Notes by a friend for Systems - 5ESB0, kept with the 5ESC0 friend notes
Laplace Transform (friend) - 5ESC0
Differential Equations
Topic: Differential Equations
2nd order DE:
Homogeneous solution:
- 2 roots:
- 1 root:
signal_block.png (not included in the repository)
Block signal:
: step response
: impulse response
u(t): input
Relationship between unit impulse and unit step
Partial fraction expansion
feedback_loop.png (not included in the repository)
Dynamic Response
Step response:
undamped natural frequency
damping
Poles:
Typical 2nd order transfer function:
Properties:
Rise time
:
Peak time:
Overshoot:
Settling time:
Theorem
Final value:
Initial value:
Zeroes:
Step response
of is derivative of of
Feedback Control
Topic: Feedback and Stability
Transfer function shortcuts:
Open:
Closed:
d: load disturbance
n: measurement noise
u: controlled variable
x: physical output
y: measured output (with noise)
F: feed forward
C=D: controller
P=G: plant (controllee)
Stability
Change root of denominator
Sensitivity
Open:
Closed:
System Type & Steady State Error
System type k:
PID
Topic: Controller Design
Second-order:
P
PI
: zero steady state error for step input - 1st-order
- Disturbance rejection:
reject constant disturbance
PD
2nd-order
