Download - 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
