On mimo optimal preview tracking control for known trajectory models

Abstract

SUMMARYA class of discrete time feed forward tracking controllers is presented for linear multivariable plants subjected to time-varying exogenous inputs with known models. The controller design is based on linear quadratic optimization techniques and the augmented system approach. The optimal controllers use state feedback for regulation purposes. For the tracking objective the future set-points along the reference trajectory vector are used. Necessary and sufficient conditions for the existence of an optimal feedforward solution are presented in terms of the relationships between the eigenvalues of the closed-loop system and those of the trajectory models. For illustration a numerical example is included which is based on a dual-stage positioning carriage modelled as a linear multivariable plant.

Preview Control for MIMO Discrete-Time System with Parameter Uncertainty

“…However, the dimension of an AES is high and the calculation is complex. In addition, through numerical simulations, we find that the preview control effect is not ideal when the reference signal is a vector, as in [11,13,15,36,37]. The components of the reference signal influence each other, and the influence is often negative.…”

“…Therefore, it is more interesting to consider the control problem of MIMO systems. For example, the preview control problem of MIMO systems was studied in [36] by combining linear quadratic optimal theory with the AES method. However, the dimension of an AES is high and the calculation is complex.…”

“…The components of the reference signal influence each other, and the influence is often negative. However, for a high-dimensional reference signal, the AES constructed in [11,13,15,36,37] not only has a high dimension, but the component signals also share the same preview length.…”