Week

Lecture Topic

Reading
Assignment

Book Homework and Laboratory Exercise Assignments

1
(8/26 - 8/30)

• course introduction
• closed loop control
  • PID control
  • video demonstrations
• MatLab introduction
• Lab 1 Hints

Course Policies,
Ch 1

group selection survey sheet
(if group members already chosen, please turn in sheets stacked together)
due Fri, 8/30

Lab 1 - MatLab (individual)
due Fri, 9/6

2
(9/2 - 9/6)

Labor Day (no class on Mon, 9/2)

Laplace Transform Approach

• properties
• LTI systems
• transfer functions
• partial fraction expansion
• inverse transform
  

App. B

HMWK 1 (App B and MatLab):
B.1 b, c, d (do b and c by hand;
use integration by parts for c);
B.2 a, c, e, g
(for e use cosine sum trig identity;
do g for a, c, e only);
B.3 a, b, e (for b, see Equations
B-12 and B-13; do e for a and b only);
B.10 (use Laplace techniques;
a constant forcing function is a
step function starting at time=0;
use Equation B-13 to handle repeated roots)
scan of Appendix-B Questions

NOTE - for B.3 and B.10, use partial fraction expansion to reduce the transfer functions to their most basic forms before using Appendix C
due Fri, 9/13

3
(9/9 - 9/13)

• ODE solution
• Simulink introduction

Modeling

• electrical systems modeling
  • basic R, L, C circuits
  • op amp circuits
• mechanical system modeling
  • spring-mass-damper systems
  • rotational systems
• block diagrams
• closed loop equations
  

2.1 - 2.3;
2.5 - 2.6

Lab 2 - Simulink (individual)
due Fri, 9/20

4
(9/16 - 9/20)

• servomotor modeling example
• signal flow graphs
• Mason's gain formula
• servomotor speed control simulation
  

2.4, 2.7, 2.12

HMWK 2 (Ch 2):
2.4 (Remember that the Laplace Transform of a unit step input is 1/s);
2.5 (Remember that for an ideal op amp, the input currents are zero and the input voltages are equal. Assume ideal op amps.);
2.11 a, b, e (for a, have the source node be 1 and create constants as branches from this single node);
2.17 b; 2.18 b;
2.25 c, d, e (Use the block diagram and definitions for G₁, G₂, G₃, and H provided in class during the solution to parts a and b. Note - the answer in the back of the book for part c is incorrect. The numerator should be G₁G₂.);
2.32 (use Equation 2-13 wherever possible, and be sure to express your final answer in standard and simplified rational-polynomial form)
due Fri, 9/27

5
(9/23 - 9/27)

System Response

• first-order system
• step response
• second-order system
  • pole locations
  • time response specs
  • frequency response

4.1 - 4.4

HMWK 3 (Ch 4):
4.2 (for b, use the closed-loop K and τ parameters for the sketch)
4.5 (for the sketch, calculate and label all time-response specs that define the shape of the response curve),
4.12 (for f, use tf and step),
4.20 (for a, express in standard second order system form; for e, use freqs, and abs, and plot over a frequency range of 0 to 5 with an increment of 0.1)
due Fri, 10/4

6
(9/30 - 10/4)

Control System Characteristics

• closed loop system
• stability
• sensitivity
• disturbance rejection
• steady state accuracy
  

Ch 5

HMWK 4 (Ch 5):
5.2, 5.4 [instead of parts a and b, determine stability conditions (ranges of values for parameters "a" and "b") for the closed-loop system, not the plant; in part d, repeat part c, not part b],
5.10 (in part e, replace "plotting" with "sketching, using part d and values at ω=∞"),
5.20
due Fri, 10/11

7
(10/7 - 10/11)

Stability Analysis

• Routh-Hurwitz criterion
• special cases
• auxiliary polynomial

Exam I Review

Ch 6

HMWK 5 (Ch 6):
6.1, 6.2 (use the conditions and special cases presented in class),
6.15 (Note - the plant transfer function in the book is wrong. It should be: 0.475 / (s(s^2 + 6s +7.5). In 6.15c, "Steady state oscillation" means "on the verge of instability," where a pole is imaginary -- giving a sinusoidal response --and the 1st column of the Routh Array is on the verge of a sign change. To simulate a PD compensator in Simulink, you can use a PID block, but you must double-click on the block and change the Filter Coefficient (N) from 100 to 1000 to limit its effect.)
due Wed, 10/16

8
(10/14 - 10/18)

Root Locus Technique

• open loop function
• graph features
• angle criteria
• graph construction techniques
• asymptotes
  

7.1 - 7.2

HMWK 6 (Ch 7):
7.6,
7.7 (for f, in verifying b-e, plot step response for an example K value in each range to verify the expected types of response),
7.8
due Wed, 10/30

9
(10/21 - 10/25)

EXAM I - Mon, 10/21
(come early and/or stay late if possible?)

• breakaway points

Frequency Response Techniques

• frequency response

7.3 - 7.5

Lab 3 - Hardware Experiments -
PID control and frequency response
(group)
due Wed, 11/6

The hardware is in Engrg B8, which is open to MECH417 students (via card-reader access) all days and times.

10
(10/28 - 11/1)

• Bode Diagram
  • magnitude plot
  • phase plot

• Nyquist criterion

8.1 - 8.3

11
(11/4 - 11/8)

• Nyquist diagram
• relative stability (gain and phase margins)
• poles at the origin

8.4 - 8.6

HMWK 7 (Ch 8):
8.1; 8.7;
8.12 a, b, c (for b, see Section 8.3.2; also, the "a" in the exponential should be an "s");
8.16
due Wed, 11/13
(WARNING: please start
this HMWK early)

12
(11/11 - 11/15)

Exam II Review

Frequency Response Design

• phase-lag compensation
• phase-lead compensation

9.1 - 9.7

13
(11/18 - 11/22)

EXAM II - Mon, 11/18
(come early and/or stay late if possible?)

• PI controller
• PD controller
• PID controller

No class on Fri, 11/22 (unless catch-up day required)

9.8 - 9.12

HMWK 8 (Ch 9):
9.2 (for part "a," just use the closest appropriate table values instead of interpolating);
9.3 (Note - the "disturbance torque" is zero for this problem. As indicated, use Hk=1 for the "Sensor," not the 0.03 shown in the block diagram. For part "d," use MATLAB instead of Simulink and right click on step response plot to add "Characteristics.");
9.4; 9.15 (Note - Figure P9.15 is slightly different from Figure P2.32, so if you use your earlier work from Question 2.32, be sure to modify it to account for the change in Figure P9.15);
9.20 a, d (also determine the expected vs. actual settling time; do part "d" for "a" only);
9.24 (Use Hk=1, as in 9.3. Use a phase-margin frequency of 5 rad/sec. Determine both the estimated and actual settling time. Part "e" should read: "In general, reducing Ki decreases settling time. In those cases, why would an integrator term still be used?")
due Wed, 12/4
(WARNING: please start
this HMWK early)

14
(11/25 - 11/29)

15
(12/2 - 12/6)

• pole balancer case study

State Variable Models and Modern Control

• state-space system

App. A;
3.1, 3.2;
10.1, 10.2

HMWK 9 (Ch 3):
3.2 a, b; 3.4 a, b
due Mon, 12/9

16
(12/9 - 12/13)

• pole placement
• Ackerman's Formula
• controller implementation options

Final Exam Review

No class on Friday, 12/13

final group evaluation
(due Wed, 12/11)