Lab Group Members: Vishuddha Pancholi, Avik Dutta, Jose Junco ​
Instructor: JuhYung Kim
Lab 6: Servo Table Speed Control
April 23, 2025
Vishuddha Pancholi
Lab Group Members: Vishuddha Pancholi, Avik Dutta, Jose Junco ​
Instructor: JuhYung Kim
Abstract
The goal of Lab 6 is to create a proportional speed controller by conducting numerous time and
frequency domain servo table characterization experiments using the myRIO device, a motor
driver box, and an electromechanical servo table. First, the calibration scaling factor was
determined via the encoder counts produced by the physical movement of the servo table. Next,
multiple tests (step response, ramp response, multi-sine) were run to determine the characteristics
of the system. “Dead Zones” were identified by analyzing the system’s ramp response. From
this, a proportional feedback controller could be created to control the speed of the servo table
based on a set point.
Introduction
Servo tables are useful tools for accurately modeling rotational motion, which is a common
component of many real-world engineering systems. They consist of a DC motor that drives a
high-inertia disk through a gear train. Servo Tables operate in closed loops where various
properties such as position, speed, and torque are measured and then sent back. The measured
values are compared to the input command value to generate an error value. The encoder is the
device that collects and evaluates the feedback of these properties. The inner shaft of the motor
spins when the conductive coils within the motor are powered in a specific order. The motor
driver of the servo table follows the input commands. The properties of the system are controlled
by the inputs and the encoder feedback; in addition, the motor driver supplies appropriate
amounts of power to the motor at appropriate times.
Servo Tables consist of an electrical circuit, a motor shaft, and a disk/gear. The circuit’s input
voltage creates a current, which applies torque to the motor shaft, causing it to rotate. The
rotation results in a back-emf voltage in the electrical circuit. Each of the subsystems can be
represented by a transfer function.
𝐺1(𝑠) = 1 / (𝑅𝐴 + 𝑠𝐿𝐴)
Equation 1: Transfer function representing the electrical subsystem
Lab Group Members: Vishuddha Pancholi, Avik Dutta, Jose Junco ​
Instructor: JuhYung Kim
𝐺2(𝑠) = 1 / (𝐽𝐴𝑠 + 𝐵)
Equation 2: Transfer function representing the motor shaft Subsystem
𝐺3(𝑠) = 1 / (𝐽𝐿𝑠 + 𝐵𝐿)
Equation 3: Transfer function representing the disk/gear Subsystem
𝐽 =
2
1
𝑀𝑅
2
Equation 4: Equation for Inertia of Thin Disk
One of the assumptions made for this experiment is that friction and energy loss between
subsystems are negligible. It is also assumed that connections are rigid and inductance is 0.
Materials and Methods
Figure 1: Labeled Picture and Diagram of Servo Table System
Lab Group Members: Vishuddha Pancholi, Avik Dutta, Jose Junco ​
Instructor: JuhYung Kim
First, a sensor calibration was performed to determine a scaling factor that represented the ratio
between encoder counts and servo disk revolutions (𝐶𝑟 ). This was done by manually spinning
the table disk 10 times and recording the number of encoder counts registered.
𝐶𝑟 =
𝐶
𝑁
Equation 5: Equation for encoder scaling factor
Using the calculated scaling factor, the system’s step response was recorded in the time domain.
From analyzing the step response, the time constant and static gain were determined. In the
frequency domain, multi-sine tests were conducted to generate Bode plots, where further
parameters were found. Then, a validation test was run that compared simulated responses to
experimental ones to check the accuracy of the calculated parameters.
The next part of the lab was about implementing a proportional feedback controller for the speed
of the servo table using a Simulink model. The controller was tuned by adjusting parameters
such as the proportional gain. It was also tested how the controller would react to different
disturbances and how different parameter values affected those reactions.
Lab Group Members: Vishuddha Pancholi, Avik Dutta, Jose Junco ​
Instructor: JuhYung Kim
Results
Figure 2: Servo Table Speed vs Time (step response)
Figure 3: Steady State Speed vs Input Data (swept step)
Lab Group Members: Vishuddha Pancholi, Avik Dutta, Jose Junco ​
Instructor: JuhYung Kim
Figure 4/5: Experimental and Measured Bode Diagrams
The Experimental and Measured Data aligned closely until very high frequencies.
Figure 6/7: Model Validation and Error Plot
The Error was relatively low and random, which demonstrates that the model is valid.
Lab Group Members: Vishuddha Pancholi, Avik Dutta, Jose Junco ​
Instructor: JuhYung Kim
Discussion
Dead band range, also known as stiction level, is a region of a system where there is an input but
no output value. The dead band range can affect the accuracy of system identification negatively,
as it adds a large amount of inconsistency between the input and the desired output. A wide
enough dead band region means the system may not respond to small changes in the input, or it
may delay the response if the input signal changes rapidly.
Friction, stiction, backlash, and other nonlinearities distort the servo table system as they result
in inconsistent step response and frequency response data. These inconsistencies lead to
inaccurate calculations of system parameters such as static gain and time constant. Nonlinearities
lead to deadband regions and offsets, this is usually compensated for by raising parameters like
static gain to achieve the desired response in the desired time. Nonlinearities can be mitigated by
introducing procedures such as one-directional multisine tests, which avoid stiction by adding a
constant input.
Time Domain system identification, which utilizes step responses, is better suited for
determining static gain and the time constant quickly when the input is relatively simple. It also
gives a good view of transient and steady-state behavior. Frequency domain identification, using
multisine tests, is ideal when the input behavior is varied across multiple frequencies and
uncovers more about the system’s gain and phase response.
Feedforward control proactively cancels out disturbances, like how the servo table compensates
for friction. It is important because it enhances system performance by compensating for
nonlinearities. Feedforward control often leads to faster abd nire precise responses to inputs.
Feedback control is implemented through a proportional controller and adjusts control input
depending on the error between the actual and desired outputs. If the error is greater then the
change to the input is greater. However, this leads to overshoot of the adjustment, which is why
raising the proportional gain leads to an increase in steady-state error. A low proportional gain
would lead to an unresponsive system that takes considerable time to eliminate errors.
Lab Group Members: Vishuddha Pancholi, Avik Dutta, Jose Junco ​
Appendix
Instructor: JuhYung Kim