- #1

shuh

- 9

- 0

## Homework Statement

The state space model of a nonlinear system is [tex]x'_1(t) = 2x^2_2(t) - 50[/tex] [tex]x'_2(t) = -x_1(t) - 3x_2(t) + u(t)[/tex] where x_1(t) and x_2(t) are the states, and u(t) is the input. The output of the system is x_2(t).

Find the zero input response (u(t) = 0) of this system linearized at the equilibrium point (-15, 5) with initial states (-14.5, 5).

**Use Matlab (expm.m) to plot these state responses from 0 to 5s.**

## Homework Equations

State Space Modeling, Matlab

## The Attempt at a Solution

The bold part is where I have an issue with this problem. Generally, if you want to find response to initial conditions, you use initial function, not expm. Expm simply takes a matrix and exponentiates it.

Anyways, MATLAB code for generating response to initial condition is:

//State Matrix

A = [ 0 20 ; -1 -3]

B = [0 ; 1]

C = [0 1]

D = 0

x0 = [ -14.5 ; 5]

sys = ss(A,B,C,d)

initial(sys, x0)

And you get a beautiful plot looking like the following:

How, and especially why on Earth would you use expm function to generate such plot?