Robust Fault Tolerant LPV Control Design for Systems Under Actuator Failures

Abstract

In this paper, we investigate the problem of fault tolerant controller (FTC) design for systems affected by actuator failures. For this purpose, we compare the performance of the closed-loop systems obtained from designing three different controllers: one is the traditional H 1 controller designed to work in the healthy condition, the second one is a robust LPV controller that is scheduled based upon an estimate of the fault signals, and finally a robust H 1 controller that takes into account the uncertainty parameters representing the fault signals. The design approaches presented in this paper are validated on a Highly Maneuverable Aircraft Technology (HiMAT) vehicle model subject to the loss of control effectiveness. I. Introduction Fault Tolerant Control Systems (FTCS) are a class of highly sophisticated control functions designed in a unified framework in order to maintain high levels of system integrity, performance and redundancy. Two classes of FTCS are defined in the literature: passive and active designs. A passive FTCS can tolerate faulty operation while maintaining satisfactory performance without any control reconfiguration. An active FTCS (AFTCS), on the other hand, needs a fault detection and isolation (FDI) scheme and a control reconfiguration mechanism. The key-role for the FDI scheme is to continuously monitor the system behavior to detect faulty operation and locate failed components. The decisions made by the FDI scheme command a reconfiguration mechanism to reconfigure (or sometimes restructure) the control law in real-time basis accordingly. A bibliographical review on the definition and classes of FTCS, major components of FTCS, and review of some of the design methodologies can be found in the survey papers. 8, 11 Since an FDI module and an FTC law are individually designed ignoring the other dynamics, it is required to analyze the whole FTC system including both FTC law and the FDI module before they are implemented in the actual system. A typical method for analyzing the FTC system is full nonlinear simulation with the known command inputs for the possible fault scenarios. After detailed simulations, the FTC system may be validated for the possible fault scenarios with expensive computational costs. Generally, an active FTC law is designed based on an open-loop system modeled as a function of fault parameters under the assumption that the parameters are immediately identified by the FDI module. Recently, using linear matrix inequality (LMI) optimization-based solutions, active FTC laws have been synthesized in the linear parameter varying (LPV) framework, whose dynamics varies as the scheduling parameters change. Open-loop dynamics of a system affected by the actuator or sensor faults is modeled as an LPV system in which the scheduling parameters are fault parameters that represent fault occurrences at actuators or sensors or both. An FTC-LPV law, designed based on the open-loop system, can robustly stabilize the closed-loop system and achieve the desired level of performance during a fault occurrence under the assumption that fault parameters can be measured in real-time. There are only few work in the literature looking at the problem of FTC control design from an LPV framework perspective. 3, 5‐7, 9, 10 Kanev 6 presents two methods for active FTC-LPV design including a deterministic approach that can deal with multiplicative sensor and actuator faults, as well as, a probabilistic design method which makes it possible to consider, in addition to sensor and actuator faults, component faults in order to schedule the LPV controller on both the fault estimates and their uncertainty sizes. The deterministic approach designs off-line a bank of LPV controllers for specific fault scenarios. Then, based on the fault estimates, the controller that achieves the best performance is switched on. This LPV controller is subsequently scheduled by the size of the uncertainty in the fault estimate. The probabilistic-based design replaces the bank of controllers from the deterministic method by only a single LPV controller. The latter approach also considers (structured) model uncertainty in addition to the FDD uncertainty. Both approaches can be