Velocity Analysis of a DC Brushed Encoder Motor using Ziegler-Nichols Algorithm: A Case of an Automated Guided Vehicle

Transcription

1 Indian Journal of Science and Technology, Vol 9(38), DOI: /ijst/016/v9i38/100884, October 016 ISSN (Print) : ISSN (Online) : Velocity Analysis of a DC Brushed Encoder Motor using Ziegler-Nichols Algorithm: A Case of an Automated Guided Vehicle Priyam Parikh 1*, Ruesh Vasani and Saurin Sheth 3 1 Deartment of Mechatronics Engineering, SAL College of Engineering, Ahmedabad , Gujarat, India; riyam.arikh@sal.edu.in Gujarat Technological University, Ahmedabad , Gujarat, India; rueshvasani@yahoo.co.uk 3 G.H. Patel College of Engineering and Technology, VV Nagar, Vidhyanagar , Gujarat, India; saurinsheth@gcet.ac.in Abstract Objectives: The use of Automated Guided Vehicles (AGV) has emerged for automation in material handling alications. These AGVs are equied ith DC brushed/ brushless motors ith encoders. The encoders feed the actual shaft osition of a DC motor to the microcontroller, hich converts the shaft osition into the angular velocity. This is called as velocity analysis of DC encoder motor. Methods/Statistical Analysis: The first hase of aer focuses on the hardare of AGV and interfacing a controller ith MATLAB. In the second hase, the transfer function of the system, tye of the system, order of the system, steady state and transient analysis are shon. In the final hase of the aer, system s resonse ith P, PI and PID controllers are shon ith the hel of Ziegler-Nicholas (Z-N algorithm) algorithm (Real time and simulation both) ith resect to ste inut. Findings: Industries have different tyes of layout for roduction. Some has rocess layout hereas some has lant layout. According to the roduction caacity and tye of the layout, industries design the ath for AGVs (for material handling). Generally AGVs do loading and unloading stuff, hich is very much useful as far as smooth roduction is concerned. Some comanies and researchers have designed AGVs ith different secifications. If AGV comes out of the track due to irregular velocity, leads the lant to higher lead time and it may damage the roductivity chain. To overcome this roblem a metrology for doing velocity analysis for different controllers and algorithms are shon. Alication/ Imrovements: This algorithm and control strategy hels AGV to move ith constant velocity. It also rotects AGV from accident or collision, hich directly affects the roductivity and better material handling rocess. Keyords: Arduino Controller, DC Brushed Encoder Motor, MATLAB, P, PI and PID Controller, Real Time Data Acquisition, Z-N Algorithm Nomenclatures: s = Lalace oerator, n = Natural frequency of oscillations, K = gain of the system, K m = Motor size constant, K b = Back emf constant, J = Inertia of the motor, daming ratio, d = damed angular velocity, K P = ositional error constant, K v = velocity error constant, K a = acceleration error constant, e ss = steady state error, G(s) =Transfer function, Z-N method = Ziegler Nichols method, T-L= Tyreus-Luyben method, C(t) = time domain outut resonse, T d = delay time, T r = Rising time, T = ick time, M = overshot in %, T s = settling time. 1. Introduction The resent research ork demonstrates the methodology of doing a real time velocity analysis of a DC motor ith Encoder. The Errors in control systems may be attributed to many factors 1,. Changes in the reference inut ill cause unavoidable errors during transient eriods, and also cause steady state errors 3. Any hysical control system inherently suffers from steady state error in resonse to certain tyes of inuts. Whether a given system ill *Author for corresondence

