I have a robotic arm model in Simulink and I'd like to control the position of the end-effector such that it follows a given trajectory. This is done by inputting joint angles and comparing the output to see whether the desired angles have been reached.
From PID controller, I have moved on to an LQR controller which requires me to linearize the plant(Robot Arm) before being able to apply the controller.
My first questions is about linearization. If I were to do this, it would be around a fixed/ equilibrium point whereby the linearization would only be valid for that given region. How can I obtain a complete linearized model of my system which would be valid for all point as I would like to control the joint angles to manipulate the position of the end effector?
Second question is how would I derive a trajectory following Linear Quadratic Regulator control law. The laws I have seen only make sense for reaching a fixed point. I would like to continuously change that fixed point. Any ideas? https://i.stack.imgur.com/uIMlO.png