AN ARDUINO CONTROLLED CHAOTIC PENDULUM FOR A REMOTE PHYSICS LABORATORY
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1 AN ARDUINO CONTROLLED CHAOTIC PENDULUM FOR A REMOTE PHYSICS LABORATORY J. C. Álvarez, J. Lamas, A. J. López, A. Ramil Universidade da Coruña (SPAIN) carlos.alvarez@udc.es, jlamas@udc.es, ana.xesus.lopez@udc.es, alberto.ramil@udc.es Abstract In this work we present the development of a remotely controlled laboratory (RCL) for the study, at undergraduate level, of chaotic oscillations in a pendulum; an important topic in non-linear dynamics. The experimental set up, located at the Physics Laboratory of the EPS (University of A Coruña) is based on conventional PASCO equipment modified by a customized control box with Arduino an open-source electronics prototyping platform. Keywords: Remotely Controlled Laboratory, Chaotic Pendulum, Arduino, Physics. 1 INTRODUCTION We have been working during some years in the improvement of laboratory experiments in physics at undergraduate level [1]. Our goal is the introduction of computers that brings these experiments closer to the students and to the current methods that are used to measure in scientific laboratories and industrial companies around the world. Moreover, this makes it possible to surpass the physical limitations of the traditional laboratories (space and time) with the result that students can be more creative and their job can be adapted to their schedule and interest. The pendulum is a well-known topic in mechanics and may be used to introduce a large number of dynamic concepts [2]. Furthermore, the chaotic pendulum is one of the simplest examples in nonlinear dynamics and there exists commercially available laboratory equipment to study the characteristics of the chaotic regime. In this sense, we have been used for years the PASCO equipment, shown in Figure 1, which, in brief, it includes a motion sensor, a harmonic oscillator/driver with a DC motor and the rotation accessories connected to a computer through an interface. PASCO also supplies the software for recording data and plotting the experimental results [3]. In this work we present a modification of the PASCO conventional set-up to allow the students to perform remotely experiments in chaotic pendulum. This was possible by replacing the interface and software by a customized control box based on Arduino microcontroller and using free software (Phyton). In brief, the microcontroller routine reads through the USB port instructions from a Python program running in the server and sends the required values of the sensors. The program running in the server can perform preliminary data process and display the plots through the dynamic web page in a Apache server. Moreover, data can be downloaded at the client computer for further analysis. 2 WEB-BASED REMOTE EXPERIMENT To perform the experiment remotely The PASCO interface was replaced by a controller board microcontroller. The Arduino [4] is an open-source electronics prototyping platform based on flexible, easy-to-use hardware and software. Within the scope of educational applications it has been used primarily on automatic and robotics issues [5]. The ease of use and the ability of controlling different kind of sensors make Arduino an attractive tool in data acquisition systems and control of experiments in a physics lab. The experimental device can be separated into the following components: 2.1 The equipment form PASCO A Rotary Motion Sensor, CI-6538, with 1440 encoder step per revolution. A Chaos/Driven Harmonic Accessory, CI-6689A, that includes a rotating disk (9.5 cm diameter, 120 g), a eccentric mass (15 g), two springs and an Adjustable Magnet for damping. A Mechanical Oscillator/Driver, ME Proceedings of INTED2013 Conference 4th-6th March 2013, Valencia, Spain 6062 ISBN:
2 A Photogate Head, ME-9498A. Figure 1. PASCO set-up which includes an interface to connect the computer via a SCSI bus. 2.2 The Arduino board The Arduino used is of the type Duemilanove, namely the ATmega328, which has a 8-bit processor with 20 MHz crystal oscillator, 32K of Flash Memory, 14 digital input / output pins (Of which 6 can be used as Pulse Width Modulation outputs) and 6 analog inputs. In our case two digital inputs are used to define the pendulum position through optic encoders and a digital output is used to control the speed of the DC motor (with the procedure of Pulse Width Modulation, PWM). The board is supplied with a voltage of 12 V at the output PWM can provide one of 256 values between 0 and 12 V. 2.3 The interface board Arduino board is integrated into an interface that contains circuitry for conditioning the signals from the digital sensors and to regulate the voltage supply of the motor. This box has the connectors for the rotation sensor and the photogate, the input of the power supply, the output to power the motor, and the USB to connect the Arduino with the computer. Figure 2: Photo of the interface board with the wiring connections. 6063
