On the basis of Peter's data set I tried to find the best control.
Data set:
Time, Position, Control Output
0,0,1 0.1,0.0280961296169728,1 0.2,0.105480069053459,1 0.3,0.22321745414104,1 0.4,0.373993446175833,1 0.5,0.551819161757164,1 0.6,0.751791317868303,1 0.7,0.96989544591241,1 0.8,1.20284477699198,1 0.9,1.44794833233238,1 1,1.70300292485492,1 1.1,1.9662047375435,1 1.2,2.23607692993412,1 1.3,2.5114103673215,1 1.4,2.79121509393783,1 1.5,3.0746806025518,1 1.6,3.36114330596755,1 1.7,3.65005990494049,1 1.8,3.94098558367094,1 1.9,4.23355615778425,1 2,4.5274734583331,1 2.1,4.82249336523072,1 2.2,5.1184160098546,1 2.3,5.41507775361695,1 2.4,5.71234462057353,1 2.5,6.01010692049863,1I found the ODE for process transfer function: y=v1
0.1666699 y'' + 0.3333319 y' - 2.096008E-07 y = 1Filter used: y=u
1.090314 y'' + 2.013555 y' + y = 0.4Benchmark scheme as shown on Pages 2/3/4
Definitions: Page 1
Solutions With disturbances but without disturbance compensation: Page 2 Without disturbances, just feedforward (PID Feedback) : Page 3 With disturbances and with disturbance compensation : Page 4