J ( k p , k i ) = ∫ 0 t 1 [ m a x { ( y 1 ( t ) − u b ) , 0 } + m a x { ( 0 − y 1 ( t ) ) , 0 } ] dt + ∫ t 1 t 2 [ m a x { ( y 2 ( t ) − u b ) , 0 } + m a x { ( l b − y 2 ( t ) ) , 0 } ] dt {\displaystyle J(k_{p},k_{i})=\int _{0}^{t_{1}}[max\{(y_{1}(t)-u_{b}),0\}+max\{(0-y_{1}(t)),0\}]{\textit {dt}}+\int _{t_{1}}^{t_{2}}[max\{(y_{2}(t)-u_{b}),0\}+max\{(l_{b}-y_{2}(t)),0\}]{\textit {dt}}}
![{\displaystyle J(k_{p},k_{i})=\int _{0}^{t_{1}}[max\{(y_{1}(t)-u_{b}),0\}+max\{(0-y_{1}(t)),0\}]{\textit {dt}}+\int _{t_{1}}^{t_{2}}[max\{(y_{2}(t)-u_{b}),0\}+max\{(l_{b}-y_{2}(t)),0\}]{\textit {dt}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6a4b70168d870ec3daf41c04765bdf3e3413227)