2 Velocity Analysis of a DC Brushed Encoder Motor using Ziegler-Nichols Algorithm: A Case of an Automated Guided Vehicle exhibit steady state error for a given inut deends on the tye of the oen loo transfer function of the system. Various alications are there here controlling of DC motors are required 3,4. The resent ork is focused on AGV, hich is required to move at constant velocity. AGV has to sto for loading/ unloading / detecting any roduct in context of material handling 4. The velocity analysis of a DC brushed encoder motor becomes essential to increase the roductivity and decrease the lead time 5. The AGV, as shon in Figure 1 detects RFID number of the roduct and sends it to the server. The AGV travels on a straight black track as shon in Figure. A Line sensor array is used to detect and to follo the black track. AGV follos only black track, hich is detected by IR sensor array. The analysis is carried out just by considering the self-eight of AGV and accordingly the control system is designed. The resent system is having 5 different roducts ith different RFID numbers. According to the given alication, AGV has to travel ith a constant velocity accet loading or unloading. The focus of this ork is on constant velocity of AGV. There is nothing to mention about RFID and IR sensor array. Encoder values are to be calculated according to the diameter of the heel. Encoder kees on calculating the shaft osition. Encoder feeds the shaft osition to the Arduino board. Arduino converts it to the angular velocity 5,6. Then Arduino tries to solve the error, hich is based on the algorithm as ell as tye of the controller. Then the solved error (maniulated signal) is given to the motor via motor driver 6. That maniulated signal is a ulse idth modulated signal. As far as error solving is concerned, P, PI and PID controllers are used. K, K i and K d arameters are chosen according to Ziegler-Nichols algorithm. The secifications of the AGV are shon in Table 1.. Block Diagram of the System ith Problem Descrition The block diagram of the overall system is shon in Figure 1. Ste inut is given to the system as 6 volts DC. Encoder s highest count values are Any set oint can be fed into the system (deends uon the alication) 7,8. Error signal generated from the summation of the set oint and feedback signal is given to the Arduino microcontroller 8. Arduino maniulates the signal and gives to the motor via motor driver, because motor driver gives PWM signals 8. The connections for exerimental velocity analysis technique are shon in Figure 3 8,9. The Prototye of the AGV is shon in Figure. The comlete setu for velocity analysis is shon in Figure 4. The feedback signal, hich is roduced by encoder, is comared ith the set oint. Error signal is solved by Arduino using various controllers (P, PI or PID) and control algorithm (Z-N algorithm). Finally the signal solved by Arduino, is given to DC motor of AGV. Figure 1. Figure. Block diagram of the system. AGV Prototye. Table 1. AGV Secifications Sr No Parameters Values 1 L B H 35cm 5cm 15cm Mass of AGV 3. Kg 3 No of Motors 4 4 Tyes of Motors DC brushed Encoder 5 Motor Secification 6 volts, 10 PRM, 3.6 Kg.cm at. Am 6 Wheel Diameter 10 cm 7 Path to be folloed Straight Dark line 8 Path Folloed by IR sensor Array 9 Motor Gear Ratio 47:1 Vol 9 (38) October 016.indjst.org Indian Journal of Science and Technology

3 Priyam Parikh, Ruesh Vasani and Saurin Sheth Figure 3. Path of AGV. 3. Methodology to Acquire the Data To acquire the real time data of velocity, Arduino controller and MATLAB real time data acquisition tool is used. Table 3 shos the all final results of simulated as ell as ractical values. Simulated results are carried out by MATLAB simulink 13,14. The methodology to acquire real time data is demonstrated in the current toic. It becomes essential to acquire real time data to comare simulated and actual data (refer Table 3). This toic ill describe some of the general usage of MATLAB s Data Acquisition Toolbox (DAT). The softare in the toolbox allos MATLAB to acquire data from sensors and to send out electrical signals that can be used to control or drive external devices. Here encoders are giving the data to microcontroller. Microcontroller is connected to MATLAB data acquisition tool box using serial communication technique 15. Figure 5 and Figure 6 shos block diagram for real time data acquit ion and time data acquired from AGV using simulink resectively. Figure 4. Setu for velocity Analysis. 