See therefore some definitions for example in:
- process and controller time response: F1(s)*F2(s) => K
- set point SP and process value PV: e = PV - SP => 0
- ITAE criteria: Integral[0...t] t*Abs(e)*dt => MIN, if applicable
Open loop (feedforward): K = 1
If you have data you can approach this with a feedforward model like:
process A1 = 0.333 A2 = 0.00106 A3 = 0.0000844 controller B1 = 0.333 B2 = 0.00106 B3 = 0.0000844
Page 2 Controller does not fit to process: result v2 ~ u
process A1 = 0.333 A2 = 0.00106 A3 = 0.0000844 controller B1 = 0.333 B2 = 0.00106 B3 = 0.0000819 -3%
In closed loop with
K=100 v2/u = 1/(1+1/(100 *0.97)) = 0.989 ~ 1 K=1000 v2/u = 1/(1+1/(1000*0.97)) = 0.999 ~ 1 K=oo v2/u = 1
Can be 'corrected' with an integrator!
Used definite filter for limiting speed v2' and acceleration v2''! This can be applied to any process values.
Page 3 Example filter (jerk 3rd order) in series
0.000033275*u''' + 0.003025*u'' + 0.11*u' + 1 = wIf MATLAB used correctly it will produce the same result as I have found. No doubt!
Used and recommended program (free usable):