Shayok Mukhopadhyay

Robustness analysis for battery-supported cyber-physical systems

This article establishes a novel analytical approach to quantify robustness of scheduling and battery management for battery supported cyber-physical systems. A dynamic schedulability test is introduced to determine whether tasks are schedulable within a finite time window. The test is used to measure robustness of a real-time scheduling algorithm by evaluating the strength of computing time perturbations that break schedulability at runtime. Robustness of battery management is quantified analytically by an adaptive threshold on the state of charge. The adaptive threshold significantly reduces the false alarm rate for battery management algorithms to decide when a battery needs to be replaced.

Fractional order networked control systems and random delay dynamics: A hardware-in-the-loop simulation study

In networked control systems (NCS), the spiky nature of the random delays makes us wonder about the benefits we can expect if the “spikiness”, or what we call “delay dynamics” are considered in the NCS controller design. It turns out that the “spikiness” of the network induced random delays can be better characterized by the so-called α-stable processes, or processes with fractional lower-order statistics (FLOS) which are linked to fractional calculus. Using a real world networked control system platform called the CSOIS Smart Wheel, the effect of modeling the network delay dynamics using non-Gaussian distributions, and compensating for such a delay in closed-loop systems using a FO-PI (fractional order proportional and integral) controller has been experimentally studied. The cases studied include the case when the delay compensated is exactly the same as the actual delay. Other scenarios are the ones when the nature of the estimated delay is similar to the actual delay, but the magnitude is slightly smaller. The effect of phase shifting between the estimated and the original delay is also considered. Finally the order of the fractional order proportional integral controller which gives least ITAE, ISE for a particular distribution of the delay is presented. The conclusion is strikingly stimulating: in NCS, when the random delay is spiky, we should consider to model the delay dynamics using a-stable distributions and using fractional order controller whose best fractional order has shown to be related to the FLOS parameter a as evidenced by our extensive experimental results on a real NCS platform.

Collaborative Autonomous Surveys in Marine Environments Affected by Oil Spills

This chapter presents results on collaborative autonomous surveys using a fleet of heterogeneous autonomous robotic vehicles in marine environments affected by oil spills. The methods used for the surveys are based on a class of path following controllers with mathematically proven convergence and robustness. Use of such controllers enables easy mission planning for autonomous marine surveys where the paths consist of lines and curves. The control algorithm uses simple dynamic models and simple control laws and thus enables quick deployment of a fleet of autonomous vehicles to collaboratively survey large areas. This enables using a mobile network to survey an area where the different member nodes may have slightly different capabilities. A mapping algorithm used to reconcile data from heterogeneous marine vehicles on multiple different paths is also presented. Vehicles with heterogeneous dynamics are thus used to aid in the reconstruction of a time varying field. The algorithms used were tested, mainly on student-built marine robots that collaboratively surveyed a coastal lagoon in Grand Isle, Louisiana that was polluted by crude oil during the Deepwater Horizon oil spill. The results obtained from these experiments show the effectiveness of the proposed methods for oil spill surveys and also provide guidance for mission designs for future collaborative autonomous environmental surveys.

Controller performance of marine robots in reminiscent oil surveys

A class of path following and formation controllers are implemented on marine robots performing autonomous surveys in regions polluted by crude oil during the Deepwater Horizon oil spill. The controllers enable the robots to follow lines and curves, and maintain formation collectively while measuring reminiscent crude oil along their paths. The controllers are mathematically sound with proven convergence and robustness. However, their performance in the surveying missions is affected by natural disturbances caused by wind and water currents, and constraints such as sensor inaccuracy, localization errors, and network delays. This paper evaluates the performance of our controllers based on data collected during a survey performed at Grand Isle, Louisiana. These results will provide guidance for mission designs and inspire the future developments of our marine robots used to perform autonomous environmental surveys.

