I am creating a closed loop controller for a motor which is part of a robotic arm. I give it a required angle, the controller calculates a control input, the motor moves, a pot feedbacks the angle, repeat, and the arm ends up at the required angle.
I am using state variable feedback, with integral action, and in order to calculate the control gains required for stability and speed I need a mathematical model of my system.
To get this model I am using statistical model identification techniques. I am inputting a random control signal into the motor, and recording this and the angle of the arm at each sample time. I'll then have sample input and output data of my system, and I can use a mathematical optimization technique to find the model parameters that best fit this data.
When under actual operation, the robot arm will be lifting a variety of weights. Does this mean the model I found with no load (intrinsic load) is invalid?
How do I get a mathematical model of this system when the load on the motor can change?