Constantine Houpis

An algebraic approach to the time-optimal output regulator†

The time-optimal output regulator is considered for a special class of linear time-invariant discrete-time systems. It is shown that a simple state feedback law achieves time-optimal output regulator response in one sampling period. For a square system, the state feedback law always assigns the invariant zeros as closed-loop poles. For a non-square system, time-optimal regulator response is achieved even if the set of invariant zeros is empty. If the set of invariant zeros is not empty, the control law always assigns these zeros as closed-loop poles. The method of this paper, for the discrete system described by the state and output equations x(k + 1) = Ax(k) + Bu(k) and z(k) = Cx(k), does not require that A be invertible and that the open-loop system S(A, B, C) be state controllable. Furthermore, the only requirement is the existence of a right inverse for the matrix CB which is sufficient for output controllability.

Stabilization of a flight control system with varying numbers of right half-plane poles and zeros

Data for a linearized model of the STOL/maneuver technology demonstrator (SMTD) with stabiliser used to control pitch-rate are examined. Six flight conditions were considered, ranging from 0.1 to 0.9 Mach, and from zero to 40000 ft. The six cases comprised one with one right half-plane (RHP) zero and one RHP pole, two cases with two RHP poles, one case with one RHP zero and three RHP poles, and two cases with one RHP pole. The problem was to stabilize the system over this range of flight conditions by means of a single, fixed compensator, i.e. without any scheduling or identification. Quantitative feedback theory (QFT) was applied in a straightforward manner to obtain such a design with phase margins >or=50 degrees and gain margins >or=6 dB (only one case with 6 dB, the five others >or=20 dB). The technique is simple and systematic, with little cut-and-try. It can be applied by anyone with classical control background since the Nichols chart is the principal design tool. Time and frequency domain simulations are included.<<ETX>>