finally, the model minimizing the mentioned quantities, as well as measuring range of investigated system were selected.
Słowa kluczowe: przemieszczenie liniowe, regulacja automatyczna, robotyka, aproksymacja Abstrakt
W artykule przedstawiono koncepcję zastosowania optycznego czujnika przemieszczenia GP2Y0A02 firmy Sharp w układzie pozycjonowania liniowego zbudowanego z wykorzystaniem siłownika beztłoczyskowego i sterownika programowalnego. Zaprojektowano układ sprzęgający czujnik ze sterownikiem z użyciem ste-rowanego napięciem źródła prądowego. Zbadano własności toru pomiarowego, a następnie opracowano kilka modeli matematycznych jego charakterystyki statycznej przy użyciu metody najmniejszych kwadratów. Do-konano analizy kwadratowego wskaźnika jakości oraz błędów resztowych aproksymacji. Wybrano model minimalizujący wspomniane wskaźniki, jak również określono zakres poprawnej pracy układu pomiarowego.
Introduction
Technique of linear displacement and multiaxial positioning systems, mobile and industrial robots, fluid level control systems are selected examples of numerous applications of control systems using measurement of distance (position) as controlled value [1, 2, 3].
The fundamental problem in mentioned above applications is respectively exact measurement of linear displacement value. Numerous kinds of sen-sors destined to measurement of distance, acting with use various physical phenomena such as: po-tentiometric, inductive, capacitive, ultrasound and optical are described in [4, 5].
As subject of this paper was chosen positioning system built with use of optical sensor type GP2Y0A02 produced by Sharp [6] and program-mable logic controller (PLC) Series 90 produced by Fanuc [7, 8].
Description and acting principle of positioning system
Positioning system is closed-loop control sys-tem. Its block diagram is shown in figure 1. The set-point value is position of movable carriage rela-tive to stationary GP2Y0A02 type sensor. Output sensor signal is a voltage, being in function of dis-tance between movable carriage and sensor is
Linear positioning system using programmable controller and optical displacement sensor
Zeszyty Naukowe 28(100) z. 1 39
converted into normalised current signal within range between 4 mA and 20 mA, and subsequently delivered to pseudo-analogue input (AI) of PLC. The result of measurement is interpreted by PLC software as natural number, whereas results of computations performed by PLC are binary vari-ables, controlling relay outputs Q1 and Q2. Con-tacts of output relays are elements controlling elec-tropneumatic selector, directing the air flux to in-puts of pneumatic rodless actuator, which moves the carriage.
Properties of distance sensor
The principle of sensor action is based on meas-urement of angle between incident and reflected rays of infrared light. Characteristic curve of GP2Y0A02 is presented in figure 2. Noteworthy is fact, that the mentioned curve consists of two seg-ments: linearly increasing, for distance within range between 0 and 15 cm, and nonlinearly decreasing,
for distances between 15 cm and 150 cm, hence is ambiguous. For this reason as useful measuring range was assumed range from 15 cm to 150 cm. Sensor output voltage signal is non-compatible with input PLC current signal. This necessitates the use of additional signal processing subsystem – voltage controlled current source [10], which schema is shown in figure 3.
Fig. 3. Voltage controlled current source Rys. 3. Źródło prądowe sterowane napięciem
Resulting reversed static characteristic of meas-uring system with distance as output value and natural number N, being measure of PLC input current is shown in figure 4. If the mentioned curve is given in analytical form, it is possible to compute the unknown distance from given value of the number N. Therefore, it was necessary to find a function approximating the reverse static charac-teristic. Due to low numerical efficiency of used PLC, assumed mathematical model of characteristic curve should have form of relatively simple func-tion, to calculate the value only four basic algebraic operations could be used.
Fig. 4. Reverse static characteristic of measuring system Rys. 4. Odwrotna charakterystyka toru pomiarowego Fig. 1. Functional schema of linear positioning system
Rys. 1. Schemat funkcjonalny układu pozycjonowania linio-wego
Fig. 2. Static characteristic of GP2Y0A02 type sensor [9] Rys. 2. Charakterystyka statyczna czujnika GP2Y0A02 [9]
Distance [cm] Ou tp ut vo lt ag e [V]
White paper (reflectance ratio 90%) Gray paper (reflectance ratio 18%)
Disp lac em en t [c m ]
Number in memory of controller N [unit]
Programmable controller Supply Voltage/current converter Screen Carriage Electro-pneumatic selector Distance
Leszek Kaszycki, Lech Dorobczyński
40 Scientific Journals 28(100) z. 1
Several mathematical models of the following forms were created:
x ax bx c y 2 (1.1)
x ax bx cx d y 3 2 (1.2)
b + ax = x y 1 (1.3)
c bx ax x y 2 1 (1.4)
c bx ax x x y 2 (1.5)where x denotes value of number N, corresponding of analog input value and y denotes approximated carriage position expressed in cm.
Coefficients of models were calculated with use of less-squares method [11]. Obtained square quali-ty indexes defined as:
2 model measured y y Q (2)are collected in table 1.
Table 1. Obtained square quality indexes
Tabela 1. Uzyskane w wyniku obliczeń kwadratowe wskaźniki jakości aproksymacji
Model Square quality index Q
x ax bx c y 2 2601.26
x ax bx cx d y 3 2 1025.57
b ax = x y 1 809.97
c bx ax x y 2 1 1142.57
c bx ax x x y 2 616.01Taking in account the mentioned results, model (1.5) was chosen. The values of coefficients are as below:
a = 0.0000042117719300, b = 0.0116472166669116, c = 0.0018611121939014.
Characteristic curve of sensor with curse of approximating function were shown in figure 5a, while figure 5b presents curse of residual error of approximation defined as difference between meas-ured value and value of approximating function.
In range of distances between 20 cm and 140 cm error value is less than 1 cm.
Fig. 5. Approximation of reverse static characteristic Rys. 5. Aproksymacja odwrotnej charakterystyki statycznej Conclusions
Described in the paper sensor was used in construction of linear positioning system, which was built in laboratories of Chair of Automatic and Robotic. The system was acting properly, ensuring the assumed accuracy of positioning in range between 20 cm and 140 cm.
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Number in memory of controller N [unit]
Number in memory of controller N [unit]
D isp la ce me nt [ cm] R esi du al e rr or [ cm] measurement model
