https://www.overleaf.com/9353475874xbfcgntrjpzb < insert link to project reports>
This function evaluates
Usage: eval_f3 is called
eval_f3(x,p, u, b, t) where the t is an optional argument. Likewise, it can be called eval_f3(x, p, u, b)
x: Vector of length = number of state variables.
p: Struct with the relevant parameters. Must contain:
* p.Area
* p.Beta
* p.Distance
* p.workFunction
* p.Radius
* p.taby
* p.invC
* p.CG
u: Vector of inputs
b: Matrix of length = length(x) and width = length(u)
This function returns the f and J for eval_f3.
Usage: fjbowtie(x,p,u,b,t) or fjbowtie(x,p,u,b). The t is optional
u: Vector. Must be precomputed.
This function computes the finite difference Jacobian of the handle function given to it
Usage: FiniteDifferenceJacobian_t(f,x,p,u,b,t) or FiniteDifferenceJacobian_t(f,x,p,u,b). The t is optional.
This function computes the forward Euler simulation.
Usage: X = ForwardEuler_t(fhand, x0,p,U,b,t) or [X, t] = ForwardEuler_t(fhand, x0,p,U,b, t_start, t_stop, del_t) or [X, t] = ForwardEuler_t(fhand, x0,p,U_func,b, 'dynamic', t_start, t_stop). Where U is the time dependant input matrix of size length(x0)*length(tvec)
Other Usages: To perform forward Euler on a linearized system with coefficients [A, B], X = ForwardEuler_t(fhand,x0, p, U, b, 'linearmodel', t, A, B)
This function computes the f and J for the trapezoidal method
Usage: FJFTrap(x, p, u, b, t, gamma, dt, fJhand)
This function does the newton method for an N dimensional vector.
Usage: newtonNd(fJfhand,x0,p, u, b, t) or newtonNd(fJfhand,x0,p, u, b) for a normal non-linear function computation.
For trapezoidal method solving, use newtonNd(TrapHand,x0,p, u, b, t, gamma, dt, integrand) where TrapHand is FJFTrap and integrand is the fJ function handle for the functin you're interested in integrating.
This function performs the trapezoidal time integration method for an input function.
Usage: TrapMethod(x0,p,u,b, fJfhand, tvec) where fJhand is the function you want to integrate.
This function returns the linearized coefficients of the system [A, B] for linearization about input state x0 AND bias point u0; or just linearization about the input state x0.
Usage: To linearize only about x0, linearization(f,x0,p,u,b,t,'onlyx0'). The t is neccessary, but u and t are just dummy variables.
To linearize about both x0 and u0, linearization(f,x0,p,u,b,t) or linearization(f,x0,p,u,b). The t is optional.