Combining Artificial Intelligence and Robust Techniques with MRAC in Fault Tolerant Control
Vargas Martínez, Adriana
The investigation of this thesis presents different approaches for Fault Tolerant Control based on Model Reference Adaptive Control, Artificial Neural Networks, PID controller optimized by a Genetic Algorithm, Nonlinear, Robust and Linear Parameter Varying (LPV) control for Linear Time Invariant (LTI), LPV and nonlinear systems. All of the above techniques are integrated in different controller�s structures to prove their ability to accommodate a fault. Modern systems and their challenging operating conditions in certain processes increase the possibility of system failures causing damages in equipment and/or their operators. In these environments, the use of automation control (i.e. adaptive and robust control) and intelligent systems is fundamental to minimize the impact of faults. Therefore, Fault Tolerant Control (FTC) methods have been proposed to ensure the continuous operations of system even in fault situation and to prevent more serious effects. Until now, most of the FTC methods that have been developed are based on classical control theory (Yu et al., 2005; Zhang et al., 2007; Fradkov et al., 2008; Yang et al., 2008). The use of Artificial Intelligence (AI) in FTC has emerged recently (Stengel, 1991; Bastani & Chen, 1998; Patton et al., 1999; Korbiicz et al., 2004). Classical Artificial Intelligence (AI) approaches such as Artificial Neural Networks (ANN), Fuzzy Logic (FL), ANN-FL and Genetic Algorithms (GA) may offer some advantages over traditional methods (Schroder et al., 1998; Yu et al., 2005; Dong et al., 2006; Alves et al., 2009; Beainy et al., 2009; Kurihara, 2009; Li, 2009; Nieto et al., 2009; Panagi & Polycarpou, 2009) in the control community such as state observers, statistical analysis, parameter estimation, parity relations, residual generation, etc. The reasons are that AI approaches can reproduce the behavior of nonlinear dynamical systems with models extracted from data. Also, there are many learning processes that improve the FTC performance. This is a very important issue in FTC applications on automated processes, where information is easily available, or processes where accurate mathematical models are hard to obtain. In the last years, FTC and control schemes based on LPV systems have been developed. In Bosche et al. (2009) a Fault Tolerant Control structure for vehicle dynamics is developed employing an LPV model with actuator failures. The methodology described in Bosche et al. (2009) paper is based on the resolution of Linear Matrix Inequalities (LMIs) using the DC-stability concept and a Parameter-Dependent Lyapunov Matrix (PDLM). In Montes de Oca et al. (2009), an Admissible Model Matching (AMM) FTC method based on LPV fault representation was presented; in this approach the faults were considered as scheduling variables in the LPV fault representation allowing the controller adaptation on-line. For instance, in Rodriges et al. (2007) a FTC methodology for polytopic LPV systems was presented. The most important contribution of Rodrigues et al. (2007) work was the development of a Static Output Feedback (SOF) that maintains the system performance using an adequate controller reconfiguration when a fault appears. On the other hand, advanced techniques from Robust Control such as H?, have also been applied to FTC with encouraging results. For example, in Dong et al. (2009), an active FTC scheme for a class of linear time-delay systems, using a H? controller in generalized internal mode architecture in combination with an adaptive observer-based fault estimator was presented. In Xiadong et al. (2008) a dynamic output feedback FTC approach that uses a H? index for actuator continuous gain faults was proposed. And, in Liang & Duan (2004) a H? FTC approach was used against sensor failures for uncertain descriptor system (systems which 3 capture the dynamical behavior of natural phenomena). To improve the capabilities of the FTC systems mentioned above, different types of controller based on Adaptive Control, Artificial Neural Networks, Robust, Nonlinear and LPV Control for LTI, LPV and Nonlinear systems are proposed in this thesis. These controllers are first tested in an Industrial Heat Exchanger and then tested in a Coupled-Tank LPV System. Different types of faults are simulated in the implemented schemes: First, additive abrupt faults and gradual faults were introduced. In the abrupt fault case, the whole magnitude of the fault is developed in one moment of time and is simulated with a step function. On the other hand, gradual faults are developed during a period of time and are implemented with a ramp function. Second, multiplicative faults were tested. All types of faults, additive and