1. Alexander Voice, Boron Delta Andrew Wilkins, Boron Delta
PID Tuning
Classical Methods
ChE 466 – Team Boron
Alexander Voice, Boron Delta
Andrew Wilkins, Boron Delta
October 18, 2007

2. PID Control
Purpose – Provide a constant system output at a specified set point
Analyze offset from set point – “error”
Instantaneous offset (proportional)
Permanent offset (integral)
Change in offset (derivative)
Objective – determine proportional, integral, and derivative scaling coefficients in the control equation

3. General Control Equation
u(t) = Kc [e(t) + (1/Ti) ∫ e(t)dt + Td(de(t)/dt]
u(t) is the controller output
e(t) is error from the system set point
Kc is the controller “gain”
Ti and Td scale the integral in derivative parameters

4. Tuning Methods Ziegler-Nichols and Tyreus-Luyben
Experimentally determine ultimate gain Ku and Pu
Start with a low value of Kc
Increase Kc until sustained oscillation is observed in the system output
Ku is the smallest value of Kc which achieves oscillation
Pu is the period of oscillation at Ku
Correlation tables are used to determine Kc, Ti, and Td from Ku and Pu

5. Tuning Methods Cohen-Coon
Generate a step impulse in a system input
Track the system response as a function of time
Determine…
the original steady state output (A)
the new steady state output (B)
the time at which output = .5*B
the time at which output = .632*B
May require curve fitting or interpolation!
Time
Voltage

6. Tuning Methods Cohen-CoonB
.632*B
.5*B

7. Conclusions Z-N, T-L, and C-C all provide good initial guesses
Z-N and T-L require more experimentation
Cohen-Coon requires more computation
Custom tuning should be used to optimize the control scheme and verify robustness