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Unformatted text preview: Click to edit Master subtitle style 3/10/11 Adriana VargasMartÃnez VicenÃ§ Puig Luis E. GarzaCastaÃ±Ã³n Ruben MoralesMenendez MRAC + H Fault Tolerant Control for âˆž Linear Parameter Varying Systems 3/10/11 Introduction The main intention of this work is to develop a passive structure of FTC able to deal with abrupt and gradual faults in actuators and sensors of nonlinear processes represented by LPV models. An MRAC controller was chosen as a FTC because guarantees asymptotic output tracking, it has a direct physical interpretation and it is easy to implement. 3/10/11 Introduction Two different approaches for FTC based on Adaptive, Robust and LPV control are proposed. First, a Model Reference Adaptive Controller for an LPV system (MRACLPV) is considered and second a combination of a MRAC with a H Gain Scheduling controller for âˆž an LPV system (MRACH GSLPV) is also proposed. âˆž To compare the performance of these schemes, a CoupledTank system was used as testbed in which two different types of faults (abrupt and gradual) 3/10/11 LPV Control Theory The Linear Parameter Varying (LPV) systems depend on a set of variant parameters over time. These systems can be represented in state space (continuous or discrete). The continuous representation of an LPV system is: xx=A x Ï† ( t) x x+B x Ï† ( t) x u y=C x Ï† (t) x x+D x Ï† (t) x u 3/10/11 Model Reference Adaptive Controller The MRAC implements a close loop controller where the adaptation mechanism adjusts the controller parameters to match the process output with the reference model output. The reference model is specified as the ideal model behavior that the system is expected to follow. This type of controller behaves as a close loop controller because the actuating error signal (difference between the input and the feedback signal) is fed to e = yy m 3/10/11 Model Reference Adaptive Controller To reduce the error, a cost function was used in the form of: where Î¸ is the adaptive parameter inside the controller. The function above can be minimized if the parameters Î¸ change in the negative direction of the J x Î¸ x = 1 / 2 e 2 x Î¸ x dÎ¸ d t x àµ— = Î³ âˆ‚ J âˆ‚Î¸ =Î³ âˆ‚e âˆ‚Î¸ e âˆ‚e âˆ‚Î¸ 1 =x a 1r s+a 0r s 2 +a 1r s+a 0r xu c â†’ dÎ¸ 1 dt =Î³ âˆ‚e âˆ‚Î¸ 1 e=Î³x a 1r s+a 0r s 2 +a 1r s+a 0r u c xe âˆ‚e âˆ‚Î¸ 2 =x a 1r s+a 0r s 2 +a 1r s+a 0r xyâ†’ dÎ¸ 2 d t =Î³ âˆ‚e âˆ‚Î¸ 2 e = Î³x a 1r s+a 0r s 2 +a 1r s+a 0r yxe 3/10/11 Model Reference Adaptive Controller Reference Model Process Controller Adaptation Mechanism Controller Parameters u y e y m u c + 3/10/11...
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This note was uploaded on 03/09/2011 for the course MECHATRONI 001 taught by Professor Avm during the Spring '11 term at ITESM.
 Spring '11
 AVM

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