**original table-formatted syllabus**

**Week**

**1**

(8/26 – 8/30)

**Lecture Topic**

- course introduction
- closed loop control
- PID control
- video demonstrations

- MatLab introduction
- Lab 1 Hints

**Reading**

Course Policies,

Ch 1

**Homework and Lab**

**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**

**Week**

**2**

(9/2 – 9/6)

**Lecture Topic**

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

*Laplace Transform Approach*

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

**Reading**

App. B

**Homework and Lab**

**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**

**Week**

**3**

(9/9 – 9/13)

**Lecture Topic**

- 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

**Reading**

2.1 – 2.3;

2.5 – 2.6

**Homework and Lab**

Lab 2 – Simulink (* individual*)

**due Fri, 9/20**

**Week**

**4**

(9/16 – 9/20)

**Lecture Topic**

- servomotor modeling example
- signal flow graphs
- Mason’s gain formula
- servomotor speed control simulation

**Reading**

2.4, 2.7, 2.12

**Homework and Lab**

**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 G_{1}, G_{2}, G_{3}, 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 G_{1}G_{2}.);**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**

**Week**

**5**

(9/23 – 9/27)

**Lecture Topic**

*System Response*

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

**Reading**

4.1 – 4.4

**Homework and Lab**

**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**

**Week**

**6**

(9/30 – 10/4)

**Lecture Topic**

*Control System Characteristics*

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

**Reading**

Ch 5

**Homework and Lab**

**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**

**Week**

**7**

(10/7 – 10/11)

**Lecture Topic**

*Stability Analysis*

- Routh-Hurwitz criterion
- special cases
- auxiliary polynomial

Exam I Review

**Reading**

Ch 6

**Homework and Lab**

**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**

**Week**

**8**

(10/14 – 10/18)

**Lecture Topic**

*Root Locus Technique*

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

**Reading**

7.1 – 7.2

**Homework and Lab**

**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**

**Week**

**9**

(10/21 – 10/25)

**Lecture Topic**

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

**Reading**

7.3 – 7.5

**Homework and Lab**

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.

**Week**

**10**

(10/28 – 11/1)

**Lecture Topic**

- Bode Diagram
- magnitude plot
- phase plot

- Nyquist criterion

**Reading**

8.1 – 8.3

**Week**

**11**

(11/4 – 11/8)

**Lecture Topic**

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

**Reading**

8.4 – 8.6

**Homework and Lab**

**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)**

**Week**

**12**

(11/11 – 11/15)

**Lecture Topic**

Exam II Review

*Frequency Response Design*

- phase-lag compensation
- phase-lead compensation

**Reading**

9.1 – 9.7

**Week**

**13**

(11/18 – 11/22)

**Lecture Topic**

**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)**

**Reading**

9.8 – 9.12

**Homework and Lab**

**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)

this HMWK early)

**Week**

**14**

(11/25 – 11/29)

**Thanksgiving Break (no classes)**

**Week**

**15**

(12/2 – 12/6)

**Lecture Topic**

- pole balancer case study

*State Variable Models and Modern Control *

- state-space system

**Reading**

App. A;

3.1, 3.2;

10.1, 10.2

**Homework and Lab**

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

**Week**

**16**

(12/9 – 12/13)

**Lecture Topic**

- pole placement
- Ackerman’s Formula
- controller implementation options

Final Exam Review

**No class on Friday, 12/13**

**FINAL EXAM (in same room as lectures) – Wednesday, December 18, 7:30-9:30am**