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Control Systems (controllers (Phase-lag (PI compensator (infinite gain at…
Control Systems
controllers
Phase-lead
increase phase margin
|pole| < |zero| (slow pole + fast zero)
Phase-lag
increase low frequency gain, deteriorates phase margin
|zero| < |pole| (slow zero + fast pole)
PI compensator
infinite gain at zero frequency => |T(0)| -> 1 => perfect ref track for a step ref)
Lead-lag PID
lag for low freq + lead around crossover
Proportional gain
same gain across all frequencies
Linearisation
Taylor expansion
equilibrium
closed-loop system
stability
Routh Array
Root Locus
Nyquist Plot
relative stability
gain margin
phase margin
sensitivity peak
sensitivity functions
Output sensitivity
= Y/D_out = Error/Ref
sensitivity peak = max(|S|) = relative stability
Complementary sensitivity
= -Y/D_measure = Y/Ref
robustness
small gain theorem
Input sensitivity
= Y/D_in
Control sensitivity
= -U/D_out = -U/D_measure
actuator saturation
Time domain responses
construction
impulse
convolution
analysis
pole
decay rate
oscillation
zero
undershoot/overshoot
Laplace Transform
what it really means
vector space explanation
centre of mass explanation
Design
loop shaping
fundamental limitation
bounds on loop gain crossover freq
ref-tracking/output disturbance rejection
D_measurement rejection/robustness
actuator saturation
structural limitation
delays
interpolation constraints
open-loop p/z find their way into sensitivity funcs
internal model principle
generating polynomail
ref tracking
disturbance rej
integral constraints
overshoot/undershoot
conservation of sensitivity dirt
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