Please how can I solve this using StateSpaceModel.
eqns := {(lp \[Theta]''[t]) + m g Sin [\[Theta][t]] + c \[Theta]'[t] - Sin [\[Theta][t]] y0''[t] == 0}; $\begingroup$ $\endgroup$
2 
- 1$\begingroup$ Do you mean put it in a state space form? $\endgroup$Suba Thomas– Suba Thomas2023-01-17 16:54:55 +00:00Commented Jan 17, 2023 at 16:54
- $\begingroup$ Yes, I need to put it in a state space form? $\endgroup$Tetrasreal– Tetrasreal2023-01-29 17:32:14 +00:00Commented Jan 29, 2023 at 17:32
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1 Answer
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1 StateSpaceModel is a linear representation. It will throw away nonlinear terms.
eqns = {lp θ''[t] + m g Sin[θ[t]] + c θ'[t] - Sin[θ[t]] y0''[t] == 0}; StateSpaceModel[eqns, {θ[t], y0[t]}, {}, {θ[t], y0[t]}, t] 
NonlinearStateSpaceModel can handle nonlinear terms, but it doesn't support descriptor systems yet. For now, we have to use an internal function as shown here.
{{f, h, e}, x} = Control`DEqns`nonaffinestatespaceForm[eqns, {{θ[t], 0}, {y0[t], 0}}, {}, {θ[t], y0[t]}, t, #[[1 ;; 2]] &, DescriptorStateSpace -> True]; The state space equations are in the form $e.x'==f$.
x 
{e.D[x, t], Table["==", 4], f}//Transpose // TableForm 
- $\begingroup$ Thanks you very much. $\endgroup$Tetrasreal– Tetrasreal2023-01-31 09:12:44 +00:00Commented Jan 31, 2023 at 9:12