Given a linear time-invariant multi variable system a design procedure is developed, representing a straightforward approach to the problem of constructing an appropriate feedback matrix of prescribed structure by successive shifting of selected system poles. Involving the concept of U1C Moore-Penrose pseudoinverse, a solution of the linearized definitive equations of the pole assignment problem can be attained, which furthermore tends to favour small feedback gains. The suggested method is simple in theory, direct in application and without ticklish steps. A simple example is included to illustrate the idea and its implications. To demonstrate its applicability and practical usefulness an incomplete state feedback is designed for the example of an lith-order system.
A new interpretation and solution of the linear multivariable steady-state tracking and disturbance rejection problem is presented. On condition of reference and disturbance input variables wit.h constant final values the proposed method prepares the ground for the calculation of a constant feedback control law, which meets the steady-state requirements exactly, although doing without the conventional prefilter or integral feedback respectively. Nevertheless the practical design reduces to the standard problem of stabilizing a precontrolled system by fictitious constant output feedback. The method is illustrated by the examples of a four-th-order-nuclear rocket engine and 6 twelfth-order chemical absorption column.
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