Commit 2c4ca44c authored by Fredrik Bagge Carlson's avatar Fredrik Bagge Carlson
Browse files

Add docs for nonlinear simulator

parent 526736d1
......@@ -106,7 +106,7 @@ end
```
hence, it just performs one iteration of
```math
x' = Ax + Bu
x' = Ax + Bu\\
y = Cx + Du
```
......@@ -134,3 +134,13 @@ the system state by calling `init_sysfilter`. The variable `beam_system` is alre
defined outside the type specification.
One of the constructors provides a default value for the sample time, in case
the user is unsure about a reasonable value.
## Non-linear process
Your first option is to linearize the process and proceed like above.
Other options include
1. Make `control` perform forward Euler, i.e., `x' = f(x,u)*h` for a general
system model ``x' = f(x,u); y = g(x,u)`` and sample time ``h``.
2. Integrate the system model using some fancy method like Runge-Kutta. See
[DifferentialEquations.jl](http://docs.juliadiffeq.org/stable/types/discrete_types.html)
for discrete-time solving of ODEs (don't be discuraged, this is almost as simple as
forward Euler above).
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