MECH 371 Lab 2 (Experiment 2 Determination of Pre-Amplifier Gain, DC Motor Constancy, Time Constant)

MECH 371 Lab #2 (Experiment 2: Determination of Pre-Amplifier Gain, DC Motor Constancy, Time Constant) 2025-2026 Concordia University Experiment 2: Determination of Pre-Amplifier Gain, DC Motor Constancy, Time Constant

Submitted by

Lab Section AI – X Fall 2025 Professor Wen-Fang Xie

Concordia University Montreal, QC, Canada

Table Of Contents Table Of Contents ..................................................................................... 2 List of Figures........................................................................................ 3 List of Tables .......................................................................................... 3 Objective ............................................................................................ 4 Introduction ......................................................................................... 4 Procedure ........................................................................................... 5 Exp 1 ............................................................................................... 5 Exp 2 ............................................................................................... 6 Experimental Results ................................................................................ 7 Experiment 1....................................................................................... 7 Experiment 2....................................................................................... 9 Discussion ......................................................................................... 12 Sources of Error ................................................................................. 12 Conclusion......................................................................................... 12 References ........................................................................................ 13 Appendix .......................................................................................... 14

List of Figures Figure 1:Preamplifier PA150C [1] .................................................................. 4 Figure 2: Servoamplifier SA 150D [1] .............................................................. 5 Figure 3: Input Vs Output Voltage ................................................................. 8 Figure 4:Experimental Results for Exp 2 for V Function Generator +2V ......................... 9 Figure 5: Experimental Results for Exp 2 for V Function Generator -2V ......................... 9 Figure 6: Matlab Simulation Results ............................................................. 11 Figure 7: Simulink Model ......................................................................... 14 Figure 8: Simulink Code .......................................................................... 15

List of Tables Table 1: Experimental Input vs Output Data ...................................................... 7 Table 2: Experiment 2 Data ....................................................................... 10

Objective The objective of this lab is to become familiar with DC motor modules, amplifiers and tachometers by

verifying

DC

motor

characteristics,

pre-amplifier

gain

calibration

and

servo-

amplifier/tachometer gain [1].

Introduction The Preamplifier PA150C is a control amplifier which can compensate for the deadband voltage and provide a fixed gain Kp [1]. This equipment has two summing input terminals and two output terminals [1]. A positive input will yield an amplified positive output in the upper terminal, with the lower terminal remaining near zero, and a negative input yields an amplified positive output in the lower terminal, and a near zero output in the upper terminal [1]. This allows the motor to change direction when the output is connected to the servo-amplifiers input based on the polarity of the Preamplifier [1]. To calibrate, both outputs must be equal when no input is provided which can be adjusted using the zero-set controller [1].

Figure 1:Preamplifier PA150C [1]

Deadband is a phenomenon caused by mechanical friction in which the motor exhibits no response until a certain input voltage threshold is met [1]. The deadband voltage is referred to as Vd while the input voltage is referred to as Vm [1]. This deadband value prevents the motor from behaving linearly and thus a bias voltage Vb is introduced at a slightly lower value than the deadband voltage as to not activate the motor [1].

The Servoamplifier SA150D is the amplifier which drives the motor using two input terminals on the left-hand side which only accept positive voltages [1]. One input terminal produces a forward motor rotation while the other one reverses it [1].

Figure 2: Servoamplifier SA 150D [1]

The DC Motor DCM150F is coupled with a Reduction Gear Tacho Unit GT150X with a highspeed input along with a 30:1 gear reduction using a worm gear connecting the input and output shafts [1]. The output shaft is then coupled with an output potentiometer which allows one to monitor the speed in rpm or external DC voltage [1]. The motor is controlled by the power amplifier PA150C and the transfer function can be written as follows: 𝐺 (𝑆) = 𝑃

𝜔𝑚 𝑉𝑚

=

𝐾𝑚

, [1]

1+𝑆𝜏𝑚

where ωm is the output angular velocity, Vm is the motor input voltage, Km is the motor gain constant, and τm is the electro-mechanical time constant [1].

Procedure Exp 1 Connect a 0V signal to both inputs while monitoring both outputs using the oscilloscope. Ensure both output signals have the same voltage by adjusting the zero-set knob. The voltages should be within a 1.0-1.5V range and is to be recorded as the bias voltage.

Set up the attenuator AU150B to obtain a small voltage signal circuit. By adjusting the top knob to about 1.6V, the bottom knob will be set into a range of 0-1.5V. A negative value can also be achieved by using the -15V connection as opposed to the +15V connection.

Make the necessary connections between the power supply, pre-amplifier, attenuator, and oscilloscope. Use the bottom attenuator knob to adjust the voltage from 0-1.5V and record the necessary data into the lab manual. Swap the +15V terminal connection to the -15V terminal and record the necessary data using the bottom attenuator knob once more.

