1. A UTOMATING PID C ONTROLS IN M ATHCAD Neil Kuyvenhoven Engr 315 December 11,2002

2. Existing / accepted methods Trial and Error Zieglar Nichols Method Cohen – Coon Method Neil’s Method Illustrations of Mathcad’s capabilities A UTOMATING PID C ONTROLS IN M ATHCAD AGENDA

3. A UTOMATING PID C ONTROLS IN M ATHCAD PID Automation Three main methods Trial and Error Zieglar Nichols Cohen-Coon Process – Trial and Error 1.Set integral / derivative to 0 2.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

4. A UTOMATING PID C ONTROLS IN M ATHCAD PID Automation Three main methods Trial and Error Zieglar Nichols Cohen-Coon Process Closed Loop 1.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.

5. A UTOMATING PID C ONTROLS IN M ATHCAD PID Automation Three main methods Trial and Error Zieglar Nichols Cohen-Coon Process Open Loop 1.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.

6. A UTOMATING PID C ONTROLS IN M ATHCAD PID Automation Method 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

7. A UTOMATING PID C ONTROLS IN M ATHCAD 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

8. A UTOMATING PID C ONTROLS IN M ATHCAD Neil’s Method

9. A UTOMATING PID C ONTROLS IN M ATHCAD Neil’s Method