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Measurements such as current and terminal voltage that are typically used to determine the battery’s state of charge (SOC) are augmented with measured force associated with electrode expansion as the lithium intercalates in its structure. The combination of the sensed behavior is shown to improve SOC estimation even for the lithium ion iron phosphate (LFP) chemistry, where the voltage–SOC relation is flat (low slope) making SOC estimation using measured voltage difficult. For the LFP cells, the measured force has a non-monotonic F–SOC relationship. This presents a challenge for estimation as multiple force values can correspond to the same SOC. The traditional linear quadratic estimator can be driven to an incorrect SOC value. To address these difficulties, a novel switching estimation gain is used based on determining the operating region that corresponds to the actual SOC. Moreover, a drift in the measured force associated with a shift of the cell SOC–expansion behavior over time is addressed with a bias estimator for the force signal. The performance of Voltage-based (V) and Voltage and Force-based (V&F) SOC estimation algorithms are then compared and evaluated against a desired ± 5 % absolute error bound of the SOC using a dynamic stress test current protocol that tests the proposed estimation scheme across wide range of SOC and current rates.

This dissertation covers the derivation of necessary and sufficient optimality condition for linear quadratic regulator (LQR) problems. Based on this, parametric sensitivity methods and real time adaption techniques from nonlinear optimization theory are applied to LQR problems. In addition to that, through dual theory, these methods are extended to linear quadratic estimator problems as well as combined regulator-estimator problems. All derived adaption techniques are numerically tested for two examples.

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included., {"references":["Athans, M., The role and use of the stochastic linear-quadratic-\nGaussian problem in control system design, IEEE Trans. Automatic\nControl, vol. 16, no. 6, pp: 529-552, 1971.","Sage, A. P. and White, C .C., Optimum Systems Control, Prentice-Hall,\nInc., Englewood Cliffs, New Jersey, 1977.","Brewer, J. W., Kronecker products and matrix calculus in system theory,\nIEEE Trans. Circuits and Systems, vol. 25, no. 9, pp: 772-781, 1978.","Rao, G. P., Piecewise Constant Orthogonal Functions and Their Application\nto Systems and Control, LNCIS 55, Springer, Berlin, 1983.","Hwang, C. and Chen, M. Y., Analysis and optimal control of timevarying\nlinear systems via shifted Legendre polynomials, Int. J. Control,\nvol. 41, no. 5, pp: 1317-1330, 1985.","Chang, Y. F. and Lee, T. T., General orthogonal polynomials approximations\nof the linear-quadratic-Gaussian control design, Int. J. Control,\nvol. 43, no. 6, pp: 1879-1895, 1986.","Jiang, Z. H. and Schaufelberger, W., Block-Pulse Functions and Their\nApplications in Control Systems, LNCIS 179, Spinger, Berlin, 1992.","Datta, K. B. and Mohan, B. M., Orthogonal Functions in Systems and\nControl, Advanced Series in Electrical and Computer Engineering, vol.\n9, World Scientific, Singapore, 1995.","Patra, A. and Rao, G. P., General Hybrid Orthogonal Functions and\nTheir Applications in Systems and Control, LNCIS 213, Springer,\nLondon, 1996.\n[10] Gupta, V., Hassibi, B. and Murray, R. M., Optimal LQG control across\npacket-dropping links, Systems & Control Letters, vol. 56, no. 6, pp:\n439-446, 2007.\n[11] Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K. and Sastry,\nS., Optimal linear LQG control over lossy networks without packet\nacknowledgment, Asian J. Control, vol. 10, no. 1, pp: 3-13, 2008.\n[12] Kar, S. K., Orthogonal functions approach to optimal control of linear\ntime-invariant systems described by integro-differential equations,\nKLEKTRIKA, vol. 11, no 1, pp: 15-18, 2009.\n[13] Mohan, B. M. and Kar, S. K., Optimal Control of Multi-Delay Systems\nvia Orthogonal Functions, Int. J. Advanced Research in Engineering\nand Technology, vol. 1, no. 1, pp: 1-24, 2010.\n[14] Kar, S. K., Optimal control of a linear distributed parameter system via\nshifted Legendre polynomials, Int. J. Electrical and Computer Engineering\n(WASET), vol. 5, no. 5, pp: 292-297, 2010.\n[15] Mohan, B. M. and Kar, S. K., Orthogonal functions approach to optimal\ncontrol of delay systems with reverse time terms, J. The Franklin\nInstitute, vol. 347, no. 9, pp: 1723-1739, 2010.\n[16] Mohan, B. M. and Kar, S. K., Optimal Control of Singular Systems via\nOrthogonal Functions, Int. J. Control, Automation and Systems, vol. 9,\nno. 1, pp: 145-152, 2011.\n[17] Mohan, B. M. and Kar, S. K., Optimal control of multi-delay systems\nvia shifted Legendre polynomials, Int. Conf. on Energy, Automation and\nSignals (ICEAS), Bhubaneswar, INDIA, December 28-30, 2011.\n[18] Mohan, B. M. and Kar, S. K., Optimal control of nonlinear systems\nvia orthogonal functions, Int. Conf. on Energy, Automation and Signals\n(ICEAS), Bhubaneswar, INDIA, December 28-30, 2011."]}