Proportional Integral Differential (PID) Control

ProportionalIntegralDifferential (PID) Control Proportional Control Equation Example PI Control Equation Numerical Integration Example PID Control Web Simulation Equation Numerical Differentiation A 3-mode opamp controller Industrial PID tuning Summary

Proportional Control-1 Error Output + Input signal Actuator (Plant) Controller e r - b Transducer Feedback Signal

Proportional Control-2 Error Output + K G e r p - b H

Proportional Control-3 Error Output + K G=8 e r p - b H=1/8

Proportional Control-4 Error Output + K=1/4 G=4 e r K=4 G=4 p - b H=1 H=1

PC-5 + ep kp p + Output Proportional controller p0 Setpoint In terms of % of span In units of the output

9.8 For a proportional controller, the controlled variable is a process temperature with a range of 500 to 1300C and a setpoint of 73.50C. Under nominal conditions, the setpoint is maintained with an output of 50%. Find the proportional offset that results from a load change which requires a 55% output if the proportional gain is (a) .1 (b) .7 (c) 2.0 and (d) 5.0 PC-6 In terms of % of span Output Temperature= • T=33.50C • (d) T=72.70C In units of the output

High heat load: air conditioner takes a while to bring temp down. PC-7 Red-line is On-Off Control (furnace on at 60) (air conditioner on at 80) Green-line is Proportional Control: above 70 air- conditioner fan speed increases proportional to the T-700 Cold wind: heater takes a while to bring temp up. Green-line is Proportional Control: below 70 amount of furnace gas increases proportional to the 700 – T. Time of day http://www.fourmilab.ch/hackdiet/www/subsection1_2_3_0_5.html

PC-8 On-Off Control http://newton.ex.ac.uk/cgi-bin/metaform?http://newton.ex.ac.uk/teaching/CDHW/Feedback/OvSimForm-gen.html Proportional Control

Proportional-Integral (PI) Control http://newton.ex.ac.uk/cgi-bin/metaform?http://newton.ex.ac.uk/teaching/CDHW/Feedback/OvSimForm-gen.html

Proportional-Integral-Derivative(PID) Control http://newton.ex.ac.uk/cgi-bin/metaform?http://newton.ex.ac.uk/teaching/CDHW/Feedback/OvSimForm-gen.html

PI, PD, and PID Composite Mode Equations PI PD PID CONTROLLER TUNING AND CONTROL LOOP PERFORMANCE, A PRIMER, SECOND EDITIONSubtitled PID WITHOUT THE MATHby David W. St. Clair http://members.aol.com/pidcontrol/booklet.html

Example 9.8 in text Equation: percent

Ex 9.8 +20% would just raise the PI curve.

Simple Numerical Integration 3 Calculations: .1*1 +0=.1 .1*2+.1=.3 .1*3+.3=.6 .1*3+.6=.9 .1*3+.9=1.2 etc. volts 2 1 0 0 0.1 0.2 0.3 0.4 seconds

PID Example

Numerical Derivative 3 Calculations: (1-0)/(1-0)=1 (2-1)/(2-1)=1 (3-2)/(3-2)=1 (3-3)/(4-3)=0 (3-3)/(5-4)=0 etc. volts 2 1 0 0 1 2 3 4 5 seconds

Opamp PID Circuit Set kp Set kI Set kD

Industrial PID Tuning • http://www.expertune.com/ • DCS: Digital Control System. DCS refers to larger analog control systems like Fisher, Foxboro, Honeywell, and Bailey systems. DCS's were traditionally used for PID control in the process industries, whereas PLC's were used for discrete or logic processing. However, PLC's are gaining capability and acceptance in doing PID control. Most utilities, refineries and larger chemical plants use DCS's. These systems cost from 20 thousand to millions of dollars. • DCS systems by: ABB (http://www.abb.com/ ), Bailey, Foxboro (http://www.foxboro.com/industries/ ), Fisher, Moore, Honeywell, Yokogawa, etc.

Matlab PID Tuning-1 http://www.mathworks.com/

Summary • Introduction • Proportional Control • Equation • Example • PI Control • Equation • Numerical Integration • Example • PID Control • Web Simulation • Equation • Numerical Differentiation • A 3-mode opamp controller • Industrial PID tuning

Proportional Integral Differential (PID) Control