Chapter 8

Performance of P-only, PI and PID Controllers

Overall Course Objectives

• Develop the skills necessary to function as an industrial process control engineer.– Skills

• Tuning loops

• Control loop design

• Control loop troubleshooting

• Command of the terminology

– Fundamental understanding• Process dynamics

• Feedback control

P-only Control

• For an open loop overdamped process as Kc is increased the process dynamics goes through the following sequence of behavior– overdamped– critically damped– oscillatory– ringing – sustained oscillations– unstable oscillations

Dynamic Changes as Kc is Increased for a FOPDT Process

Time Time Time

Time Time Time

Root Locus Diagram(Kc increases a to g)

-8

-4

0

4

8

-5 -4 -3 -2 -1 0 1Real Axis

Imag

inar

y A

xis

-8

-4

0

4

8

a ab bc

d

d

e

e

f

f g

g

Effect of Kc on Closed-Loop

-0.5

0

0.5

1

1.5

0 2 4 6 8K c

Dam

ping

Fac

tor

(') overdamped

underdamped

unstable

Effect of Kc on Closed-Loop p

0

0.2

0.4

0.6

0 2 4 6 8K c

Tim

e C

onst

ant

(' p

)

P-only Controller Applied to First-Order Process without Deadtime

• Without deadtime, the system will not become unstable regardless of how large Kc is.

• First-order process model does not consider combined actuator/process/sensor system.

• Therefore, first-order process model without deadtime is not a realistic model of a process under feedback control.

PI Control

• As Kc is increased or I is decreased (i.e., more aggressive control), the closed loop dynamics goes through the same sequence of changes as the P-only controller: overdamped, critically damped, oscillatory, ringing, sustained oscillations, and unstable oscillations.

Effect of Variations in Kc

Time Time Time

Effect of Variations in I

Time Time Time

Analysis of the Effect of Kc and I

• When there is too little proportional action or too little integral action, it is easy to identify.

• But it is difficult to differentiate between too much proportional action and too much integral action because both lead to ringing.

Response of a Properly Tuned PI Controller

Time

Lag

c

ys

Response of a PI Controller with Too Much Proportional Action

Time

Lag

c

ys

Response of a PI Controller with Too Much Integral Action

Time

Lag

ys

c

PID Control

• Kc and I have the same general effect as observed for PI control.

• Derivative action tends to reduce the oscillatory nature of the response and results in faster settling for systems with larger deadtime to time constant ratios.

Comparison between PI and PID for a Low p/p Ratio

Time

PI

PID

Comparison between PI and PID for a Higher p/p Ratio

Time

PID

PI

An Example of Too Much Derivative Action

Time

y s

Effect of D on Closed-Loop

0

0.5

1

1.5

0 0.25 0.5 0.75D

Dam

ping

Fac

tor

()

overdamped

underdamped

Demonstration: Visual Basic Simulator

Effect of Kc, I, and D

Overview

• As the controller aggressiveness is increased (i.e., Kc is increased or I is decreased), the response goes from overdamped to critically damped to oscillatory to ringing to sustained oscillations to unstable.

• Too little proportional or integral action are easy to identify while too much proportional or integral results in ringing. Differentiating between too much integral or proportional action requires comparing the lag between the controller output and the CV.