3. Hardare Descrition and Methodology 3.1 Hardare Descrition of the System The hardare is develoed using Arduino board, as it is an oen source hysical comuting latform. It can be used to develo interactive objects 8,9. Taking inuts from a variety of sitches or sensors, controlling of variety of lights, motors, and other hysical oututs can be achieved. It has 14 digital I/O and 6 Analog I/O. It orks on +5volts DC, 10 bit analog to digital converter and 14kb ROM 8,9. The DC motor used in this alication is a brushed DC motor ith 47:1 metal gear box 9,10. It is equied ith 48 CPR quadrature encoders on the motor shaft. It rovides 49 counts er revolution of the gear box s outut shaft. These motors are intended for use at 6 V. Key secifications of motor at 6 V: 10 RPM and 80 ma free-run, 50 oz-in (3.6 kg-cm) and. Am stall current. A to-channel Hall Effect encoder is used to sense the rotation of a magnetic disk on a rear rotrusion of the motor shaft. The quadrature encoder rovides a resolution of 48 counts er revolution of the motor shaft hen counting both edges of both channels Table gives the comlete idea about the motor arameters and system arameters. Table. Physical arameters of the motor 17 Sr. No. Motor Parameters Symbol Information 1 Motor Inductance La 0.5 Henry Armature Resistance Ra Ω 3 Motor Inertia J 0.03 Kg.m 4 Torque Constanta Ka 0.01 N.m/Am 5 Tye of the system See Eq Tye Zero 6 Order of the system See Eq 1 Second Order 7 Tye of feedback - Unity Table 3. Routh s Criteria 8 Lalace Oerator First Coefficient Second Coefficient Figure 5 S K S S K - Block Diagram for real time data Acquisition Vol 9 (38) October 016.indjst.org Indian Journal of Science and Technology 3

4 Velocity Analysis of a DC Brushed Encoder Motor using Ziegler-Nichols Algorithm: A Case of an Automated Guided Vehicle Here the hole system is controlled by the combination of Arduino, MATLAB simulink, Serial communication, motor driver, DC encoder motor and data acquisition tool box 15,16. Arduino ill send the encoder data to MATLAB serially and MATLAB lots it. These readings are rovided in chater 4. They are calibrated in the form of RPM. 4. Simulation of the System Figure 7 shos the simulated block diagram of the system and Table 4 gives the information about all hysical arameter of the DC brushed encoder motor 15,16. Equation 1 shos the tye of the system and equation shos the order of the system. From belo to equations, it could be observed that, the resent system is a second order system and tye of the system is zero (as j = 0 in equation ). Ka (motor torque constant can be found from Routh s criteria and Equation 4, hich is a characteristic equation for stability) (1 + T1( s))(1 + T( s))...(1 + Tn ( s)) G( s) H( s) = K (1 + T ( s))(1 + T ( s))...(1 + T ( s)) a b m (1) (1 + T1( s))(1 + T( s))...(1 + Tn ( s)) G( s) H( s) = K s j (1 + T ( s ))(1 + T ( s ))...