I have a scenario where I have a bar of 0.1 m in length, 10N weight is applied in the center. Two forces are applied on the bar at both ends vertically, right one if 5.1 N and the left one is at changing magnitude, I denoted as F+5 N.
F is a value to be determined with the controller, initially 0. I want to be able to keep the bar facing upwards (upside down is prohibited), and not deviating from x = 0 much by controlling the changing force. F cannot be negative.
Initially system is at rest. After t = 0 system will rotate CCW as expected.
I implemented a basic P controller in Simulink as shown below to get following.
I have several questions related to this:
- With this system(one input), can I obtain a solution which will keep both horizontal error and orientation error within a certain limit? If so, what kind of controller should I implement?
- I wanted to add PID controller block of Simulink to tune the gains. However it raised error of 'the system cannot be linearized'. At first I thought this was related to underactuation (since I use only 1 input, but need 3 actually). But now I start to think that it is related to nonlinearity. What is the main reason that prevents non-linearization?
- If I add 2 more forces, can I use PID for my purpose? Or the system becomes MIMO and I cannot?
Thank you for your help.