Integration of invariant‐set‐based FDI with varying sampling rate virtual actuator and controller

Abstract

We present a new output feedback fault-tolerant control strategy for continuous-time linear systems with bounded disturbances. The strategy combines a digital nominal controller under controller-driven (varying) sampling with virtual actuator (VA)-based controller reconfiguration to compensate for abrupt actuator faults and invariant-set-based fault detection and isolation. Two independent objectives are considered: (a) closedloop stability with setpoint tracking and (b) controller reconfiguration under faults. Our main contribution is to extend an existing fault detection and isolation and VA-based controller reconfiguration strategy to systems under controller-driven sampling in such a way that if objective (a) is possible under controllerdriven sampling (without VA) and objective (b) is possible under uniform sampling (without controllerdriven sampling), then closed-loop stability and setpoint tracking will be preserved under both healthy and faulty operations for any possible sampling rate evolution that may be selected by the controller. Copyright 394 E. OSELLA, H. HAIMOVICH AND M. M. SERON range. In addition, a residual signal is constructed for each VA directly from its available measurable signals. A switching rule engages the suitable VA from the bank according to an FDI decision based on sets defined for the residual signals. This set-based approach for FDI (see, e.g., [5,6]) relies on the principle that each residual signal will belong to an invariant 'correct-matching' set when the associated VA model 'matches' the actual actuator fault situation and will shift to a 'fault-transitionmatching' set when a change to a 'non-matching' fault situation occurs. An important advantage of this invariant-set approach to FDI is that fault tolerance and closed-loop stability can be guaranteed when the relevant sets have no intersection.In the present paper, we extend the approach of [4] to continuous-time linear systems operating under a controller-driven (varying) sampling setting, where both the nominal controller and the bank of VAs operate under a varying sampling rate administered by the controller. The motivation for considering this class of systems stems from the increasing popularity of networked control systems [7,8], which broadly refers to control systems that include some kind of shared communications network. In this setting, acceptable control performance and communication bandwidth preservation may be conflicting objectives: increasing control performance by sampling at a higher rate may require too much bandwidth and prevent other processes from accessing the network. Thus, research effort has been directed at control strategies able to modify the sampling rate online, according to time-dependent performance and bandwidth requirements (see [9] for further details). As opposed to the general networked control systems setting where the different component elements (sensors, actuators, and controllers) may operate asynchronously, we consider a setting with a centralized controller, with synchronous o...

An actuator fault tolerant strategy under controller-driven sampling and measurement losses

“…x ref , u ref are state and input constant reference signals respectively, andx,x + are the current and successor states of the observer (5). Every sampling period is selected from a finite set H := {h 1 , · · · , h ns }, with every h i non-pathological (see [13]).…”

“…The nominal controller signal given in (4) uses the reference values satisfying (7), which define an equilibrium point for both the continuous-time systemẋ = Ax + Bu, and the discrete-time system x + = A h x + B h u for every sampling period h, that is (see [5] for details)…”

“…As in [12], [5], we consider a bank of VAs where each VA is designed to compensate for a specific fault situation. The VA associated to the i-th fault situation is given by…”

“…We consider a particular NCS setting with a centralised controller in synchronous operation, which is in charge of both computing control actions and determining the appropriate sampling rate. This controller-driven sampling (CDS) setting is akin to that in [3], and has been used in some of our previous publications [4], [5], where we have provided conditions for the design of the controller feedback matrices that ensure stability for any sampling period sequence.…”

“…The VA design is independent of the nominal controller and is aimed at preserving specific closed-loop properties, such as stability and setpoint tracking, in the presence of faults. In previous work [5], [10], [11], we have adapted the VA technique to the CDS context by extending the 'bank of VA' approach of [12] through the derivation of conditions under which constant reference tracking and stability are ensured under both on-line sampling period variation and total actuator losses.…”