- Design a continuous time lead-lag compensator for the inverted pendulum example from class on Monday except change two numbers:
- change the damping coefficient from 0.7 to be your age in years divided by 30, unless you are 21 in which case use any number other than 21 between 19 and 24 for your age, and
- change the 7 in -37 to be the last digit of your NDID number, e.g., if your id number is 90002112, then use -32.
- Implement it in simulink.
- Change the controller to be discrete with a time step of 0.01. Do not change the controller design, i.e., the discrete controller is by emulation. You may use matlab for the detailed calculations for the transformation of the controller from continuous to discrete.
- Increase the step size of the controller incrementally and determine how the performance changes as delta t increases.
- Refine the controller by plotting the root locus for the discrete system and choosing a new gain to improve the performance when implemented with a discrete controller in the case where the time step is 0.1. If you are feeling ambitious you can change the pole and zero locations in the controller, but all that is absolutely required for the homework is to improve the design by changing the gain.