pid temperature controller

AUTOMATING PID CONTROLS IN MATHCAD

Neil Kuyvenhoven

Engr 315

December 11,2002

Existing / accepted methodsTrial and ErrorZieglar Nichols Method Cohen – Coon Method

Neil’s MethodIllustrations of Mathcad’s capabilities

AUTOMATING PID CONTROLS IN MATHCAD

AGENDA

AUTOMATING PID CONTROLS IN MATHCAD

PID Automation•Three main methods

•Trial and Error

•Zieglar Nichols

•Cohen-Coon

Process – Trial and Error

1. Set integral / derivative to 02. Increase proportional until sustained

oscillations result – Set proportional to half of this value

3. Increase integral until sustained oscillations result – Set Integral to three times this value

4. Increase derivative until sustained oscillations result – Set derivative to one third of this value

AUTOMATING PID CONTROLS IN MATHCAD

PID Automation•Three main methods

•Trial and Error

•Zieglar Nichols

•Cohen-Coon

ProcessClosed Loop1. With integral and derivative set to 0,

increase proportional until sustained oscillations result.

2. Apply the period and gain values to the Zieglar Nichols closed loop formulae.

controller output (p)

Time

Time

self regulating

system response

(T)

0

p

T

S = T/

Time

unstable system

response (T)

t

T

S = T/t

= not determined

AUTOMATING PID CONTROLS IN MATHCAD

PID Automation•Three main methods

•Trial and Error

•Zieglar Nichols

•Cohen-Coon

ProcessOpen Loop1. Apply the values from the first two figure

to the Cohen-Coon formulae.2. If the output is similar to the third figure,

use the Zieglar Nichols open loop formulae.

controller output (p)

Time

Time

self regulating

system response

(T)

0

p

T

S = T/

Time

unstable system

response (T)

t

T

S = T/t

= not determined

AUTOMATING PID CONTROLS IN MATHCAD

PID AutomationMethod Comparison

Trial and Error

Zieglar Nichols

Cohen-Coon

Disadvantages

•Time consuming

•Some processes have no ultimate gain.

•Open loop – if disturbance introduced during testing, no way of filtering it out.

•Noisy signals give hard to read data for the slope.

•Not good for oscillatory open loop systems

•Result often contains oscillations due to the objective ¼ damping ratio

Advantages

•Tune to degree of satisfaction

•Single experiment required

•Does not need to be stable

•Settings are easily calculated

•Same as Zieglar Nichols

AUTOMATING PID CONTROLS IN MATHCAD

Mathcad Example

Neil’s Method

•Set up the Transfer functions

•Convert to time domain

•Solve for the rise time, overshoot, settle time

•Vary controller values based on these values compared to the requirements

AUTOMATING PID CONTROLS IN MATHCAD

Neil’s Method

AUTOMATING PID CONTROLS IN MATHCAD

Neil’s Method