Bharath Bhikkaji

A flexible structure model with collocated sensor/actuator pairs is considered. The resonant modes of the collocated structure are damped by designing a suitable Positive Position Feedback Controller (PPF). The control design frame work involves matching the eigen-structure of a desired reference system with that of the closed loop system. Matching of the eigen-structure reduces to solving a set of over determined linear equations in the controller parameters. If the linear equations do not have solution, then a least squares solution under stability constraints (both closed loop and controller stability) is computed. The stability constraints are found to be Linear Matrix Inequalities (LMIs) in the controller parameters; thus making the control design convex. Numerical examples illustrate the utility of the proposed control design.

A problem of load balancing in isolated DC microgrids is considered in this paper. Here, a DC load is fed by multiple heterogeneous DC sources, each of which is connected to the load via a boost converter. The gains of the DC Converters (DCC's) provide for a means to control the division of load current amongst the DC sources. The primary objective of the control scheme is to minimise the total losses in the network, while maintaining the output voltage within a desired range, serving the load current demand and adhering to VI-characteristics of the power sources. Under assumptions of concavity/monotonocity/piece-wise-linearity of the VI-characteristics, the problem is solved using a convex relaxation. It is shown that the solution to the relaxed problem is tight. Thus, the resulting algorithm is guaranteed to reach global optimality in a numerically efficient manner [1]. Simulations are provided for corroboration.

The target guarding problem (TGP) comprises two players, an evader and a pursuer. The evader tries to reach a stationary target while avoiding the pursuer, and the pursuer tries to intercept the evader before the target is reached. Optimal strategies for the TGP have been studied in detail. These strategies assume the availability of noise-free measurements of positions and speeds of the respective players. The pursuer may lose the game from a position of advantage du to lack of perfect data. In this work, a strategy is derived for the pursuer when the evader's position and speed measurements are corrupted by noise. A non-linear state space model is developed for the evader's maneuver. An Extended Kalman filter is then designed to estimate the evader's position and speed. This estimated data is used for calculating the probability of the target falling within the dominance regions of the pursuer or the evader. Based on this, a real time strategy is designed for the pursuer. Performance of this strategy is simulated and also validated through experiments conducted on a test-bed consisting of mobile robots.

Atomic Force Microscopes (AFM) are used for generating surface topography of samples at micro to atomic resolutions. Many commercial AFMs use piezoelectric tube nanopositioners for scanning. Scanning rates of these microscopes are hampered by the presence of low frequency resonant modes. When inadvertently excited, these modes lead to high amplitude mechanical vibrations causing the loss of accuracy, while scanning, and eventually to break down of the tube. Feedback control has been used to damp these resonant modes. Thereby, enabling higher scanning rates. Here, a multivariable controller is designed to damp the first resonant mode along both the x and y axis. Exploiting the inherent symmetry in the piezoelectric tube, the multivariable control design problem is recast as independent single-input single-output (SISO) designs. This in conjunction with integral resonant control is used for damping the first resonant mode. © 2013 American Institute of Physics.

This paper presents a new combined electrostatic-triboelectric energy harvester. One of the practical limitations of Electrostatic Vibration Energy (EVE) harvesting technologies is the need for an initial priming voltage source. In the proposed scheme, the triboelectric effect is used to provide initial charges necessary for EVE harvester. This harvester converts vibration to electrical energy and stores it in two storage capacitors. The new harvester has a triboelectric part and an EVE part. The triboelectric part charges one of the storage capacitors and at the same time supplies necessary initial charge for EVE part which charges the other storage capacitor. In this way, charges generated by triboelectric part are fully transferred from it, which ensures best and continuous triboelectric charge generation. Without proper transfer of charges, the triboelectric part will saturate in few cycles of vibration. Thus, in the combined harvester both schemes aid each other. A prototype of the new harvester has been built and tested. The developed unit generated about 45 nW of power from a low frequency vibration source of 3 Hz. © 2012 IEEE.

