Table 2 Rules of the adjustments

Rule 1

 The 3rd axle

\(sat\left( {A_{{ltr3_{k} }} - B_{{ltr3_{k} }} } \right) = \left\{ \begin{aligned} & 0, \quad {if} {\left| {A_{{ltr3_{k} }} - B_{{ltr3_{k} }} } \right| < K_{ltr3} }, \hfill \\ & sign\left( {A_{{ltr3_{k} }} - B_{{ltr3_{k} }} } \right), \quad {else}. \\ \end{aligned} \right.\)

 The 4th axle

\(sat\left( {A_{{ltr4_{k} }} - B_{{ltr4_{k} }} } \right) = \left\{ \begin{aligned} & 0, \quad {if} \; {\left| {A_{{ltr4_{k} }} - B_{{ltr4_{k} }} } \right| < K_{ltr4} }, \\ & sign\left( {A_{{ltr4_{k} }} - B_{{ltr4_{k} }} } \right), \quad {\text{else}}. \end{aligned} \right.\)

Rule 2

 The 3rd axle

\(sat_{l} \left( {\phi_{k} } \right) = \left\{ \begin{aligned} & sign\left( {\phi_{k} } \right), \quad {if \;{\phi_{k} < 0} }, \\ & 0, \quad {\text{else}}. \end{aligned} \right.\) \(sa{t_r}\left( {{\phi _k}} \right) = \left\{ \begin{aligned} &sign\left( {{\phi _k}} \right),\quad if\quad {\phi _k} > 0, \hfill \\ & 0,\quad {\text{else}}. \hfill \\ \end{aligned} \right.\)

Rule 3

 The 3rd axle

\(N_{{3ma_{y} }} = \left\{ \begin{aligned} & 0, \quad {if \quad {\left| {ma_{{y_{k} }} } \right| > K_{{1ma_{y} }} } }, \\ & 1, \quad {\text{else}}. \end{aligned} \right.\)

 The 4th axle

\({N_{4m{a_y}}} = \left\{ \begin{aligned} & 0,\quad if\;\left| {m{a_{{y_k}}}} \right| < {K_{2m{a_y}}}\;{\text{or}}\;\left| {m{a_{{y_k}}}} \right| > {K_{3m{a_y}}}, \hfill \\ & sign\left( {m{a_{{y_k}}}} \right),\quad {\text{else}}. \hfill \\ \end{aligned} \right.\)