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Controller Tuning for Non Self-regulating Process
Looking for a straightforward method for measuring the parameters of a 2nd order non self-regulating process, and then use them to calculate controller tuning parameters.

The step test method for bumping a self-regulating process in order to determine dead time, process time constant, and process gain is straightforward when dealing with a self-regulating process. However, I've been unable to find any equivalent test procedure for a non self-regulating process. Obviously, a non self-regulating process will never reach any equilibrium after making a step change. So, a different approach would be needed, but I've been unable to find any source of information that deals with this situation. Can anyone point me to a procedure that will determine the process parameters?

The process that I'm trying to tune is second order with minimal dead time. This is a motion control process where we are trying to lock onto a slowly moving target (in one dimension), but the process variable that we are controlling is acceleration (which can be positive or negative). So, what the controller is controlling is the 2nd derivative of what we are measuring.

With controlled tracking, you are dealing with a position or angular orientation of the tracking element and that of the object being tracked. Together these are converted into a tracking error.

This error (+/-) is to be minimized by the controller which issues a command to the final control element.

However, to make any such system work you will need position feedback signal from the tracking element being controlled and possibly a second controller that regulates its rate of acceleration.

With servo-controls you have to focus on the state variables of the system, if you want to control it.