The project considers the problem of designing a controller such that the position of the cart can asymptotically track a sinusoidal input. It is a typical output regulation problem in control theory. The solvability of the output regulation problem relies on the solution to the so-called regulator equations which are a set of partial differential equations (PDEs). It is usually impossible to obtain an analytic solution for a nonlinear PDE, so the approximate Taylor series solution is widely used in practice. In this project, this approximate approach will be utilized to find a regulator for the inverted pendulum on a cart system. This project requires mathematical derivation and numerical MATLAB simulation, in particular, on dynamic equations, e.g. ode23.
Please refer to attachment for required text (Nonlinear Output Regulation: Theory and Applications by Jie Huang) to read on (especially Chapter 2, 3, 4, 5). Please use the parameters stated in Chapter 4 pg 130.
1) Mathematical working and Matlab simulation of tracking of both reference and linear controller as from the required text.
2) Mathematical working and Matlab simulation of tracking of both reference and 2nd order approximation controller as from the required text.
3) Mathematical working and Matlab simulation of tracking of both reference and existing 3rd order approximation controller as from the required text.
4) Derivation and design of 4th order approximation controller and Matlab simulation of tracking of both reference and the designed 4th order approximation controller.
5) Try to change one of the parameters to see changes in simulations.
6) Find out the limits of the controllers through simulations
7) Design an internal model to the 3rd and 4th order approximation controllers to enhance its robustness.
Deadline till 12 Jan 2010.