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Download EE 4343 Lab#1 – Part 1
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EE 4343 Lab#1 – Part 1 Identification of Static Motor Module Parameters The goal of this lab is to determine values for the static parameters in the linear model of the DC motor module (Figure 1). Static parameters are those parameters in the model, which can be determined by steady-state measurements. The parameters to be determined are Gear Reduction Armature Resistance N Ra Potentiometer Constant K pot Tachometer Constant K tach Back EMF Constant Kb Torque Constant Kt Power Amplifier Gain A Brake Constant Bj V rev V rpm N m oz in , A A N m oz in , rpm rpm j 0,1,2 We will also find it useful to express the braking constant in a dimensionless form, which is shown below. Dimensionless Brake Constant C j Ra B j KtKb j 0,1,2 In every instance in which we have to take measurements to determine the value of a static parameter, we will determine the value as the slope of a line. Due to nonlinearities in the physical motor module, some of the measured characteristics will exhibit saturation or a deadband. In these cases, the value we will use for the parameter is the slope of the linear part of the characteristic. You should also determine the saturation and deadband limits in case we wish to construct a more detailed model in the future. Two LabVIEW VIs (Virtual Instruments) are used in this lab. The "Static Test" VI is used to collect all data. The "Linear Fit Stored Data" VI is used to perform linear least-squares fits on the collected data. You can print the front panel of the Linear Fit VI in order to get a hard copy of your data. Procedure: 1. Gear Reduction: The gear reduction (motor shaft revs per load shaft rev) can be determined by counting teeth on the gears. Fortunately, the manual for the motor module tells us that the gear reduction is 9, i.e. the load shaft rotates one revolution for every nine revolutions of the motor shaft. 2. Back EMF Constant: Since the tachogenerator and the motor on our DC motor module are identical (within manufacturing tolerances), we will assume that they have the same back EMF and torque constants. The back EMF constant is the ratio of the back EMF voltage generated to the angular 1 04/30/17 velocity of the motor. The back EMF voltage is more accessible on the tachogenerator, so we will measure it there and assume that the motor back EMF constant is the same. Refer to Figures 2 and 3 when making connections to the DC motor module. a) Connect the data acquisition systems analog ground to the motor control module ground. This connection should be made any time the data acquisition system is used. b) Connect the Command Potentiometer to the amplifier input (Vin) of the motor drive input.. Connect the enable line to ground, this is labeled ‘E’ with a over-bar. c) Lift the tachogenerator connector slightly in order to gain access to the armature connection (see Figure 2.) Use a wire clip to connect the non-inverting lead of Analog Input Channel 0 (labeled ACH0) to the V+ side of the armature. Connect the inverting lead (labeled ACH1) to motor module ground. Note: The tachogenerator connector connects the tachogenerator’s armature to the main circuit board. ACHO and ACH1 are part of the data acquisition system. Turn off the power when making this connection. Before turning the power on make sure that the wire clip is not shorting the V+ and 0V pins. d) The brake should be in the off position. Vary the Command Potentiometer voltage manually. For each voltage, type the resulting load shaft rpm's displayed on the motor module' digital tachometer into the LabVIEW data acquisition VI, then click on the "Take Measurement" switch to measure the tachogenerator voltage. The data acquisition VI will record the load shaft velocity you typed in along with the measured tachogenerator voltage. Notice that you will have to provide the minus sign on the velocity when the tachogenerator voltage is negative, since the digital tachometer displays only the magnitude of the velocity. Calculate the back EMF constant. When calculating the back EMF constant, remember that it is the ratio of back EMF voltage to motor shaft velocity, but the slope of the best-fit line for the data you collected has units back EMF Volts per load shaft rpm. 3. Torque Constant: The torque constant of a DC motor is identical to the back EMF constant when they are expressed in the same units. Determine the torque constant in both Newton-meters per Amp and ounce-inches per Amp by performing unit conversions on the back EMF constant. 