3 2.4 Software Figure 3: Schematic diagram of the connections between hardware and web user. The Arduino program configures the rotary motion sensor and reads the USB port while waiting for orders. These orders are the duration of the experiment, the level of the PWM output and signal to start or stop the experiment. Once the experiment is going on, one of the triggers is used to detect a change in the rotation encoder system, and the other to detect the obstacle coupled to the motor crank crossing the photogate. The first interruption is used to update the angle counter and the second to determine the frequency of the motor. Every 100 ms the values of time counter and angle encoder are sent through the USB port. These values are also sent when the obstacle cross the photogate. A flag is used to differentiate the values corresponding to the first and second case. This experiment can be performed by sending the corresponding orders through the serial port associated with Arduino and reading the data sent back. For this task a Python program was wrote that also performs a first data processing. The Python program reads an XML file with the parameters of the experiment and waits the start order written in the same file. When Python detects the start order a command is sent to the Arduino to run the experiment and after finish performs processing and writes the data and graphs of experiment in a compressed folder in ZIP format. <Experiment name="testchaosportatilasus" user="alberto.ramil"> <MotorRPM value="percentage">12</motorrpm> <Time value="s">60</time> <Command>1</Command> <OutputFile>alberto.ramil_PortatilASUS</OutputFile> </Experiment> Figure 4: A XML file example. This program is started as a service on the server so it works independently, getting orders through the XML file. To perform the experiment through the web form, it is only necessary to modify the fields of the XML file and then to download the ZIP file with the results. Owing that we have chosen open 6064
4 source software, the operative computer system was Ubuntu Server to which we have added the Apache server, the PHP language and MySQL database. The website is written in PHP and uses a MySQL database to verify the identity of users, the availability of the experiment, and to set other parameters such as the maximum duration of the session. After authenticated access, it is possible to fill out the experiment form with the parameters (filename, experiment duration in seconds and the value of motor PWM percentage) that modify the XML file. After the experiment, two graphs are displayed; the angle versus time and the Fourier transform, and the button to download the ZIP file in the user's computer. Figure 5: Web form Figure 6: Preprocessed graphs obtained after completing the data acquisition. 6065
5 3 RESULTS AND CONCLUSIONS The data obtained in the experiment are written to a text file separated by tabs. The file has a header with two lines of comments and a single line footer, the rest of the file contains the data in four columns: the time in milliseconds, the rotary sensor encoder value, the output PWM motor value, and finally a flag that indicates whether the data line corresponds to the passage through the photogate. Selecting the data with value 1 in the fourth column it is possible to determine the period of the motor as a function of the value of the PWM output (Fig. 7). Figure 7: Drive period versus the Arduino PWM value. Figure 8: Graphic examples of regular (left) and chaotic (right) motion. 6066
6 In Fig. 8 plots of the angle versus time, and the Fourier transform allow us to characterize the regular movement (The Fourier transform concentrated in one or several peaks) or the chaotic regime (with more dispersion in the frequency distribution). The time of passing through the photogate can be used to obtain a Poincaré section, by plotting the position and velocity of the pendulum to the same phase of the motor. Figure 9 depicts the phase diagrams in the case of regular movement and the chaotic regime. Figure 9: Poincaré sections of the phase diagram for the passage through the photogate corresponding to the regular regime (left) and chaotic (right). To conclude, we have shown that Arduino platform is a promising tool for improving Remotely Controlled Labs in physics topics, as the chaotic pendulum. Furthermore, open source software and hardware reduces the costs of the experimental set up and results to be more versatile than the conventional equipment and may allow the students to understand and participate in the design of the data acquisition system as well as further analysis. The procedure described in this work can be easily applicable to other experiments in physics. REFERENCES [1] J. Lamas, J.C. Álvarez, A.J. López, A. Ramil Analysis of standing waves in a string by remotely controled laborator. Proceedings of INTED2011 Conference.7-9 March 2011, Valencia, Spain. [2] Baker, G. L.; Blackburn, J. A. (2005). The Pendulum: A case study in physics. Oxford University Press. [3] PASCO web page: [4] Arduino web page: [5] Sarik,J.; Kymissis, I. (2010). Lab Kits Using the Arduino Prototyping Platform. 40th ASEE/IEEE Frontiers in Education Conference, T3C
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