Needs["VariationalMethods`"]
params = {jb -> 870 (10^(-5)) + 75 (10^(-6)), p -> 2, mw -> 0.75,mb -> 10, r1 -> 0.000001, r2 -> 0.000001, jm -> 7800 0.002π ((((0.165/2)))^4)(1/2), r3 -> (0.165/2), k1 -> 1, k2 -> 1}; 
displacement = 0;

ke = (1/2)mw ((((p/(2π)) α'[t]))^2)+ (1/2)jm ((α'[t])^2)  + (1/2) mb ((((p/(2π)) α'[t]))^2);
kp = mb g h1 + mb g (h1 + h2);
l = ke - kp;
eqns =EulerEquations[l, {α[t]},t] //FullSimplify;
deqns = {First@eqns[[1]] == -r1 α'[t]-f[t]+4.3u[t]};
MatrixForm[deqns]

symmodelqr =StateSpaceModel[deqns,{{α[t],0},{α'[t],0}},{u[t],f[t]},{α'[t] 2(π/60),f[t]},t] //FullSimplify;
model = symmodelqr /. params

init = {0,0};
times = RandomInteger[{10,60},3];
disturb = (*{0,Table[1 UnitBox[((t-times[[i]])/25)](E^(-1(((t-times[[i]]))^2))),{i,1,Length@times}]};*)
{0,1UnitBox[((t-15)/25)]-1UnitBox[((t-40)/25)]};
q = DiagonalMatrix[{1,10}];
r =1{{1}};
lineargains =Join[Last@CoefficientArrays[LQRegulatorGains[{model,1},{q,r}]]//Normal,{ConstantArray[0,2]}];
First@lineargains
controlmodel =SystemsModelStateFeedbackConnect[model,lineargains];
{alphadot,force}=StateResponse[{controlmodel,init},disturb,{t,60}];
Plot[{alphadot,force,disturb[[2]] },{t,0,60},PlotLegends->"Expressions", PlotRange->All, FrameStyle-> Black, Frame-> True]

feedback=StateSpaceModel[{{},{},{{}},{{1,-1}}}];
integrator = TransferFunctionModel[(1/s),s];
tracker = SystemsModelMerge@SystemsConnectionsModel[{feedback,integrator,model}, {{1,1} -> {2,1},{2,1}-> {3,1},{3,1} -> {1,2}},{{1,1},{3,2}},{{3,1},{3,2}}]

init2 = {0,25,25};
times2 = RandomInteger[{10,60},3];
disturb2 = {1UnitStep[t],0UnitBox[((t-10)/5)]-0UnitBox[((t-40)/5)]};
q2 = DiagonalMatrix[{1000,10,100}];
r2 =1{{1}};
lineargains =Join[Last@CoefficientArrays[LQRegulatorGains[{tracker,1},{q2,r2}]]//Normal,{ConstantArray[0,3]}];
First@lineargains
controlmodel2 =SystemsModelStateFeedbackConnect[tracker,lineargains];
{int,alphadot2,force2}=StateResponse[{controlmodel2,init2},disturb2,{t,100}];
Plot[{int,alphadot2,force2,disturb2 },{t,0,100},PlotLegends->"Expressions", PlotRange->All, FrameStyle-> Black, Frame-> True,ImageSize->Large]

N[7800 0.002π ((((0.165/2)))^4)(1/2)]

Plot[{Sin[2π 3 t]+10Ramp[t-2]},{t,0,2π}]

Plot[(E^(-t)) Sin[t], {t, 0, 10}, ImageSize->Large]