Exp 2 Set function generator to square signal and set frequency to 0.3Hz, HiLevel to 2.0V, LoLevel to 0V, and offset to 1.0V. Make the necessary connections between the power supply, function generator, servo-amp, and oscilloscope. Adjust the oscilloscope to properly see full cycles from the function generator.

Run the motor and ensure that it comes to a stop for every cycle. Stop the scope of the oscilloscope when a motion cycle is on screen. Use the oscilloscope cursors to find the highest and lowest voltages of the cycle and find the difference between them. Calculate 63.2% of the difference to find the voltage value of the time constant and move the cursor on the right to the proper voltage value to find the time constant in milliseconds. Fill in the necessary information into the lab manual, connect the function generator to terminal 2 of the servo-amp, and repeat the steps.

Experimental Results Experiment 1

Input Terminal

CH1 Input Voltage

Output Terminal

CH2 Output Voltage

1

-1.5

4

13.7

1

-1.19

4

13.7

1

-1

4

12.3

1

-0.803

4

10.5

1

-0.6

4

8.16

1

-0.41

4

6.43

1

-0.2

4

4.08

1

0.1

1

0.21

3

1.18

1

0.399

3

3.2

1

0.6

3

5

1

0.798

3

7.32

1

1

3

9.16

1

1.21

3

11

1

1.5

3

13.7

Table 1: Experimental Input vs Output Data

0.9

Figure 4: Input Vs Output Voltage 16

14

12

Axis Output Voltage (V)

10

8

6

4

2

0 -2

1.5

-1

0.5

0

Input Voltage (V)

Figure 3: Input Vs Output Voltage

0.5

1

1.5

2

Experiment 2

Figure 4:Experimental Results for Exp 2 for V Function Generator +2V

Figure 5: Experimental Results for Exp 2 for V Function Generator -2V

1. From the recorded table and plot, get average time constant.

V Function Gen.

Vin (CH1) 3.36 V 3.36 V

0-2 V -2-0V

Tachometer (Vt CH2) 6.55 V -6.55V

Time Constant (𝜏𝑚) 130 ms 130 ms

Table 2: Experiment 2 Data

Sample calculation of the time constant for 0-2V: 𝑉𝑡(𝜏𝑚) = 0.632 𝑉𝑡(∞) 𝑉𝑡(𝜏𝑚) = 0.632 × 6.55 𝑉𝑡(𝜏𝑚) = 4.1396 𝜏𝑚 = 𝑡(4.1396)

⇒ 𝜏𝑚 = 130 𝑚𝑠 2. Find servomotor gain from the final value and input square-wave amplitude. 𝑉𝑡 𝐾𝑚 = 𝑉𝑖𝑛 × 𝐾𝑡 Since 𝐾𝑡 =

𝑉𝑡 𝜔𝑡

𝐾𝑚 =

𝑉𝑡

𝑉𝑡 𝑉𝑖𝑛 × 𝜔 𝑡

6.55 𝑉 𝐾𝑚 = 6.55 𝑉 3.36 𝑉 × 325 𝑟𝑎𝑑⁄𝑠 ⇒ 𝐾𝑚 = 96.726 𝑟𝑎𝑑⁄𝑠. 𝑉

3. Using above obtained parameters to simulate the DC motor Matlab Simulink

Figure c: Matlab Simulation Results

Discussion Sources of Error A source of error that is predominant in these experiments is the motor deadband which is due to static friction. The Pre-amplifier gain, and servo-amplifier gain are calibrated to fix this issue by offsetting the deadband. Unfortunately, there still exists this problem which in turn affects the experimental data collected. Another source of error is adjusting the input voltage reading by hand for the given values. It is quite difficult to get an exact reading for the input which is turn gives an output voltage that is also varied by a slight difference which affects the results of the experiment. This can be due to human error for not finding the exact values but also it is difficult to achieve this due to human error. Using more calibrated and accurate equipment to mitigate this would help.

Conclusion In conclusion the output voltage recorded compared to that of the input voltage follows the Vshape characteristic that indicates the preamplifier is well balanced. Given small inconsistencies due to sources of error, the general shape was achieved in our experiment. For the second experiment the Matlab generated follows the same pattern and shape as our experimental data collected as well. Overall the experiment was a success with a minimal margin of error due to equipment inaccuracies and slight human errors.

References [1] Department of Mechanical, Industrial, and Aerospace Engineering, MECH 371 Laboratory Manual, “Analysis and Design of Control Systems”, Concordia University, Montreal, Fall 2025.

Appendix

Figure 7: Simulink Model

Figure 8: Simulink Code