P, PI, Lead, Lag Compensators
Transcript of P, PI, Lead, Lag Compensators
P, PI, Lead, Lag compensators
Control engineering and signal processing
Michala Srnová2009/2010
Content Compensator P compensator PI compensator Lead compensator Lag compensator PID controller
Compensator Additional component Compensate a deficient performance Alter of root locus or frequency response Suitable place
Compensator II Classical compensators
P PI PID Lead Lag PD/Lead Lag/Lead
P compensator Proportional control Transfer function
Frequency independent Steady state problems Stability problems Error multiplication → small fluctuation of error signal
→ great changes of control signal
P compensator Step response
Steady state error or oscillations Not often used alone With connection with integral part (PI) or in PID
PI compensator Proportional + Integral compensator
Ki – integral gain Changes type of the system No steady state error to step Can make system slower
PI compensator II Frequency response
Ti = Kp/Ki
High-frequency attenuator PI introduce a phase lag !
Lead compensator Lead phase → phase of compensator +
Lead: |z| < |p|
Lag compensator |z| > |p|
PI
Lead and Lag Compensators Alter of frequency response Calculations
Definition of α, ωm ,τ
Transfer function
Calculation for maximum phase angle ( ω=ωm)
System gain = -10 log α → frequency = ωm
System with comp.: gain = 0 db by frequency ωm
PID controller Proportional + integral + derivative
Transfer function:
KD – derivative gain
Used in majority of closed-loop industrial processes
PID controller Step response
Rise time Overshoot Settling Time Steady state Error
Effect of increasing the parameters:
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