State of charge (SOC) estimation of a LiFePO4 battery exhibiting significant hysteresis is considered. The dynamics of the battery is modeled as a linear system in conjunction with a non-linear hysteresis block. The linear part is assumed to be of a second order equivalent circuit model along with an open circuit voltage (OCV) source Voc. The circuit model is descretised and the resulting parameters are modeled as a multivariate random walk with a diagonal noise covariance matrix. These parameters are estimated using a Kalman filter. The linear model is then validated using a hybrid pulse power characterisation (HPPC) current profile. The major loop of the non-linear hysteresis relating Voc and SOC is experimentally determined by charging and discharging the battery with low magnitude currents. Using Chebyshev polynomials, a model is fit for the hysteresis curves. Constrained unscented Kalman filter (CUKF) is used for estimating the minor loops of the hysteresis, and the SOC. The SOC estimation is then validated from a full electrochemical model simulation of the battery using COMSOL software.

A XYZ scanner is designed for fast and high resolution atomic force microscopy. The objective of this paper is to achieve a large scanning bandwidth along the X and Y axis of the scanner. Finite element analysis of the designed scanner is reported along with the experimental determination of the dynamics. Both suggest the presence of first resonant modes around 8.8 kHz and 8.9 kHz along the X and Y axis respectively. Actuating the scanner at frequencies beyond 1% of the first resonance causes mechanical vibrations and hence degradation of the images generated. Controllers are designed, using the Integral Resonant Control methodology, to damp the resonant modes, to enable fast actuation. Due to the large bandwidth of the designed scanner, a Field Programmable Analog Array (FPAA) is used for analog implementation of the controllers. High resolution images are generated at faster scanning rates in closed loop. © 2011 IEEE.

The aim of this paper is to design a band-limited optimal input with power constraints for identifying a linear multi-input multi-output system, with nominal parameter values specified. Using spectral decomposition theorem, the power spectrum is written as (Formula presented.). The matrix (Formula presented.) is expressed in terms of a truncated basis for (Formula presented.), where (Formula presented.) is the cut-off frequency. The elements of the Fisher Information Matrix and the power constraints become homogeneous quadratics in basis coefficients. The optimality criterion used are (Formula presented.) -optimality, (Formula presented.) -optimality, (Formula presented.) -optimality and (Formula presented.) -optimality. This optimization problem is not known to be convex. A bi-linear formulation gives a lower bound on the optimum, while an upper bound is obtained through a convex relaxation. These bounds can be computed efficiently. The lower bound is used as a suboptimal solution, its sub-optimality determined by the difference between the bounds. Simulations reveal that the bounds match in many instances, implying global optimality.

This paper considers finding a path in real time for a robot from the given initial position to the goal position. The environment is assumed to be mapped (known completely) and the resulting path should avoid all the obstacles, both static and dynamic in the mapped environment. The robot's (agent) dynamics is assumed to be discrete LTI with process noise and is controlled with a finite set of inputs. An MDP formulation and a solution based on Deep Reinforcement Learning framework are presented for the problem. Numerical experiments are performed for the proposed method using Deep Q-Network algorithm and the results are compared with the state of the art sampling based path planning algorithms for both static and dynamic environments. It is shown that even though the proposed algorithm provides a sub-optimal path, the computational time is shown to be significantly faster compared to the traditional methods of path planning.

Piezoelectric tubes exhibit a highly resonant mode of vibration which, if uncontrolled, limits the maximum scan rate in nano-scale positioning applications. Highly resonant systems with collocated sensor/actuator are often controlled using resonant shunt dampers. Unfortunately, in the configuration used here, this approach is not possible due the non-minimum phase property arising from the presence of a right-half plane zero. This problem is solved by: (i) interpreting the resonant shunt damper in the context of physical-model-based control (PMBC) and (ii) extending the PMBC approach to handle non-minimum phase systems. The resultant controller combines the physical insight of the resonant shunt damper with the ability to control the non-minimum phase piezoelectric tube. A digital implementation of the controller was experimentally evaluated and found to successfully eliminate the resonant mode of vibration during an accurate and fast scan using a piezoelectric tube actuator. © 2009 Elsevier Ltd. All rights reserved.