Lecture 1 Notes
Active learning if an important part of the class. Come prepared to learn, think, contribute every class.
Text is Franklin, Powell, Emami-Naeni, Feedback Control of Dynamic Systems, 5th Edition.
Note: NOT 4th editi
Lecture 5 Notes
Usually, we nd the response of a system using Laplace techniques. Often, do within Matlab.
Example: DC Motor.
J 0.01 kgm2 ; b 0.001 N-m-sec
Kt Ke 1 n-M/A 1 V/
(rad/sec) Ra 10, L 1 H
s3 ` 10.1s2 ` 101s
Lecture 2 Notes
Reasons for using automatic control:
Perform tasks people cant
Reduce the eects of disturbances
Reduce the eects of plant variations
Stabilize an unstable system
Improve the performance of a system (time response)
Lecture 4 Notes
Block Diagram Manipulations:
G1 + G2
The gain of a single loop feedback
sys-tem (with sign -1 in the loop)
forward gain divided by the sum of
1 plus the loop gain.
Lecture 6 Notes
Time Domain Specications:
Many control systems are dominated by a second order pair of poles. So look at time
response (to step input) of
s2 ` 2nn s+n
Time, t (sec)
Lecture 3 Notes
1. Identify the states of the system:
2. Use physics to nd dx1 cfw_dt, dx2 cfw_dt,.
3. Organize as:
f px, uq
y gpx, uq
Lecture 8 Notes
The Routh Stability Criterion
Suppose we have a transfer function
Y psq b0 sm ` b1 S m1 ` . `
bm Rpsq sn ` a1 sn1 ` .
We can always factor as
The closed-loop system is stable if
Rppi q 0, @ i
NB: It might turn out
Lecture 10 Notes
A common way to design a control system is to use PID control.
PID = proportional-integral-derivative
Will consider each in turn, using an example transfer function
s2 ` a1 s ` a2
Proportional (P) control
Lecture 9 Notes
Unity Feedback Control With Noise
Consider a typical unity feedback control system
disturbance controller plant
e1 is the error perceived by the control system; e is the actual error. The important
Lecture 7 Notes
Eects of Zeros on Step Response
Weve looked at the response of a second-order system:
s2 ` 2(nn s+n
What if we had a zero in the numerator? How would that change the response? Consider:
1qn s2 `
2( n s+n
The step response is t