Dear David
I am sure that you can easily solve this without consultants. PID motor control is a classic application of control systems theory. I took the course in 1965. We used a bode plotter from ESI to find the effects ofmp?les and zeros, with special Teledeltos plotting carbon paper and an HV stylus.
The engineering application of the second order differential ¨¦quations are well documented in many papers, textbooks and courses. I highly recommend my old 1965 CCNY textbook Control System Theory by Dr Professor delToro, pub. McGraw Hill or Willey
The damping and bode plots are essential to understand how to tune a system response. Best system response is usually critical damping or slightly underdamped.
Are you simulating or have built hardware to test and tune? type and size of motor? load eg pump, fan, v¨¦hicule ?
bon courage et bon chance
Jon
Froggie the Gremlin