4. Power Amplifier Gain: To measure the power amplifier gain: a) Connect Analog Output Channel 0 (labeled DACH0OUT) of the data acquisition system to the amplifier input (Vin) of the motor drive input. b) Use a wire clip to connect the non-inverting lead of Analog Input Channel 0 (ACH0) to the V+ side of the motors armature. You may need to lift the motor connector slightly in order to gain access to the armature connection, but the motor must remain connected to the amplifier in order to provide a load while you are measuring the amplifier gain. Note: The motor connector connects the motor’s armature to the main circuit board. Turn off the power when making this connection. Before turning the power on make sure that the wire clip is not shorting the V+ and 0V pins. c) Connect the inverting lead of Analog Input Channel 0 (ACH7) to motor module ground. d) Use the LabVIEW data acquisition VI to vary the amplifier input voltage and measure the amplifier output voltage. Calculate the power amplifier gain constant. The slope of the amplifier voltage transfer characteristic is the amplifier gain. It should be positive. 2 04/30/17 5. Armature Resistance: In order to properly measure the armature resistance of a DC motor, you must lock the rotor, apply an armature voltage, and measure the armature current. A standard Ohmmeter will not usually give a correct measurement because it does not use enough test current. For the small DC motor on our motor module, however, the armature resistance measured by a standard Ohmmeter has been found to be reliable. Remove the armature connector from the main board for this step. The lab TA will give values to the students if no ohmmeters are available. 6. Tachometer Constant: The tachometer constant is simply the gain of an inverting operational amplifier circuit. In order not to have minus signs running amok in our transfer functions, we will extract the minus sign from the tachometer constant and place it instead on the block diagram. Hence, our tachometer constant K tach will be positive. a) To measure the tachometer constant, use a wire clip to connect Analog Output Channel 0 (DACH0OUT) to the V+ side of the tachogenerator’s armature. The tachogenerator connector should be removed from the main circuit board. b) Connect the non-inverting Analog Input (ACH0) to the output voltage of the tachogenerator circuit on the motor module. Use the LabVIEW data acquisition VI to measure the voltage transfer characteristic. Calculate the tachometer constant. The slope of the characteristic is Ktach . 7. Brake Constant: We can determine the brake constant by applying a voltage to the amplifier input and measuring the steady-state tachometer voltage. If we apply the final value theorem to the Laplace transform of the tachometer voltage for a step input of magnitude Vin , we find that the steady-state tachometer voltage versus amplifier input voltage characteristic predicted by our linear model is Vtach ss AK tach V , 1 C j in where C j is the dimensionless form of the brake constant. (If you are just now taking the controls course, you probably won't be able to verify this fact for yourself for another couple of weeks. If you have already completed the controls course, you should derive this result yourself.) a) Connect Analog Output Channel 0 (DACH0OUT) of the data acquisition system to the input of the power amplifier on the motor module. b) Connect the non-inverting Analog Input Channel 0 (ACH0) to the tachogenerator circuit output voltage. Use the LabVIEW data acquisition VI to measure the steady-state tachometer voltage characteristic. Calculate the dimensionless brake constant and the brake constant for the brake in the ‘off position’ (C 0) and for the brake in position C1 . You do not need to calculate the brake constant for position C2. 3 04/30/17 EE 4343 Lab #1 – Part 2 Identification of Effective Motor Inertia The goal of this section is to determine the value of the effective motor inertia J in the linear model of the DC motor module. Two LabVIEW VIs (Virtual Instruments) are used in this lab. The "Step Response" VI is used to collect all data. The "Analyze Stored Step Response" VI is used to identify the time constant of the step response. You can print the front panel of the analysis VI in order to get a hard copy of your data. Procedure: The mechanical time constant of the motor module can be determined from either the tachometer or the potentiometer step response. We will use the tachometer response because it has one less pole than the potentiometer response. Measure the tachometer step