multiplicative, can be implemented in sensors (feedback), in which the properties of the process are not affected, but the sensor readings are mistaken. And it also can be implemented in actuators (process entry) causing changes in the behavior of the process or interruption. The controllers developed to test the Industrial Heat Exchanger are a Model Reference Adaptive Controller (MRAC), an MRAC with a PID controller whose parameters were optimized using a GA (MRACPID), an MRAC with an ANN (MRAC-ANN), an MRAC with a PID and an ANN (MRAC-ANN-PID), an MRAC with a Sliding Mode Controller (MRAC-SMC) and finally, an MRAC with an H? control (MRACH?). These MRAC controllers were design using the MIT rule. The controller with the best response against the faults is the MRAC-ANN-PID controller because was robust against the tested sensor and the actuator were imperceptible with almost a 0% error between the reference model and the process model. For the Coupled-Tank LPV system, an MRAC (MRAC-4OP-LPV), an MRAC with an ANN (MRAC-ANN4OP-LPV) and an MRAC with an H? controller (MRAC-H?4OP-LPV) were designed for 4 operating points of the LPV system. For the sensor faults, the controller with the best results was the MRACNN4OP-LPV because it was fault tolerant against the tested sensor faults no matter the value of the operating point. This method resulted the best scheme because is a combination of two type of controllers, one is a Model Reference Adaptive Controller (MRAC) and the other one is an Artificial Neural Network designed to follow the ideal trajectory (non-faulty trajectory). For the actuator faults, the MRAC-H?4OP-LPV was the best scheme because it was fault tolerant to the applied faults and also could accommodate the faults faster than the MRAC-4OP-LPV scheme. In addition, for the Coupled-Tank system, an MRAC (MRAC-LPV) controller and an MRAC with an H? Gain Scheduling controller (MRAC-H?GS-LPV) that work for all the operating points of the LPV system were developed. Both controllers were tested using the LPV system of the plant and also were tested using the nonlinear model of the system. In general, for additive and multiplicative faults, the MRAC-H?GSLPV showed better results because is a combination of two type of LPV controllers, one is a Model Reference Adaptive Controller (MRAC) and the other one is a H? Gain Scheduling Controller, both controllers were designed for an LPV system giving them the possibility of controlling any desired operating point between the operation range of the dependent variables (? and ? ). In addition, the manipulated variable was plotted and it can be observe on this figure how the system compensates the fault. 4 The main contributions of this research are the development of the MRAC with an Artificial Neural Network and a PID controller optimized by a Genetic Algorithm (MRAC-ANN-PID) and the development of an MRAC with an H? Gain Scheduling Controller that works for all the operating points of an LPV system (MRAC-H?GS-LPV). The MRAC-ANN-PID controller as mentioned above resulted to be robust against sensor and the actuator faults were imperceptible with a very low error between the reference model and the process. The PID parameters of this controller Kp, Ki and Kd were optimized in order to follow the desired trajectory (no faulty system) and the ANN was trained also to follow the desired system trajectory no matter the fault size. The MRAC-ANN-PID controller is different from the controllers that already exist in the literature first because none of them had the controller structure of the MRAC-ANN-PID, second because most of them do not use any Artificial Intelligence methods such as ANN or GA. And third, in the literature, the ANN is used to represent or estimate the plant not as a controller which is the case of this research. On the other hand, for the MRAC-H?GS-LPV controller the main contribution was the development of a passive structure of FTC able to deal with abrupt and gradual faults in actuators and sensors of nonlinear processes represented by LPV models. This controller can accommodate the tested faults for any operating point between the operating ranges. The MRAC and the H? Gain Scheduling controller were specially designed to switch from one operating point to another in less than a second. The MRAC controller was chosen as a FTC because guarantees asymptotic output tracking, it has a direct physical interpretation and it is easy to implement. The H? Gain Scheduling Controller was also chosen because it increases the robust performance and stability of the closed loop system. In the existing literature, the H? technique has been combined with other schemes to control systems but to the best of our knowledge there are no reports concerning the combination of an MRAC with an H? Gain Scheduling controller.