Further Work of Real M.Phil Thesis | What is a nonlinear systems dynamics and control?
euler.bonjour@gmail.com / https://github.com/khj1977
金輝俊 / Hwi Jun KIM
In this article, a research log will be written down as further work of: The Real M.Phil Thesis: The Mathematical Foundation of Smart Material Systems / Yet Another Mori-Tanaka.
Physics of Smart Material Systems: Digital Lagrangian and nonlinear model
Yet Another Physics of Smart Material Systems: Micro cell analysis and nonlinear model
Linear nominal system with nonlinear dumper and/or spring.
It would be written later.
Anaylsis of nominally nonlinear system
Nonlinear void dynamics as a nominal system
It would be written later.
Nonlinear turbulance as a nominal system
f = lambda t, x, xDot: -3.0 * x - 0.1 * math.sin(2.0 * x) * x * xDot
disturbanceF = lambda t, x, xDot: 0.0
Nominal system is nonlinear. It may be better to analyze by FFT and tangent space with 3D which are basic data;i.e. x: xdot, y: x, z: ||x||^2 which is kind of Lyapunov function with taylor series with each (t, x) which is tangent space.
Since the dynamics might go towards potential lower, it is better to analyze animated lyapunov like function with time t. It is also better to analyze vector flow with time t. Since it is nonlinear, Lyapunov function and vector flow would be changed time by time.
The question is is there nonlinear sliding mode surface which is curved but smooth? Which should be investigated by numerical calculation. Check sensibility of changing dynamics or tangent space with different control input or coefficient of dynamical system. Then, which would be first step to think about control.