See therefore some definitions for example in:

Aim is compensating by approbiate means if high quality counts:

- 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

- set point SP and process value PV: e = PV - SP => 0

- ITAE criteria: Integral[0...t] t*

Open loop (feedforward): K = 1

If you have data you can approach this with a feedforward model like:

Page 1 Controller fits to process: result v2 = u

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 = w

If MATLAB used correctly it will produce the same result as I have found. No

doubt!

Used and recommended program (free usable):