Self-Tuning PID Controller to implement in a PLC without having the plant model?

I need to implement a self-tuning PID controller in a PLC. I know the behavior of the plant (I mean, I know that if the speed is reduced the tension gets higher and vice versa), but I do not have a mathematical model of it. Which method would you recommend?

The case is the following:

I have a system which consists of a warp beam in which a thread is wound and an AC motor to rotate the warp beam (“Process” according to the picture below). This thread should be fed at a constant tension to another machine (The whole system is a weaving machine, but I am just controlling the speed of the warp beam using a tension sensor). The motor is connected to a control motion system in which we have just to specify the speed at which the motor should rotate, so we have a PID controller to calculate the speed at which the motor should run. To measure the tension of the thread we have a tension sensor.

By the nature of the process itself, the tension on the thread has oscillations, and depends of the pattern of the woven fabric and speed. It is a “high speed” process. So we specified a target tension, which the “motor” should try to achieve, but we also specified a Max. and Min. if the tension gets out of this range the whole machine will stop. As an example the behavior of the tension in a loom is depicted below.

• Actually it is used just a PI controller to calculate the motor speed. A self tuning is required because the machine has a different behavior depending also in the material used (strength) and speed of the looom. Sep 16 '15 at 10:04
• Honestly, controlling tension on a yarn by regulating motor speed is extremely difficult to do. You would be much better if you were to control the torque, as that is directly related to tension; speed isn't. Sep 16 '15 at 10:14
• @RDrast: Thanks for your comment. Actually I think it could be a better option, as you pointed out, but one general/basic questions: if I go to control the torque, will I need some sort of torque sensor, or is it possible to do it without torque sensor? it is because I have already the hardware, and I am constrained to work with what I have (encoders, tension sensor) Sep 21 '15 at 18:05
• Any modern Vector drive has the ability to send a torque reference to the drive and run it in torque mode. For modern AC (and just about all DC) drives, the velocity (speed) loop is the outer loop, and its output feeds to the inner torque/current loop. That is one reason the torque/current loop control is much faster and more precise when controlling tension, which is actually torque. Sep 22 '15 at 10:39