Class Notes (904,290)
US (350,055)
UC-Irvine (14,123)
Lecture 1

ENGRMAE 106 Lecture 1: MAE106_s2016_lab5

7 Pages

Engineering, Mechanical and Aerospace
Course Code
David Reinkensmeyer

This preview shows pages 1 and half of page 2. Sign up to view the full 7 pages of the document.

Loved by over 2.2 million students

Over 90% improved by at least one letter grade.

Leah — University of Toronto

OneClass has been such a huge help in my studies at UofT especially since I am a transfer student. OneClass is the study buddy I never had before and definitely gives me the extra push to get from a B to an A!

Leah — University of Toronto
Saarim — University of Michigan

Balancing social life With academics can be difficult, that is why I'm so glad that OneClass is out there where I can find the top notes for all of my classes. Now I can be the all-star student I want to be.

Saarim — University of Michigan
Jenna — University of Wisconsin

As a college student living on a college budget, I love how easy it is to earn gift cards just by submitting my notes.

Jenna — University of Wisconsin
Anne — University of California

OneClass has allowed me to catch up with my most difficult course! #lifesaver

Anne — University of California
MAE106 Laboratory Exercises Lab # 5 PD Control of DC motor position University of California, Irvine Department of Mechanical and Aerospace Engineering Goals Understand how to implement and tune a PD controller to control the position of a DC motor. Explore the frequency response of the PD controller by testing how it responds to sinusoidal inputs of different frequencies. Parts & equipment Qty Part/Equipment 1 Seeeduino board 1 Motor driver 1 DC motor with encoder Introduction to PD Control The most common controller used by engineering designers to control the movement of a motorized part is the PD (proportional-derivative) controller (sometimes an integral control term is added to create a PID controller, but we will not explore I control in this lab). In this lab you will implement a PD position controller. Such controllers are also used in robot arms, radars, numerically controlled milling machines, manufacturing systems, and control surfaces on aerospace vehicles. The PD control law is: 𝜏 = −𝐾 𝑝𝜃 − 𝜃 𝑑 − 𝐾 𝑑𝜃 − 𝜃 𝑑 where: 𝜃𝑑 desired motor angular position 𝜏 desired motor torque 𝜃̇ desired motor angular velocity 𝐾𝑝 proportional gain 𝜃𝑑 actual motor angular position 𝐾 derivative gain ̇ 𝑑 𝜃 actual motor angular velocity Note that the controller has two terms – one proportional to the position error (the “P” part), and one proportional to the derivative of position (i.e. velocity, the “D” part). Thus, it is called a “PD” controller. The implementation of this controller for a DC motor with inertia, J, is shown in Figure 2. Figure 1. Block diagram that you will implement to make the PD controller for the motor. J is the inertia of the motor shaft. To understand how the actual system behaves we need to first understand its dynamics. First, let's look at the dynamical equation that describes how θ evolves with time when the controller is attached to the motor. Dynamics of the motor and shaft: 𝜏 = 𝐽𝜃 ̈ Dynamics of the controller system: 𝜏 = 𝐽𝜃 = −𝐾 (𝜃 𝑝 𝜃 ) − 𝑑 (𝜃 − 𝑑 )̇ 𝑑 Re-writing to make input-output clear: 𝑱𝜽 + 𝑲 𝜽 + 𝑲 𝜽 = 𝑲 𝜽 + 𝑲 𝜽 𝒅 𝒑 𝒅 𝒅 𝒑 𝒅 This differential equation has similar dynamics to a mass-spring-damper system with Force as the input and Position as the output. That is, it follows the same equations of motion. This allows us to use our intuition about mass-spring-damper systems when designing and tuning a PD controller. Recall that the differential equation of motion for a mass-spring-damper system is given by: 𝑚𝑥̈ + 𝐵𝑥̇ + 𝐾𝑥 = 𝐹 and thus using the analogy to the PD controller we have that: mass-spring-damper system PD controller m mass J motor inertia B damper 𝐾𝑑 derivative control term K spring 𝐾𝑝 proportional control term F input force 𝜏 desired motor torqueIn a mechanical system, if you wanted the system to respond more quickly, you would increase the natural frequency (ω ) ny picking a stiffer spring (higher K). Which variable would you change in your differential equation for the PD system to make your system respond more quickly (i.e. increase its natural frequency)? Note: there is a limit to how big you can make this variable because of the time delays in this sampled data system. By adding the derivative gain (K ) do control the position of the motor we must now take into account the concept of damping when designing and implementing the controller. With damping in the controller we can have four types of behaviors: Undamped (i.e. zero damping): The system oscillates at its natural frequency. These oscillations are a function of the controller's gain, Kp. Underdamped: The system will move to its desired position and oscillate about this position with is oscillations gradually decreasing to zero. Critically damped: The system will move to its desired position as quickly as possible without oscillating. Overdamped: The system will move asymptotically towards its desired position without oscillating, but at a slower rate than the critically damped case. Suppose you didn’t want your motor to oscillate too much. This is an important issue! You usually want your motor to go to a desired value quickly and accurately without oscillating. You will have to change the derivative gain K untid you get the system to be critically damped.Yellow Pin 2 White Pin 3 01 01IN. OTINr OICS OGND Pololu MDO3A O.SVEINI Dual VNH25P 30 OVIN I O2PWM O2IN. O2INs Blue 5V Green GND 12V power supply fritzing Yellow Pin 2 White Pin 3 01 01IN. OTINr OICS OGND Pololu MDO3A O.SVEINI Dual VNH25P 30 OVIN I O2PWM O2IN. O2INs Blue 5V Green GND 12V power supply fritzingPart I: Step response of the actual system Construct the Arduino circuit in Figure 2. Download the code for this lab from the website and run it on the Arduino. As in previous labs, when you open the Serial Monitor (or when you press the 'reset' button on the Arduino), the code will re-initialize, then run a step response and send time, position, and desired position of the motor to the monitor for the duration of the response. You can copy and paste this into
More Less
Unlock Document

Only pages 1 and half of page 2 are available for preview. Some parts have been intentionally blurred.

Unlock Document
You're Reading a Preview

Unlock to view full version

Unlock Document

Log In


Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.