(1 + T ( s )) a b m () ( K ) G( s) H( s) = a (3) (0.5s+ 13)(0.003s+ 0.1) 1 + K a G( s) H ( s) = 0 (4) 4.1 Steady state Analysis of the System Equation 5 is alicable for under damed system. The time domain resonse is calculated based on Eq. 5. No it is imortant to kno the steady state arameters (K P, K v, K a and e ss) of the system 15. ( ) (( n xn C t = ) e t sin dt) (1 x) K K v s 0 (5) = lim ( G ( s ) H ( s )) (6) = lim ( G ( s ) H ( s )) (7) s 0 lim = ( ( ) ( )) (8) s 0 K s G s H s E ss 6 = K (9) v Figure 6. Real time data acquired from AGV using simulink 18. Figure 7. Block Diagram for simulation 15 Table 4. Result of Routh s Criterion 7 Parameter Value K >-0. Ku (Ultimate Gain) 0. S jω ω=π/pu 5.16 rad/sec Pu (Ultimate Time) 1.1 sec 4. Transient Analysis of the System It becomes essential to find transient arameters of the system. Every system ooses an oscillatory behavior (daming). This tendency controls the closed loo oles of the system. The closed loo oles decide the resonse of the system. Eqn. 10 to 14 belongs to the transient arameters of the system. Table shos all motor arameters. T d T r ( x) = (10) d ( b ) = (11) T d = (1) d 1 x M in% = 100( e ) (13) T d n x (4x) = (14) 4 Vol 9 (38) October 016.indjst.org Indian Journal of Science and Technology

5 Priyam Parikh, Ruesh Vasani and Saurin Sheth 4.3 MATLAB Simulation Figures 8 and Figure 9 shos the simulated block diagram and simulated resonse resectively. Figure 10 shos the combined simulation for P, PI and PID controller. Hoever a system ithout controller is also simulated in the Figure 11. Figure 1 shos the combined simulated resonse of the system. Above to figures are related ith simulation only. In the ucoming toic, Figures 13 sho the actual resonse of the system. 4.4 Ziegler Nichols Algorithm for P,PI and PID Controller It can be observed from Figures 10 and 11, that system ithout any controller is oscillatory and bit slo. It is n ecessary to design a comensator to make system stable and fast. Ziegler and Nichols ublished in 194 a aer here they described to methods for tuning the arameters of P, PI and PID controllers 16. These to methods are the Ziegler-Nichols closed loo method, and the Ziegler-Nichols oen loo method. Among these to methods, the closed-loo method is the most useful, and it is alied in the resent ork. Table 5 shos the Z-N tuning chart for K, ki and kd. Equation 16 shos the transfer function of the lant. Equation 17 shos the overall transfer function of the system. Equation 18 shos the characteristic equation of the system 17, C( s) = K + ( )( ) Tds T s + (15) G( s) = (0.015s s+ 0.) i K K T. F = (0.015s s K ) (16) (17) = (18) C. C. Eq. (0.015s 0.11s 0. K ) 0.015s + K + 0. = 0 (19) Table 3 shos the Routh criterion technique alied on the current system to find the stability of the system. Routh s criterion is useful for finding stability and gain of the system. Table 4 shos the results of Routh s criterion. Main aim of this ork is to reduce steady state error, less settling time, less overshoot and less velocity gain. A roortional integral derivative controller (PID Figure 8. Matlab Simulation. Vol 9 (38) October 016.indjst.org Indian Journal of Science and Technology 5

6 Velocity Analysis of a DC Brushed Encoder Motor using Ziegler-Nichols Algorithm: A Case of an Automated Guided Vehicle Table 5. Ziegler Nichols Tuning Chart Controller K K i k d P K u / - - PI K u /. P u /1. - PID K u /1.7 P u / P u /8 Figure 9. MATLAB Simulated resonse of uncomensated system, P, PI and PID controller. controller) is a generic feedback controller 19. It can be used henever a mean osition has to be achieved but the controls of the system do not react instantaneously and accurately. The PID algorithm, takes in account the folloing three things are to be taken in account- the existing error, the time the system has stayed aay from the mean osition and the ossibility of overshooting the mean osition. Using these three quantities, the system is controlled better, alloing it to reach the mean osition faster and ithout over shooting it. Table 6 shos values of K, Ki and Kd according to the Z-N algorithm. Figure 10. Resonse of AGV ith P controller. 