• Purdue University

• ME 375

ME 375: Systems, Measurement, and Control II

PRELAB 2

Pole Placement Controller Design

LAST REVISED: SPRING 2019

In Lab 2, you will apply feedback compensation to control the angular rotation of a servo table. To

prepare you for that exercise, this prelab assignment familiarizes you with designing a controller

(using direct pole placement), building a standard program for implementing closed-loop control,

and observing the response of a closed-loop system in LabVIEW.

Figure 1: NASA engineers developed feedback controls to permit the speed and location of Martian

rover Spirit to be remotely directed from Earth, at an average distance of around 225 million kilometers.

Before the semester is finished, you will be designing controls for your own autonomous robot! (Image:

NASA)

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ME 375 Prelab 2: Pole Placement Controller Design

Deliverables

You may treat this assignment as you would regular homework; you do not need to use a memo

format. Print out this assignment, write your answers into the designated boxes, and bring these

pages with you to lab so that they might serve as reference material. Carry out the following activities:

D1: Construct a position control VI as described in the steps below. Take a screenshot of your

wiring diagram and submit in PDF format as assignment “Prelab 2 Wiring Diagram” within the

Gradescope course “ME 375 Lab.”

D2: Create a PDF that includes scans of all answer box pages for this prelab assignment, in the

order they are found below. Your PDF file should consist of five pages. Before the start of Lab 2,

submit your PDF file as assignment “Prelab 2” within the Gradescope course “ME 375 Lab.”

Note 1: Entries for all answer boxes requiring a response should be neatly printed (no cursive), so that TAs may

easily evaluate your response.

Note 2: If you fail to print neatly, you may be later asked to transcribe (type out) your answers word-for-word, so

that a TA may score your effort without having to spend undue time interpreting your work. Handwriting is

encouraged so that your solutions are integrated with the prelab procedure, and are available for quick reference

during the lab. (Additionally, research indicates that students better retain what they write by hand.)

Note 3: If you are unable to print neatly by hand, you may type out your solutions—but you must paste your

responses into the answer boxes provided below. Again, Gradescope will be looking for your work to appear in

particular locations on particular pages.

Note 4: For this assignment, you do not need to show your calculations or derivations in the answer boxes, but you

should be prepared to explain your reasoning during the lab, if asked to do so by your TA. You will lose prelab

credit if you are unable to adequately explain your answers.

Design the Position Controller

The feedback loop structure to be used for position control during your upcoming lab period is shown

in Fig. 2. A servo table is represented by transfer function G(s) and your controller by transfer function

C(s).

Figure 2: Closed-loop system block diagram

In Lab 4 of ME 365, you used system identification to develop a 1st-order model relating servo table

input voltage to rotational speed. That model was a transfer function of the form

Gvelocity(s) ˘

K

¿s ¯1

,

where K was the static gain, and ¿ was the time constant. Since position is the integral of velocity, we

can model the servo table position with the transfer function

G(s) ˘

1 s

¢Gvelocity(s).

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ME 375 Prelab 2: Pole Placement Controller Design

Let the plant input be U(s) and the plant output Y (s). Then

G(s) ˘

Y (s)

U(s)

˘

K

s(¿s ¯1)

. (1)

Assume that both reference position R(s) and output position Y (s) have units of degrees. Since

tracking error is defined as E(s) ˘ R(s)¡Y (s), the signal coming out of the summing junction (and

into the controller) is position error E(s), which also has units of degrees. Emerging from the

compensator is control input U(s), in volts. Therefore, transfer function G(s) has units of degrees/volt.

Assume the controller form is

C(s) ˘

U(s)

E(s)

˘

b1s ¯b0

a1s ¯a0

. (2)

This necessitates that transfer function C(s) has units of volts/degree. Since our system has unity

feedback, the closed-loop characteristic equation can be expressed as

DCL ˘ DCDG ¯NCNG ˘ 0.

Applying the appropriate polynomials of s from Eqs. (1) and (2),

DCL ˘ (a1s ¯a0)(¿s2 ¯s)¯(b1s ¯b0)(K)

˘ a1¿s3 ¯(a0¿¯a1)s2 ¯(a0 ¯K b1)s ¯K b0 (3)

Determining the Desired Characteristic Polynomial

Using the background information given above, determine the desired closed-loop characteristic

polynomial by completing the following steps:

1. How many closed-loop poles result from the characteristic polynomial of Eq. (3)? Why?

A