response for a large (4V - 5V) step and a medium (2V - 2.5V) step input with the brake in the off position, C0 and for position C1. Use the analysis VI to calculate the final value and the time constant of each step response. The tachometer voltage response to a step input is Vtach (t) K(1 e t/ ) where the final value and the time constant are given by K AVstep K b (1 CB j ) , m 1 CBj . Cv is a conversion constant, if Kb is expressed in terms of Radians and seconds Cv is not needed. m is the motor time constant and CB j is the dimensionless brake constant for the brake in position j . In terms of the model parameters, they are given by m JR a , K t K bC v CB j R a Bj . KtKb Values were determined in part 1 for all of the above parameters except the motor inertia J . The step response analysis VI was used in this lab to determine values for K and . Hence, you can calculate values for m and J for each step response. Note that these values should ideally be the same for each step response you measure. 4 04/30/17 Lab Report for Part 1: Prepare a table of the motor model parameters you identified. Be sure to identify the motor module you were working with. Give some thought as to how many of the figures in each parameter are significant. As a rule, only the least significant digit you report should be substantially uncertain. Include a copy of the graph from the linear regression VI for each parameter you measured. Show your calculations for the cases when you had to derive the parameter value from the slope of the graph. Your report should also include values for the output saturation voltage of the power amplifier and for the static friction torque on the motor shaft. Show how the static friction torque can be calculated from the steady-state tachometer voltage characteristics you measured in part 8. Lab Report for Part 2: Your lab report should include a table showing Vstep , K , , m , and J for each step response you measured. Compare the measured final value with the final value calculated from the parameter values you identified in part 1 of this Lab . If they are significantly different, try to explain why. Average the values for m and J from each trial (omitting any values that appear to be out of line) to arrive at your best estimate for those parameters. Also estimate the uncertainty (standard error) of m and J . Now that you have identified all of the parameters in the model, draw a block diagram of the motor model. Include the amplifier saturation and the static friction in your block diagram. Use the parameter symbols in the diagram and give the values of the parameters beside the diagram. Be sure to identify the motor module you were working with. Derive the following transfer functions from figure 1. m/Vin and Vtach/Vin Use the assumption that the model is a linear system (no deadband or static friction). These transfer functions will be needed in later labs. 5 04/30/17 TL Vin Va A + 1 Ra TB 1 N Bj Tm - Ia Kt - + 1 J m 1 s m 1 s m 1 N L Vpot Kpot Vtach Kb A - Power amplifier voltage gain Bj - Brake constant (j= 0,1,2) J - Total inertia of all moving parts Kb - Back EMF constant of motor Kpot - Potentiometer constant Kt - Torque constant of motor Ktach - Tachometer constant N - Gear reduction ratio Ra - Armature resistance of motor -Ktach Va - Applied motor armature voltage Vpot - Potentiometer output voltage Vtach - Tachometer output voltage Ia - Motor armature current m - Motor acceleration m - Motor velocity m - Motor position L - Position of load shaft Figure 1. Model of Analog DC motor control module 6 04/30/17 TB - Braking torque TL - External load torque Tm - Motor torque 5V 0V +12V -12V Motor Drive Input Vin E 0V tachogenerator Output V+ 0V Vout 0V Armature connections* (Motor) Potentiometer Output Vout OV 0V V+ Gray Coded Disk Armature connections * (tachogenerator) Slotted Disk *Note that the armature connections are marked 0V and V+. On some motor modules the polarity of the pins may be different. Verify the polarity of these pins during step 2 of experiment 1. Figure 2. Motor Module 7 04/30/17 Description ACHO non-inverting analog input ACH1 inverting analog input. ACH1 and ACHO are inputs to a differential amplifier that is part of the computer data acquisition system. For this lab course ACH1 will always be connected to ground. Measurement range is –5 to +5 volts. DAC0OUT Analog output Output range is –5 to +5 volts AGND Analog ground. AGND needs to be connected to the motor module ground whenever measurements are taken or the analog output is used. Figure 3. Data Acquisition Board I/O Wiring Block 8 04/30/17