Controlling plots with sliders without using Manipulate

Question

Why are the sliders in the following code not affecting the plot? (Without using Manipulate)

Module[{t, o, z}, f[t]];
{Slider[ Dynamic[o], {1, 5, 0.1}], Dynamic[o]}
{Slider[ Dynamic[z], {0.1, 1.4, 0.1}], Dynamic[z]}
{Slider[ Dynamic[Ts], {5, 20, 1}], Dynamic[Ts]}
tf[o_, z_] := TransferFunctionModel[ω^2/(s^2 + 2 z o s + o^2), s];
f[t] = OutputResponse[tf[o, z], UnitStep[t], t];
Plot[f[t], {t, 0, T}, PlotRange -> {{0, T}, {0, 2}}]

Answer 1

Your code modified and with syntax errors fixed

DynamicModule[{o, z, capTs, ω, s},
tf[o_, z_, ω_, s] := TransferFunctionModel[ω^2/(s^2 + 2 z o s + o^2), s];
f[t_, o_, z_, ω_] := OutputResponse[tf[o, z, ω, s], UnitStep[t], t];
Grid[{{"o", Slider[Dynamic[o], {1, 5, 0.1}], Dynamic[o]},
 {"z", Slider[Dynamic[z], {0.1, 1.4, 0.1}], Dynamic[z]},
 {"ω", Slider[Dynamic[ω], {0.1, 1.4, 0.1}], Dynamic[ω]},
 {"Ts", Slider[Dynamic[capTs], {5, 20, 1}], Dynamic[capTs]}, 
 {Dynamic@ Plot[Evaluate@f[t, o, z, ω], {t, 0, capTs}, 
  PlotRange -> {{0, capTs}, {0, Automatic}}], SpanFromLeft}}]]

gives

Answer 2

One of the problems is that you use Set (=) to define f[t]. This means that f[t] will be equal to the evaluated form of the right-hand side of its definition where o and z are replaced by their values as they were at the time that f was defined.

What you want is SetDelayed (:=) which leaves the right-hand side in its unevaluated form. In that case the right-hand side will be re-evaluated with the current values for o and z every time f is called.

The second issue is that to get a plot that is updated dynamically, you would need to do something Dynamic[Plot[f[t], ...]]. I don't have access to Mathematica at the moment but I suspect that since o and z don't appear explicitly in Plot[f[t],...] you would also need to set TrackedSymbols -> {o, z} in Dynamic[Plot[...]].