MIT OpenCourseWare http://ocw.mit.edu 2.004 Dynamics and Control II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.K t V r e f 9 v t a c h i T m T v Massachusetts Institute of Technology Department of Mechanical Engineering 2.004 Dynamics and Control II Lab Session 2: Calibration of Lab System Components1 Introduction: In the future lab sessions you will be studying closed-loop control of the rotational plant. The elements of the complete system are shown below: P l a n t K m , K v N J , B v t a c h T a c h o m e t e r C o n t r o l l e r S e r v o A m p K a In Lab 1 you looked at the mechanical properties J and B of the rotational plant, but it is also important that we have an adequate model, and numerical values for the parameters, of the electro-mechanical motor/load and the rotational speed sensor (tachometer) at your lab station. In this session your goal is make measurements on the other system components and to determine their parameters. The specific objectives are: • To measure the gain Ka of the servo-amplifier. • To measure the motor torque constant Km. • To measure the motor back-emf constant Kv. • To measure the tachometer gain constant Kt. • To demonstrate that a DC electric motor obeys power conservation. Preparation: • Read the class handout The DC Motor • Do Problem 1 of Problem Set 2. • Data sheets for the Maxon 148867 DC servo motor, and the US Digital ETACH2 optical tachometer are attached. 1February 25, 2008 1 M o t o r G e a r t r a i n I n e r t i a l l o a dMeasurements: Amplifier Gain Constant Ka: The servo-amplifier is a voltage-controlled current-source, that is it generates an output current that is proportional to the voltage that is applied at the BNC input connector. The amplifier will adjust its output voltage to maintain the output current (up to its saturation limits of ±40 volts). Within the linear range the input/output relationship is Iout(t)= KaVin(t) The nominal amplifier gain is Ka = 2 A/V, and the maximum sustained current that the amplifier can supply is 5 A. Individual amplifiers may vary from this value and your task is to measure the actual gain constant Ka of the amplifier at your lab station. I ( t ) = K V ( t ) T e k t r o n i x S e r v o - A m pS e r v o A m p l i f i e r a i n A F G 3 1 0 r e d D M MV ( t ) i n Ka F u n c t i o n b l a c k 1 . 2 3 4 G e n e r a t o r 2 0 a m p C o m m o n Note: The black terminal on the servo amp is not ground (0v DC). You must NEVER connect a grounded connection from an instrument, such as an oscilloscope, to this ter-minal. Serious damage to the instrument and the servo amp could result. The digital multi-meter (DMM) is not grounded, and is therefore safe to use. Procedure: Your instructor will show you how to set up the the Tektronix AFG310 Function Generator to generate a steady (DC) voltage. Connect the Function Gen-erator output to the servo-amplifier input. Make sure the amplifier is turned off and disconnect the servo-motor from the red and black terminals. Connect the Wavetek DMM using its 20 amp current input terminal. Set the meter to the AMP range and press the yellow button to select DC measurements. Note: Be careful making these connections – you can damage the DMM and/or the amplifier through incorrect connections. Choose a set of three appropriate input voltages, and for each turn on the function generator and measure the current. Plot a graph (use Excel or MATLAB) and calculate the gain constant from the slope of your graph. Record your measurements and your estimated value of Ka in the box below. 2The Tachometer Gain Constant Kt: The tachometer serves as the angular velocity sen-sor for closed-loop control. The US Digital ETACH2 uses a transparent optical disk, with 2048 radial lines scribed around the circumference. As the shaft spins these lines interrupt a beam of light, and the electronic unit measures the rate of the interruptions and produces a voltage vt proportional to the angular velocity Ω of the shaft, vt(t)= KtΩ(t). The task is to measure the constant Kt for your tachometer. The ETACH2 data sheet is attached. The tachometer should already be set up for a gain constant Kt = 16 mv/rpm, (0.016 volt/rpm), with a maximum angular velocity of ±256 rpm, and an output voltage range of ±4.095 volts. Your task is to verify this value of Kt. S e r v o A m p m o t o r i 1 . 2 3 4 D M M E T A C H 1 . 2 3 4 h a n d - h e l d d i g i t a l t a c h o m e t e r s h a f t F u n c t i o n G e n e r a t o r v m a g n e t s o p t i c a l e n c o d e r Procedure: Place two magnets under the flywheel to create some viscous drag. Con-nect your DMM to the tachometer output. Use the Tektronix function generator to apply a small DC voltage to the servo amp and let the motor spin. (You can vary the speed by changing the function generator output.) The lab instructor will help you to measure the angular velocity with a digital tachometer. Record both the measured speed and the tachometer voltage and compute the gain constant Kt. Compare your measured value with the manufacturer’s nominal value. Repeat for three values of motor speed and compute the slope of the resulting speed/voltage curve. Note: The lab has only two portable digital tachometers, and it will be necessary to share them between groups. 3i ( t ) V i n s The Motor Torque Constant Km: For a permanent-magnet DC motor the torque produced is proportional to the armature current: T (t)= Kmi(t) where Km is a constant. The task is to measure the torque constant Km. " V e r n i e r " f o r c e s e n s o rm o t o r s t r i n g g e a r s P o w e r A m p U S B p o r t o n c o m pu t e r Procedure Estimate the value of the torque constant Km . The general approach will be to determine the torque generated by the motor …
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