Backstepping Control and Transformation of Multi-Input Multi-Output Affine Nonlinear Systems into a Strict Feedback Form

This dissertation presents an improved method for controlling multi-input multi-output affine nonlinear systems. A method based on Lie derivatives of the system\u27s outputs is proposed to transform the system into an equivalent strict feedback form. This enables using backstepping control approaches based on Lyapunov stability and integrator backstepping theory to be applied. The geometrical coordinate transformation of multi-input multi-output affine nonlinear systems into strict feedback form has not been detailed in previous publications. In this research, a new approach is presented that extends the transformation process of single-input single-output nonlinear. A general algorithm of the transformation process is formulated. The research will consider square feedback linearizable multi-input multi-output systems where the number of inputs equals to the number of outputs. The preliminary mathematical tools, necessary and sufficient feedback linearizability conditions, as well as a step-by-step transformation process is explained in this research. The approach is applied to the Western Electricity Coordinating Council (WECC) 3-machine nonlinear power system model. Detailed simulation results indicate that the proposed design method is effective in stabilizing the WECC power system when subjected to large disturbances