Fundamental performance limitations of feedback control systems.

摘要

This thesis has investigated the fundamental performance limitation and tradeoff issues for finite-dimensional, linear, time-invariant feedback control systems. Both single-input single-output and non-square systems have been considered. Our approaches involve both frequency domain sensitivity integral constraints and time domain $H2$ performance measures. The emphasis in our development is to relate the inescapable performance limitations to system intrinsic characteristics, such as, nonminimum phase zeros, unstable poles, and plant structure.; For single-input single-output systems, we develop a number of extended versions of the argument principle for both continuous-time and discrete-time applications. By using these extended integral formulas, it has been shown that the classical Bode/Poisson integral constraints can all be unified in a coherent way. More importantly, based on the extended integral formulas, we develop a number of new sensitivity integral constraints, which then enable a more refined performance study together with the known results. Additionally, we also build connections between the extended Bode type sensitivity integral relations and such time domain performance measures as minimum tracking error and regulation energy. These connections help us to get deeper insights into both branches of performance study.; For non-square systems, both time and frequency domain performance measures have been studied. In particular, we have examined the optimal tracking and regulation performances, which are achieved over all stabilizing controllers. For single-input multi-output systems, it has been shown that the variation of the plant direction with frequency has a close pertinence on the tracking error. For non-left-invertible systems, our result indicates that the plant structure also imposes constraints upon the minimum regulation energy. Furthermore, we develop the Bode type complementary sensitivity integral relation, in both equality and inequality forms, for single-input two-output systems. For all these problems, explicit results have been obtained, which in general characterize, other than the nonminimum phase zeros and unstable poles of the plant, how the non-square structure may impose additional difficulties for the control design. These results thus reveal and quantify the structural constraints that arise in different settings, which can not find their counterparts in square systems.; The results presented in the thesis are expected to contribute to the understanding of the fundamental performance limitations and tradeoff issues in feedback control design.