Equilibrium manifold linearization model for normal shock position control systems

A method for modeling nonlinear shock motion based on the equilibrium linearization method was proposed. Modeling nonlinear shock motion may be divided into three steps: steady-state modeling, dynamic modeling, and combined modeling. The proposed method approximates the nonlinear system of shock motion by a linearization family, which is more accurate than the small-perturbation linearization method and is simplr than the piecewise linear method. The equilibrium manifold linearization is based on Taylor series expansion to the first order about its equilibrium manifold subspace, and the quality of equilibrium manifold linearization mainly depends on the properties of the second-order Taylor series expansion about the subspace.