The paper presents a phenomenon of directional change in the case of a LQR controller applied to multivariable plants with amplitude and rate constraints imposed on the control vector, as well as the impact of the latter on control performance, with the indirect observation of the windup phenomenon effect via frequency of consecutive resat- urations. The interplay of directional change of the computed control vector with control performance has been thoroughly investigated, and it is a result of the presence of con- straints imposed on the applied control vector for different ratios of the number of control inputs to plant outputs. The impact of the directional change phenomenon on the control performance (and also on the windup phenomenon) has been defined, stating that performance deterioration is not tightly coupled with preservation of direction of the computed control vector. This conjecture has been supported by numerous simulation results for different types of plants with different LQR controller parameters.

The head loss is a decrease in compressive height caused by friction and direction changes of flow at the sliced bend. This method expected to provide is easy, fast, and economical. The elements of influence are the velocity of flow, the num-ber of slices, average length of sliced walls, angle changes of the sliced, coefficient of friction, acceleration of gravity, and slope of the pipe. Equation for coefficient of head loss (Kb) is an analysis method for the head loss (hL) calculation. The analysis results that have obtained are the larger diameter of the pipe, and the more slices with a fixed discharge, the coefficient of hL becomes small. Conversely, if the diameter of the pipe is getting smaller, and the slice is getting less, then the coefficient of hL becomes bigger. This method, expected to give new knowledge in pipeline network applications, especially for the large diameter of pipelines.