Experimental Studies of a Fractional Order Universal Adaptive Stabilizer

This work performs experimental verification of the asymptotic stability of two different types of fractional scalar systems by using universal adaptive stabilization as in. The types of systems verified experimentally are: (I) Fractional dynamics with integer order control strategy (II) Fractional dynamics with fractional order control strategy. The Mittag-Leffler function Ealpha(-lambdatalpha), forallalphaisin (2, 3] and lambda > 0 is used as a Nussbaum function as per [1]. Extensive hardware in the loop simulation of the mathematically developed results have been included in the paper. The results of the experiment serve not only to improve the understanding of fractional order universal adaptive stabilization but also proves that the methodology works well on real world systems.

Purely Analog Fractional Order PI Control Using Discrete Fractional Capacitors (Fractors): Synthesis and Experiments

This paper presents the results of experiments related to analog fractional order PI control of a coupled tank system. A custom circuit board has been built to perform analog PID/FOPID control. Specialized circuit elements called ‘Fractors’ [1] are used to perform fractional order integration/differentiation of the error signals. The design of the board, subsequent experimentation and its comparison to similar digital control techniques have been presented. The benefits of purely analog control when dealing with non-linearities are also discussed. Further, methods of approximating a particular fractional order α* with any number of practically available orders α1 , α2 , ....αn has also been presented. The conclusion of this work examines the need for purely analog control as opposed to widespread digital methods and also lays down definite directions for future work.Copyright

A high-gain adaptive observer for detecting Li-ion battery terminal voltage collapse

We use a high-gain adaptive observer and a trend filtering algorithm to detect early stages that lead to terminal voltage collapses in Li-ion batteries. This approach allows accurate detection without having sophisticated battery models. Theoretical analysis proves that the physical Li-ion battery becomes unstable when the estimated states of the observer enter instability. The trend filtering algorithm is able to detect such instability under large perturbations from the discharge current. Extensive simulation and experimental results demonstrate the effectiveness of the algorithms and its robustness under realistic perturbations.

Adaptive detection of terminal voltage collapses for Li-ion batteries

We introduce a novel approach for detecting and predicting terminal voltage collapses in Li-ion batteries without having complete knowledge of a battery model. We present a simplified dynamic model for a Li-ion battery that is forced to track the output voltage curve of a physical Li-ion battery by using universal adaptive stabilization (UAS). We prove that when the physical Li-ion battery becomes unstable, then the simplified dynamic model becomes unstable. Our results do not require a sophisticated model for a battery that faithfully captures all dynamics. Using our results, we present an algorithm for detecting impending voltage collapses for Liion batteries.

Fractional order plasma position control of the STOR-1M tokamak

This work deals with plasma position estimation, modeling, and control for the ‘Saskatchewan Torus 1 - Modified (STOR-1M)’ tokamak. The basic operating mechanism and system details are presented initially to provide the reader with a complete understanding of the plant and the control objective. The data required for plasma position estimation and the methodology used is briefly presented, followed by plasma position modeling. An effective method for offline plasma position estimation is presented. The simulated results for position control using a standard (Ziegler-Nichols) ZN-PID controller and a (Fractional Order) FO-PI controller are compared with each other. The problems that arise when dealing with such a fast-operating and challenging system are detailed throughout. The results obtained using analog hardware to emulate the plasma position and purely analog FO-PI control are also included.

A comparison of adaptive trajectory tracking controllers for wheeled mobile robots

Two adaptive trajectory tracking controllers for wheeled mobile robots are tested in this work. Adaptively tuned proportional control is one approach, where as the other controller uses a Universal Adaptive Stabilization (UAS) based technique. Using simulations, the robustness of the above controllers is quantified in the presence of measurement noise. The robustness is measured in terms of the Integral of absolute magnitude of the error (IAE), the Integral of square of the error (ISE), and the Integral of time multiplied by the absolute value of the error (ITAE) criteria. It is observed that the UAS based technique shows fast convergence in the absence of noise. To combat the effect of noise, the authors reset the adaptation gains after the adaptation gains reach a preset bound. With this technique it is found that the UAS based technique converges to the trajectory being tracked faster than the adaptively tuned proportional controller, and also faster than a traditional inputoutput state feedback linearization based controller.