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Abstract:In recent years, there has been considerable interest in the study of feedback systems containing processes whose dynamics are best described by fractional order derivatives. Various situations have been cited for describing heat flow and aspects of bioengineering, where such models are believed to be superior. In many situations these feedback systems are not linear and information on their stability and the possibility of the existence of limit cycles is required. This paper presents new results for determining limit cycles using the approximate describing function method and an exact method when the nonlinearity is a relay characteristic.

This study demonstrates an application of multiloop Model Reference Adaptive Control (MRAC) structure for enhancement of fault tolerance performance of closed-loop PID control systems. The presented multi-loop MRAC-PID control structure can be used to transform a conventional PID control system to an adaptive control system by combining an outer adaptation loop. This study shows that the proposed control structure can improve fault tolerance and fault detection performance of the existing closed-loop PID control systems without modifying any coefficients of PID controllers, and this asset is very useful for increasing robust control performance of the existing industrial control systems. This advantage originates from the reference input shaping technique that is implemented to combine adaptation and control loops. Numerical and experimental studies are presented to illustrate an application of the MRAC-PID control structure for rotor control applications.

This study presents a model reference adaptive control scheme based on reference-shaping approach. The proposed adaptive control structure includes two optimizer processes that perform gradient descent optimization. The first process is the control optimizer that generates appropriate control signal for tracking of the controlled system output to a reference model output. The second process is the adaptation optimizer that performs for estimation of a time-varying adaptation gain, and it contributes to improvement of control signal generation. Numerical update equations derived for adaptation gain and control signal perform gradient descent optimization in order to decrease the model mismatch errors. To reduce noise sensitivity of the system, a dead zone rule is applied to the adaptation process. Simulation examples show the performance of the proposed Reference-Shaping Adaptive Control (RSAC) method for several test scenarios. An experimental study demonstrates application of method for rotor control.

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