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

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

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

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

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

Tuning Methods Cohen-Coon B .632*B .5*B

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