On Convergence of Tracking Differentiator with Multiple Stochastic Disturbances

In this paper, the convergence and noise-tolerant performance of a tracking differentiator in the presence of multiple stochastic disturbances are investigated for the first time. We consider a quite general case where the input signal is corrupted by additive colored noise, and the tracking differentiator itself is disturbed by additive colored noise and white noise. It is shown that the tracking differentiator tracks the input signal and its generalized derivatives in mean square and even in almost sure sense when the stochastic noise affecting the input signal is vanishing. Some numerical simulations are performed to validate the theoretical results

A jittered-sampling correction technique for ADCs

In Analogue to Digital Converters (ADCs) jittered sampling raises the noise floor; this leads to a decrease in its Signal to Noise ratio (SNR) and its effective number of bits (ENOB). This research studies a technique that compensate for the effects of sampling with a jittered clock. A thorough understanding of sampling in various data converters is complied

Investigations of Model-Free Sliding Mode Control Algorithms including Application to Autonomous Quadrotor Flight

Sliding mode control is a robust nonlinear control algorithm that has been used to implement tracking controllers for unmanned aircraft systems that are robust to modeling uncertainty and exogenous disturbances, thereby providing excellent performance for autonomous operation. A significant advance in the application of sliding mode control for unmanned aircraft systems would be adaptation of a model-free sliding mode control algorithm, since the most complex and time-consuming aspect of implementation of sliding mode control is the derivation of the control law with incorporation of the system model, a process required to be performed for each individual application of sliding mode control. The performance of four different model-free sliding mode control algorithms was compared in simulation using a variety of aerial system models and real-world disturbances (e.g. the effects of discretization and state estimation). The two best performing algorithms were shown to exhibit very similar behavior. These two algorithms were implemented on a quadrotor (both in simulation and using real-world hardware) and the performance was compared to a traditional PID-based controller using the same state estimation algorithm and control setup. Simulation results show the model-free sliding mode control algorithms exhibit similar performance to PID controllers without the tedious tuning process. Comparison between the two model-free sliding mode control algorithms showed very similar performance as measured by the quadratic means of tracking errors. Flight testing showed that while a model-free sliding mode control algorithm is capable of controlling realworld hardware, further characterization and significant improvements are required before it is a viable alternative to conventional control algorithms. Large tracking errors were observed for both the model-free sliding mode control and PID based flight controllers and the performance was characterized as unacceptable for most applications. The poor performance of both controllers suggests tracking errors could be attributed to errors in state estimation, which effectively introduce unknown dynamics into the feedback loop. Further testing with improved state estimation would allow for more conclusions to be drawn about the performance characteristics of the model-free sliding mode control algorithms

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Active Fault Tolerant Control Based on a Novel Tracking Differentiator for Elevating Stage Control System

In view of the speed sensor faults in elevating stage control system, an active fault tolerant control approach based on a novel tracking differentiator is proposed in this paper. First, the analytical redundancy relationship between the velocity and displacement signals in a dual closed loop control system is used to detect a fault. When the deviation between the differential of normal displacement sensor signal and the fault speed sensor output exceeds a certain threshold value, a fault can be considered to occur. Secondly, after a fault is detected, the output of the fault sensor is replaced immediately with the differential signal of the output from a normal sensor to ensure the safety of the postfault system. In the process of signal differential, considering the drawbacks of the traditional method which uses inertial element to approximate differentiator and complex parameter tuning of Han’s Tracking Differentiator (TD), a novel tracking differentiator based on hyperbolic tangent function (Tanh-TD) is designed. Thirdly, in order to avoid the switching vibration and improve the reliability of FDD, a continuous smooth switching tactic based on exponential function is constructed. The simulation results show that the fault diagnosis method is simple and timely, the designed tracking differentiator is fast and effective, and the effect of the fault tolerant control based on smooth switching strategy is also satisfactory