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Where Ot) is the practical position signal, and 0() is the ideal position signal Therefore; we have 5() = ce(t) + e()=ce() +06) -0,() =ced) +1"-6) (13) and s=s ce + J"-64) Secondly; to satisfy the condition ss < 0, we design the = sliding - mode controller as 1, s >0 u(t) = J(-ce+ 0, ~ nsgn(s)), sgn(s) = 0_ s=0 (144) 6(-1, s < 0 Then; we get s =-nlsk0
where Ot) is the practical position signal, and 0() is the ideal position signal Therefore; we have 5() = ce(t) + e()=ce() +06) -0,() =ced) +1"-6) (13) and s=s ce + J"-64) Secondly; to satisfy the condition ss < 0, we design the = sliding - mode controller as 1, s >0 u(t) = J(-ce+ 0, ~ nsgn(s)), sgn(s) = 0_ s=0 (144) 6(-1, s < 0 Then; we get s =-nlsk0
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Determine the position function if the acceleration function is $a(t)=t^{2}+1,$ the initial velocity is $v(0)=4$ and the initial position is $s(0)=0$
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