# Implementation of Fault-Tolerant Control for
## 1 Introduction  
During the past two decades, fault detection and fault-tolerant control (FTC) have become attractive research subjects that can be used to improve system reliability and guarantee system stability in all situations. Implementation of fault-tolerant control in robot manipulators has encountered a number of challenges due to high nonlinearities, dynamic uncertainties, and external disturbances. In addition, the time delay inherent to mechanical systems also affects the performance of FTC. FTC strategies can be divided into two categories: passive FTC (PFTC) [1; 2] and active FTC (AFTC) [3; 4]. In PFTC, the control performances mainly depend on the robust capability dealing with uncertainties/disturbances of the controller such as sliding mode control [5] or adaptive control [6; 7]. In this strategy, the controller does not have a faults estimation process. The advantage of PFTC is the fast response when faults occur, because it does not need time to estimate faults. However, the ability to deal with high magnitude faults is limited. Unlike PFTC, AFTC reconfigures the control system based on the estimation process. The fault information from the estimation process is used to compensate the conventional controller. The disadvantage of this strategy is slow response after faults occur, which leads to the occurrence of a picking phenomenon, because the controller needs the time to estimate the faults. Most studies in active fault-tolerant control [3; 8; 9] have focused on increasing the ability to deal with uncertainties/disturbances of the controller. Therefore, the performance degradation of the system with the AFTC strategy due to the slow response still remains an open problem. However, AFTC has better ability when dealing with high magnitude faults than PFTC. As above-mentioned, usingPFTC or AFTC depends on the characteristics of the system and type of faults. In robot manipulator control, AFTC generally outperforms PFTC because AFTC includes a fault estimation (FE) step. The estimated faults can be compensated for by online controller reconfiguration. In this way, the stability and acceptable performance of the robot can be maintained. In AFTC, the quality of the fault-tolerant control depends on the accuracy of both FE and the system reconfiguration after faults occur. In fault estimation processing, several techniques [10; 11; 12; 13; 14; 15] have been used. The parameter estimation method [10] is used to early detect faults applied for dynamic linear and nonlinear systems. The parity relations [11] used the parity equations to be combined with the least-square method to estimate faults. The sliding mode observers [12] have been given lot of attention by researchers. However, this method is limited in real applications due to the disadvantages such as the chattering phenomenon, the requirement of the knowledge of the fault's bound to choose the observer parameters, and the stability issue. In addition, other techniques such as the Kalman Filter [13], zonotope [14], and nonlinear observer [15] were developed to estimate the faults as well as uncertainties/disturbances. After faults are estimated, they are compensated for by using various control strategies [16; 17; 18]. In this study, an extended state observer [19] was adopted for on-line observation of the dynamic uncertainties, disturbances, and faults. An extended state observer (ESO) is a simple technique for estimating faults in which simply adjusting the observer parameters leads to simple application in real systems, and the observer can detect and isolate faults without a fault diagnosis process. In addition, the upper bound of faults does not have to be exactly known in the design of ESO. A synchronization technique based on cross-error was first introduced by [PERSON] [20] in the 1980s for a computerized numerical control (CNC) machine. In his idea, a CNC with independent axes control is extended to enable the control of each access to consider the effects of the other axes through cross-errors. [PERSON] et al.