A high‐performance robust control method based on the gain and phase information of uncertainty

Abstract

SummaryThe well‐known small‐gain and passivity approaches to robust control only make use of either the gain or the phase information of uncertainty in system design. This results in a limitation on the achievable control bandwidth in practical applications. To relax the limitations associated with these approaches, we explore the possibility of utilizing both the gain and the phase information of uncertainty in robust control design. In this paper, the modeling of uncertainty accounting for both gain and phase is discussed first. Then conditions for robust stability and robust performance (sensitivity and bandwidth) are derived respectively. These robustness conditions are described as phase or gain constraints on the nominal system in different frequency bands. Further, it is revealed, both theoretically and via a hard disk drive benchmark, that a much higher robust performance can be achieved by using the gain and phase information of uncertainty. Copyright © 2013 John Wiley & Sons, Ltd.

Optimal design of robust feedforward compensator with gain and phase specifications

“…respectively, as in the works of Liu and Shirnen 19 and Liu,20 which demonstrated the importance of using phase information in the analysis and synthesis of control system.…”

“…It is supposed that the gain and phase boundaries of the uncertainty Δ T ( s ) are represented as and respectively, as in the works of Liu and Shirnen and Liu, which demonstrated the importance of using phase information in the analysis and synthesis of control system.…”

Gain‐phase information based robust control theory

“…This is the extension of the results of Reference 6 and is more general than that of Reference 12. The proposed approaches treat MIMO systems in contrast to the papers of Liu et al [2][3][4][5] that deal with SISO systems. Secondly, a new GP-mixed sensitivity method was formulated and the W -K iteration algorithm was proposed to solve it.…”

“…The H ∞ -control based postmodern control theory has made a great success theoretically and practically; however, it has the limitation of neglecting the phase information in the stability analysis and the control design. [2][3][4][5][6][7][8][9][10][11] The H ∞ -robust control theory is essentially based on the small-gain theorem, therefore, it does not use the phase information in the robust stability analysis, [2][3][4][5][6][7][8][9][10][11] and it also uses only the gain information (H ∞ norm) as the optimality criterion. 1,12 In other words, this theory neglects the phase information in two aspects: stability analysis and design criterion.…”

“…However, they could not extend their approaches to MIMO systems nor establish the design methodology. 5 Some researchers have used the phase information as optimality criterion. Tomizuka 19 proposed the zero phase error tracking control (ZPETC) whose control objective is to make the phase error of the overall system zero, which was further investigated by several researchers.…”