A Reduced Method of Partial Pole Placement and its Application to Controlling the Lateral Motion of a Maneuverable Aircraft

A reduced method of partial pole placement is proposed to solve modal control problems in which it is required to change only a part of poles of a linear time-invariant system. Due to reducing the control system, the method simplifies calculating a modal controller by classical decomposition scheme, which is important for real-time control. The method also allows optimizing the transients due to both choosing the values of poles to be replaced and the controller parameterization, which does not affect the rest poles. A theorem on obtaining a reduced system by equivalent transformation using matrix zero-divisors and pseudo-inverse is proved. The efficiency of the proposing approach is confirmed by an example of controlling the lateral motion of a maneuverable aircraft. It is shown that replacing the pole with low stability margin and additional parameterization made it possible to decrease the duration of transient as well as to prevent exceeding the given thresholds for angles and angular rates.