Design and MATLAB Simulation of Feedback Linearization Controller for Nonlinear Systems

This project focuses on designing a feedback linearization controller for nonlinear systems, accompanied by comprehensive MATLAB simulations. Feedback linearization enables the transformation of nonlinear dynamics into equivalent linear systems through coordinate changes and nonlinear feedback control laws. The implementation involves calculating Lie derivatives to determine the system's relative degree and constructing a diffeomorphism that linearizes the input-output map. Key MATLAB functions include jacobian for derivative calculations and ode45 for system simulation. The controller design process requires verifying exact linearization conditions through involutivity checks of vector fields. MATLAB scripts will demonstrate the transformation using symbolic math toolbox for algorithmic implementation and Simulink for closed-loop performance analysis under varying initial conditions and disturbances. The project provides insights into stability analysis of the linearized system using pole placement techniques and explores practical limitations such as internal dynamics stability and modeling uncertainties.