4.5 Alying Ziegler Nichols Algorithm to AGV (Actual Obtained Results) The actual resonse of the system ith all the controllers (P, PI, PID and no controller) are shon in Figure 13. resectively. The set oint is 100 RPM of encoder. Arduino is connected serially ith MATLAB and acquired the real time data according to the values of K, K i and K d. Observing the above figures, it could be concluded that, PID settles don the system quickly but gives higher overshooting. Figure 11. Figure 1. Resonse of AGV ithout any controller. Resonse of AGV ith PID controller. 5. Results and Analysis The resent research aer elaborates the interfacing technique beteen Arduino and DC encoder motor, simulation of the system in SIMULINK, real time data Acquisition in MATLAB. Moreover it demonstrates the use of Ziegler-Nicholas algorithm for P, PI and PID controller for real time alications 16. It can be concluded that: Overshoot in P controller is lesser but system becomes sloer ith higher steady state error. It clearly shos that AGV ith P controller consumes more time to get settled. AGV ith PI controller becomes unstable. It ill not be able to sto itself at the exact location. PI controller is not suitable according to the simulated results. 6 Vol 9 (38) October 016.indjst.org Indian Journal of Science and Technology

7 Priyam Parikh, Ruesh Vasani and Saurin Sheth AGV ith PID controller orks ell in all criteria. System becomes fast ith less steady state error and negligible overshoot for PID controller. Z-N Algorithm & PID controller suits ell as far as simulated results are concerned. Figure 13. Resonse of AGV ith PI controller. Table 6. Values of K, K i and K d based on Z-N Algorithm Controller K K i k d P PI PID Referring actual results as er Table 7, AGV orks ell for PID and PI controller, but becomes oscillatory for P controller. The error beteen simulated and actual resonse is due to misalignments of motors and heels, voltage fluctuations in ste inut, viscous friction, heel mounting, motors inductance and internal resistance. Delay time is almost same for all controllers. Positional gain is 100 for all the controllers since this system is a tye zero system. Velocity and acceleration gain are zero since this system is a tye zero system. It is a under damed system Steady state error is higher for P and PI controller. Steady state error is lesser for PID controller. PID and PI controller have given lesser overshooting comared to P controller. In future the same aroach may be adoted for acceleration analysis of AGV. The aroach may be evaluated in context of constant acceleration of AGV, achieving constant RPM of a servo Motor in CNC machines and automatic stir u bending mechanism 13,14, color based sorting system automation 19, motor of a conveyor belt, back lug ress fitting assembly 4,5, checking arallelism of a railay track 13. The methodology ill be very useful in electro hydraulic circuits used for retrofitting of machine tools 10. Table 7. Actual and simulated control arameters Sr No Parameters Without Controller Theoretical Without Controller Practical Theoretical Values P Practical Value P Theoretical PI Practical Value PI Theoretical PID Practical Value PID 1 K Kv Ka Ess 0.8 volt 80 RPM 0.65 volts 60 RPM 0.47 Volts 50 RPM 0. volts 30 RPM 5 M 73 % 61% 36.6 % 30. % 6 % 5.3 % 4.6 % 19% 6 Ts 1.05 sec 1.1 sec 0.95 sec 1 sec 0.3 sec 0.5 sec 0. sec 0. sec 7 T 0.09 sec 0.09 sec 0.06 sec 0.06 sec 0.03 sec 0.04 sec sec 0.03 sec 8 Tr 0.03 sec 0.03 sec sec 0.1 sec sec Sec 0.010sec sec 9 Td sec 0.01 sec 0.01 sec 0.01 sec 0.01 sec sec 0.01 sec Vol 9 (38) October 016.indjst.org Indian Journal of Science and Technology 7

