I’m trying to figure out the best way to pose a (control) system model of form:
and use this model with DifferentialEquations
. The “problem” is to merge two contradicting constraints:

DifferentialEquations
requires the model to be posed as \frac{dx}{dt} = f(x,t;\theta), and  I would like to be able to pose the model in the form with input u, so that I can use Automatic Differentiation to linearize the model.
To test my idea, I used the “academic” model of level h [h
] in a water tank, with input \dot{m}_\mathrm{i} [mdi
], and effluent \dot{m}_\mathrm{e} driven by gravity, \dot{m}_\mathrm{e} = K\sqrt{h/h^\varsigma} where K is some valve constant, and h^\varsigma [hs
] is some scaling level to keep the square root argument dimensionless. With density \rho [rho
] and cross sectional area A [A
], the model for the system is:
I use the following parameters:
 K=5, h^\varsigma = 3, \rho = 1, A=5.
I use the following initial value:
 h(0) = 1.5.
At first, I want to set \dot{m}_\mathrm{i} = 2. Later on, I want to change this input value, e.g., by setting \dot{m}_\mathrm{i} = 2 + 0.1\sin(2\pi t/10), or by using a proportional controller \dot{m}_\mathrm{i} = K_\mathrm{p}(h_\mathrm{ref}  h). The point is: I want to make it as flexible as possible, while also allowing for Automatic Differentiation.
So… first I created a parameter tuple:
p = (rho=1.,A=5.,K=5.,hs=3.)
Next, I created a model function with input:
function mod_i(h,mdi,p,t)
dh = (mdip.K*sqrt(h/p.hs))/(p.rho*p.A)
end
With an operating point (h^*=1.5,\dot{m}_\mathrm{i}^*=2), I can now linearize the model using ForwardDiff
:
julia> ForwardDiff.derivative(h > mod_i(h,2,p,0),1.5)
0.2357022603955158
julia> ForwardDiff.derivative(mdi > mod_i(1.5,mdi,p,0),2)
0.2
So far, so good. Next, I need to create a model function suitable for DifferentialEquations
… and I attempt:
function mod(h,p,t)
mdi = 2.
return mod_i(h,mdi,p,t)
end
and set up the simulation case as:
h0 = 1.5
tspan = (0.,15.)
prob = ODEProblem(mod,h0,tspan)
sol = solve(prob)
Problem is: Julia crashes “big time”, with error message:
type Nothing has no field K
......
QUESTION:
 What have I done wrong? Why does Julia crash?