Voltage Control System: Proportional Integral (PI) Controllers Team Purple: John Pangle Jessica Raymond Justin Whitt ENGR 329 November 30, 2005

Outline Voltage System Background Previous Work: SSOC, Step, Sine, Bode, P-Only PI Model Results PI Experimental Results Conclusions Luyben Method Review Recent Results Conclusions

Purple Team 9/14/05 Voltage System Schematic

Block Diagram M(t) is measured in % and C(t) is in Volts.

Purple Team 10/25/05 Operating Range: Output = 50V to 140V Operating Range: Input = 70% to 100% 75%-100% Input Slope = 2 V/%

Background: Step Input Voltage System K – Gain (Volt/%) t 0 – Dead Time (s) τ – Time Constant (s)

Background: FOPDT Fit

FOPDT Model

Background: Sinusoidal Input K – Gain (Volt/%) t 0 – Dead Time (s) τ – Time Constant (s)

Values taken from Point A  AR = 1.5  f = 4 Hz Bode Plot  K = 2 V / %   = 0.04 sec  t o = 0.08 sec

Background: Sinusoidal Input

Background: FOPDT Averages

Background: Feedback Loops Kc 1 0   s Ke st  R (volts) E ( ) M (%) C (volts) + - CE =

Background: P-Only Controllers

PI Controllers

PI Controllers (Kc = 0.8)

PI Controllers (Kc = 0.5)

PI Controllers (Kc = 0.4)

PI Controllers (Kc = 0.2)

PI Controllers (Kc = 0.1)

PI Controllers (Kc = 0.05)

PI Controllers

τIτI

Conclusions Recommend PI over P-only Recommend τ I = 0.1 Yields widest range of desirable decay ratios. Provides acceptable settling times.

Luyben Method Presented by William L. Luyben, Ph.D at Reno AIChE Meeting Nov. 6, 2001

Luyben Method 1.Insert relay into feedback loop. Relay 1 0   s Ke st  R (volts) E ( ) M (%) C (volts) + -

Luyben Method 2.Specify upper & lower limits of m(t)

Luyben Method

3.Find T u from c(t) 4.Calculate K cu

Luyben Method

What about t o and τ? I still have to run another test right?

Luyben Method

F=1 for Voltage System t o /τ = 2

Luyben Method t o = 2τ τ = 0.01 and t o = 0.02

Luyben Method

Conclusion Only one simple test required (7 steps) Works well for any order systems Similar Results to Bode