Hi there! I’m new to Julia and have been experimenting with it the past few months. I had been using it more as a workspace by which I could complete my school work than as a programming language. That changed recently as one of my classes is all about simulations. The assignments in class were made with MATLAB in mind, but I wished to attempt them in Julia instead.

I was wondering if anyone might have some tips for making the code below more Julian or might be able to point out any glaring mistakes I am making with for example array manipulation or my current use of global variables.

While the code does compile and run in Julia 1.6.0 and give an output, the simulation itself seems to be incorrect, so please ignore that.

Thank you for your time!

-Vero

## Code

```
using Markdown
using InteractiveUtils
using Plots
function midpoint_method(f::Function, x, u, t, h)
k1, y = f(x, u, t)
k2, _ = f(x + h/2*k1, u, t + h/2)
k3, _ = f(x - h*k1 + 2*h*k2, u, t + h)
x_VPG = x + h*k2
d_VPG = h/6*(k1 - 2*k2 + k3)
return x_VPG, y, d_VPG
end
function pt1(x, u)
Tm = 10
xdot = -1/Tm * x + 1/Tm * u
y = x
return xdot, y
end
function subtractor(u1, u2)
return u1 - u2
end
function hysteresis(u)
h_e = 0.085
h_a = 0.065
if u >= h_e
y = 1;
elseif u <= -h_e
y = -1;
else
y = 0;
end
if i > 1
if hys_state[i - 1] == 1 && u <= h_a
y = 0;
elseif hys_state[i - 1] == -1 && u >= -h_a
y = 0;
end
end
append!(hys_state, y)
return y
end
function sys_PRM(x, u, t)
_, y1::Float64 = pt1(x, 0)
y2::Float64 = subtractor(u, y1)
y3::Float64 = hysteresis(y2)
xdot1, _ = pt1(x, y3)
return xdot1, [y1 y2 y3]
end
t_step = 1;
Tm = 10
t0 = 0
tf = 20
epsilon = 1e-3
h_max = 2*Tm
h_min = 12*epsilon
u_values = []
x_values = []
y_values = Vector{Float64}()
d_values = []
t_values = []
h_values = []
hys_state = []
x = 0
h = 0.2
t = 0
i = 1
while t <= tf
if t < t_step
global u = 0
else
global u = 0.17
end
global x, y, d = midpoint_method(sys_PRM, x, u, t, h);
global h = 0.9*h*min(max((epsilon/max(abs(d)))^(1/3), 0.3), 2)
global h = min(max(h, h_min), h_max)
append!(x_values, x)
append!(y_values, y)
append!(d_values, d)
append!(h_values, h)
append!(t_values, t)
global t = t + h
global i = i + 1
end
y_values = reshape(y_values, (3, :))
p1 = plot(t_values, y_values[1, :])
p2 = plot(t_values, y_values[2, :])
p3 = plot(t_values, y_values[3, :])
p4 = plot(t_values, h_values)
p5 = plot(t_values, d_values)
plot(p1, p2, p3, p4, p5, layout=(5, 1))
```