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Aug
14
comment Convert DE to first order?
Thanks again. Thus far, I had never bothered to hover over an image on MSE!
Aug
14
comment Convert DE to first order?
Ok Michael E2, I think it is better now thanks to your suggestion. I think you still may have to strain a little to see the expressions.
Aug
14
revised Convert DE to first order?
Improved formatting
Aug
14
revised Convert DE to first order?
Updated answer after equations were fixed
Aug
13
comment Convert DE to first order?
NonlinearStateSpaceModel only does a Taylor linearization of the highest order derivatives. I looked at the equations and it doesn't seem to have any nonlinear second derivative terms? I agree that it will be better to have good code before spending too much time on analysis.
Aug
13
answered Convert DE to first order?
Aug
13
comment Convert DE to first order?
@Marco, I will do this shortly. @ Jens, I will elaborate this in my answer, and the the OP can see if he can use the built-in function or if he will need to improvise.
Aug
13
comment Convert DE to first order?
You could do NonlinearStateSpaceModel[eqs, {x[t], y[t]}, {}, {x[t], y[t]}, t] or even just StateSpaceModel[eqs, {x[t], y[t]}, {}, {x[t], y[t]}, t].
Aug
13
comment Convert DE to first order?
Did you try following this example wolfram.com/xid/0v5g4hmcblbdp-imlwho. Are you still having problems after that?
Aug
10
comment Assigning the numerical results of Minimize to variables
res = Minimize[...]; a = res[[1]]; {b, c} = {x, y} /. res[[2]]
Aug
10
comment Solving algebraic looping problem by introducing a unit delay
Aaron, this is a paraphrase from p.262 of the book 'Continuous System Simulation' by Cellier and Kofman: "How can we deal with the algebraic loop? ... we can solve for the unknowns...". The algebraic loop you have should have a solution for u1 and u2. Otherwise it makes no sense. "I have no idea how to insert an initial value for u2 in the u1 equation." There is no 'u1 equation' (or 'u2 equation'), because you cannot solve for u1 (or u2). You are stuck with an unsolvable algebraic loop involving both u1 and u2.
Aug
4
answered Solving algebraic looping problem by introducing a unit delay
Jul
16
awarded  Nice Answer
Feb
19
awarded  Yearling
Feb
9
comment OutputResponse in V9 vs V10
This is a bug. The workaround for now is to convert thisWcA, Wp23, or the final system to a StateSpaceModel.
Jan
28
comment Selecting values over lists for discrete inputs in NDSolve
@antonio 1)Are you sure that this is a model of a tank system. See wolfram.com/xid/0jvpj762zmgvepb9y3y1-veaqch, Bernoulli's law does not end up with the equation you have. 2) Are you mixing discrete- and continuous-time dynamics?
Jan
13
answered StateSpaceModel- damped oscillator
Nov
26
answered Numerically Simulating a Simple Differential Equation: RC Circuit
Nov
21
revised Why does LyapunovSolve solve non-standard form?
Updated based on commnets
Nov
21
comment Why does LyapunovSolve solve non-standard form?
And that goes back to the original point - there is no standard form. Now for stability analysis we have to use the transpose but to obtain the controllability gramian we need not transpose...