8 Velocity Analysis of a DC Brushed Encoder Motor using Ziegler-Nichols Algorithm: A Case of an Automated Guided Vehicle 6. References 1. Gajjar B, Sheth S. Design and Automation in Back Plug Press Fitting Process of Ball Pen Assembly. Alied Mechanics and Materials. 014; 59(): Gajjar B, Sheth S. Investigation of Automation Strategy and Its effect on Assembly Cost: A Case Study on Ball Pen Assembly Line. International Journal of Current Engineering and Technology, Secial. 01; 3: Bhavsar S, Parikh P. Actuation of hydraulic and Pneumatic system using DTMF technology. Proceedings of International Conference on Innovations in Automation and Mechatronics Engineering, G.H. Patel College of Engineering and Technology, India. 013 Feb Parikh P, Joshi K, Sheth S. Color Guided Vehicle-An Intelligent Material Handling Mechatronic System. Proceedings of the 1st International and 16th National Conference on Machines and Mechanisms (ina- CoMM013), IIT Roorkee, India Parikh P, Shah H, Sheth S. A Mechatronics design of a line tracker robot using Ziegler Nichols control technique for P, PI and PID controllers. International Mechanical Engineering Congress (IMEC-014), NIT Trichy, India. 014; 3(10): Parikh P, Shah H, Sheth S. Develoment of a multi- channel ireless data acquisition System for sarm robots - A Mechatronic Aroach using Arduino UNO and MATLAB. International Journal of Engineering Develoment and Research (IJEDR). 014; (1): Patel T, Sheth S Patel P. Design of Semi-automatic Hydraulic Blanking Machine using PLC. National Conference on Innovative and Emerging Technologies (NCIET- 015). 015 Ar Sheth S, Kher R, Shah R, Dudhat P, Jani P. Automatic Sorting System using Machine Vision. Multi-Discilinary International Symosium on Control, Automation and Robotics. 010; Tamboli K, Sheth S, Shah V, Modi V, Gandhi, Amin N. Design and Develoment of a Mechatronic System for the Measurement of Railay Tracks. Discovery. 015; 43(00): Virani M, Vekariya J, Sheth S, Tamboli K. Design and Develoment of Automatic Stirru Bending Mechanism. Proceedings of 1st International and 16th National Conference on Machines and Mechanisms (inacomm013), IIT Roorkee, India Parikh P, Sheth S, Patel T. Positional Analysis of a DC brushed Encoder Motor using Ziegler-Nichols Algorithm. CAD/CAM, Robotics and Factories of the Future, Sringer India. 016; 5(): Chauhan V, Sheth S, Hindocha B, Shah R, Dudhat P, Jani P. Design and develoment of a machine vision system for art color detection and sorting, Proceedings of Second International Conference on Signals, Systems and Automation, ICSSA- 011, Gujarat, India Vaghasiya M, Moradia H, Nayi R, Sheth S, Hindocha B. Modeling of an automatic ositioned, A mechatronics aroach. 4th National Conference on Recent Advances in Manufacturing Desai S, Sheth S. Study and roosed design of Centrifugal Casting Machine for manufacturing of turbine bearing. International Conference on Mechanical, Material, Industrial, Automotive and Aeronautical and Nano- Technology (MIANT-015) Jaaharlal Nehru University, Ne Delhi, India Desai S, Sheth S. Proosed Design of Centrifugal Casting Machine for Manufacturing of Turbine Bearing. National Conference on Advances and Challenges in Engineering and Science (NCACES-01), L. C. Institute Of Technology, Bhandu, Mehsana, India Desai S, Sheth S, Chauhan P. Design and Modelling of Dual facelate Centrifugal casting equiment for manufacturing of turbine bearing, CAD/CAM, Robotics and Factories of the Future, Sringer India. 016; Sheth S, Patel Kavit H, Patel H. Design of Automatic Fuel Filling system using a mechatronics aroach. CAD/CAM, Robotics and Factories of the Future, Sringer India. 016; Gangadia H, Sheth S, Chauhan P. Design and modelling of secial Purose Equiment for shell-diahragm elding in conveyer ulley. Procedia Technology. 014; 14: Rizan JM, Krishnan PN, Karthikeyan R, Kumar SR. Multi layer ercetion tye artificial neural netork based traffic control. Indian Journal of Science and Technology. 016 Feb 9; 9(5): Vol 9 (38) October 016.indjst.org Indian Journal of Science and Technology