Directional change and windup phenomena in LQR-controlled systems with actuator failure

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 resaturations. 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 constraints 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.