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.
And also please read the attached file ([url removed, login to view]) for guidelines of how Matlab code and report should be written.
1) Derivation and design of 5th order approximation controller and Matlab simulation of tracking of both reference and the designed 5th order approximation controller.
2) Design an internal model to the 5th order approximation controller to enhance its robustness.
Deadline: 2nd Feb 2010