# Lab Session 4 Introduction to the DC Motor

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1 Lab Session 4 Introduction to the DC Motor By: Professor Dan Block Control Systems Lab Mgr. University of Illinois Equipment Agilent 54600B 100 MHz Ditizing Oscilloscope (Replacement model: Agilent DSO5012A 5000 Series Oscilloscope) Agilent 33120A Function/Arbitrary Waveform Generator (Replacement model: Agilent 33220A Function / Arbitrary Waveform Generator) Agilent 6632A Power Supply (Replacement model: 6632B 100 Watt System Power Supply) Agilent 34401A 6 1/2 Digit DMM Agilent 35670A Dynamic Signal Analyzer Agilent VEE 5.0 software (Replacement model: Agilent VEE Pro) Matlab software (www.mathworks.com) Amplifier/Motor/Potentiometer test set (hybrid, built in-house) Analog computer: Comdyna GP6 Purpose Several basic features of control systems can be understood by careful examination of dc motor control as a case study. Moreover, the dc motor is an important component in myriad control systems. The first of three dc motor experiments emphasizes system modeling in the time domain. The motor to be studied is shown in Fig. 4.1, and a functional block diagram is shown in Fig A diagram describing the motor dynamics is shown in Fig This will be used to develop the motor transfer function. Figure The DC Motor. The parameters under consideration have the following units: the pot. gain K pot is in volts/rad; the tach. gain K tach is in volts-s/rad.; Armature resistance R a is measured in ohms; the back emf constant K V is in volt-s/rad.; the torque constant K T is in N-m/amp; the total inertia seen by the motor J = J M + J L is in Kg-m 2 ; the viscous friction coefficient is b in 1

2 N-m-sec/rad.; the Coulomb friction coefficient is c in N-m; and the armature inductance L a is measured in Henries. Figure 4.2. Motor Block Diagram. Figure 4.3. Motor Schematic Diagram. Preparation Readings: A basic description of the system components may be found in B. C. Kuo, Automatic Control Systems, 7th edition. See Sections 4.5 and 4.6, which cover potentiometers, tachometers and dc motors. Prelab: a. The dc motor, with the flywheel clamped (ω = 0), is described by the electrical schematic of Fig The resistance R s has been added to obtain voltage measurements, so that the current s time response can be viewed on an oscilloscope. Find V o (s)/v i (s) in terms of R a, R s, and L a, What is the electrical time constant, τ e, for the motor? 2 Note: The final model of the motor we will develop will not have R s. This is only used for identification.

3 Figure 4.4. Motor Electrical Diagram: Flywheel clamped. b. The electrical parameters R a and L a (assuming R s is known) can be determined from the step response of the motor with clamped flywheel. Describe how τ e can now be found from a best-fit line of ln (y s s - y(t)) vs. t. This will give a reliable estimate in spite of noise. Load the MATLAB data in the file f:\labs\ee386\prelab4.mat. The variable Elect contains time points and voltage points from a step response in columns 1 and 2, respectively. Determine L a from these data, after finding tau e. Assume R s = 2.5Ω, R a = 3.3Ω, compare the value you find from the plots to the value used to generate them: 1 mh. (In the Laboratory Exercises below you will collect your own data points.) c. Now consider the dc motor with the rotor free to turn. The back emf constant, K V, the torque constant, K τ (= K V in SI units), the viscous friction coefficient, b, and the Coulomb friction coefficient, c, can be obtained from steady-state step response data, that is from measurements of ω( ) and i a ( ), when a known constant input voltage V i is applied. Explain how (more than one trial will be needed). If we perform two experiments, with following results: V Steady state I a steady state ω A 77.0 rad/s 5 Volts 10 Volts.304 A 163 rad/s what are the values for K τ = K V, b and c (R s is not used in this measurement, R a and L a are as above)? d. The mechanical time constant, and hence the total moment of inertia, J, can be determined by opening the motor circuit (I a = 0), when the motor is rotating, and observing the time-constant of the resulting decay of the motor speed. The situation is shown in Fig

8 D.C. DYNAMICS AND MODELING DATA TABLES The following data is to be collected by hand IN ADDITION to the data to be collected from AgilentVee for MATLAB analysis. Do not forget to indicate units. 1. ARMATURE RESISTANCE AND INDUCTANCE Resistance, R s, of resistor box: Resistance, R a,, of armature :, Smallest: 2. CALIBRATION OF THE TACHOMETER V i Δ t Tach. Voltage 5 Volts 10 Volts 15 Volts Where Δ t is the time the rotor takes for 2π radians of revolution 3. BACK-EMF CONSTANT AND FRICTION COEFFICIENTS V i steady state I a Tach. Voltage 5 Volts 6 Volts 7 Volts 8 Volts 9 Volts 10 Volts These experiments have been submitted by third parties and Agilent has not tested any of the experiments. You will undertake any of the experiments solely at your own risk. Agilent is providing these experiments solely as an informational facility and without review. AGILENT MAKES NO WARRANTY OF ANY KIND WITH REGARD TO ANY EXPERIMENT. AGILENT SHALL NOT BE LIABLE FOR ANY DIRECT, INDIRECT, GENERAL, INCIDENTAL, SPECIAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE USE OF ANY OF THE EXPERIMENTS. 8

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