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I need to use Simulink to determine an approximate numerical solution to the equation of motion for a robotic arm (link to image below). The equation of motion for the system is J (\theta)'' = \tau - mgl cos (\theta). (An ordinary, 2nd order nonlinear differential equation.)
Assuming zero initial conditions and a small desired angle of the robot arm, verify the following rules of thumb for PID control for a step input. This should be for an original nonlinear model.
- for proportional control (Kp > 0, Kd = 0, Ki = 0), the solutions are oscillatory, and Kp increases the frequency of oscillation (which decrease the rise time and peak time), but decreases the mean steady state error. The settling time is finite (Hint: pick a starting value of Kp = 5)
- Add derivative control to the proportional controller (i.e., Kp > 0, Kd > 0, Ki = 0) and verify the following:
a) for small Kd, solutions are decaying oscillations
b) increasing Kd deceases settling time
c) increasing Kd to sufficiently large value eliminates oscillatory behavior; solution experimentally decays to final steady state value.
d) increasing Kp decreases the final steady state error
e) increasing Kp decreases rise time
(Hint: pick a starting value of Kd = 0.5)
I am really struggling with how to use Simulink, and especially how to do this in Simulink. Any tips/advice for a starting place to solve this problem would be GREATLY appreciated! Thank you so much, in advance. I would really, sincerely appreciate any and all help with this. Simulink was not gone over in class, and then suddenly we had an assignment entirely based on using Simulink. This is for a Differential Equations/Controls course.
Note that I also attached a screenshot of the .slx Simulink file that my professor sent out to help us with this nonlinear model (and also attached the .mdl version of the actual file). I'm not sure what to do with it however (when I run it, it says that "J is an undefined variable"). Thanks again!
