Abstract
The paper presents the design conditions adequate in design of virtual actuators and utilizable by nominal static output control structures in fault-tolerant control for strictly Metzler systems. The positive stabilization with H∞ norm performance is also addressed for virtual actuator design for strictly Metzler systems with interval uncertainty matrix representations of single actuator faults. Taking into account disturbance conditions and changes of values of variables after the virtual actuator activation, the design conditions are outlined in the terms of linear matrix inequalities. The approach provides a way to obtain acceptable dynamics of the closed loop system after virtual actuator activation.
Highlights
To increase the reliability of systems, fault-tolerant control structures (FTC) usually fix a system with faults so that it can continue its mission with certain limitations of functionality and quality
Bearing in mind that reconfiguration after occurrence of an actuator fault can be related to disturbance decoupling, the trend using the terms of a finite set of linear matrix inequalities (LMI) in virtual actuator (VA) design condition formulation is rather natural (Tabatabaeipour et al (2015); Krokavec et al (2016); Bessa et al (2021); Hu et al (2021))
The main illustrative contribution of this example is the detailed explanation of the VA design steps, based on the system constraint interpretation and a single actuator fault interval limits incorporation in the LMI algorithm, including the implementation algorithm for strictly Metzler continuoustime linear systems
Summary
To increase the reliability of systems, fault-tolerant control structures (FTC) usually fix a system with faults so that it can continue its mission with certain limitations of functionality and quality. The primary goal is to find the stabilizing nominal controller for the Metzler system, being consistent with the positive configuration, as well as to design the VA parameters to retain that the positive continuous-time system properties will be preserved in the faulty regime after VA activating, when a single actuator fault occurs. Such defined class of systems prescribes the set of strong structural parametric constraints, the proposed design conditions allow obtaining numerical solutions in the straightforward access. In indicates the n-th order unit matrix, R (R+) qualifies the set of (nonnegative) real numbers, Rn+×+r (Rn+×r) refers to the set of n × r strictly positive (nonnegative) real matrices and Mn−×+n, (Mn−×+n◦) is the set of strictly (purely) Metzler matrices
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