D.S. Bernstein

University of Michigan, Ann Arbor, Michigan, United States

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Publications (621)456.19 Total impact

  • Source
    Xin Zhou, Tulga Ersal, Jeffrey L Stein, Dennis S Bernstein
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    ABSTRACT: Previous work framed the battery State of Health (SoH) monitoring problem as an inaccessible subsystem identification problem and conceived an approach to monitor SoH via side reaction current density estimation when State of Charge (SoC) is perfectly known. In practice, however, SoC is only estimated, and even an SoC estimation error of less than 1% can significantly undermine the accuracy of the SoH estimation. In this paper, the development of a new inaccessible subsystem identification technique, called the Two Step Filter, is presented in a linear setting to estimate the SoC error and SoH variable simultaneously and hence allow for SoH monitoring even under SoC estimation errors. The potential of the Two Step Filter is demonstrated on a linearized battery model example. The result shows that the filter can successfully track the side reaction current density despite the presence of an SoC estimation error of 1%.
    American Control Conference, Chicago, IL; 07/2015
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    Khaled F. Aljanaideh, Dennis S. Bernstein
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    ABSTRACT: In some applications, multiple measurements are available, but the driving input that gives rise to those outputs may be unknown. This raises the question as to whether it is possible to model the response of a subset of sensors based on the response of the remaining sensors without knowledge of the driving input. To address this issue, we develop time-domain sensor-to-sensor models that account for nonzero initial conditions. The sensor-to-sensor model is in the form of a transmissibility operator that is a rational function of the differentiation operator. The development is carried out for both SISO and MIMO transmissibility operators. These time-domain sensor-to-sensor models can be used for diagnostics and output prediction.
    Automatica 03/2015; 53. DOI:10.1016/j.automatica.2015.01.004 · 3.13 Impact Factor
  • E. Dogan Sumer, Dennis S. Bernstein
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    ABSTRACT: We consider adaptive control of non-square plants, that is, plants that have an unequal number of inputs and outputs. In particular, we focus on retrospective cost adaptive control (RCAC), which is a direct, discrete-time adaptive control algorithm that is applicable to stabilisation, command following, disturbance rejection, and model reference control problems. Previous studies on RCAC have focused on control of square plants. In the square case, RCAC requires knowledge of the first non-zero Markov parameter and the non-minimum-phase (NMP) transmission zeros of the plant, if any. No additional information about the plant or the exogenous signals need be known. The goal of the present paper is to consider RCAC for non-square plants. Unlike the square case, we show that the assumption that the non-square plant is minimum phase does not guarantee closed-loop stability and signal boundedness. The main purpose of this paper is to establish the existence of time-invariant input and output subspaces corresponding to the adaptive controller. In particular, we show that RCAC implicitly squares down non-square plants through pre-/post-compensation of the non-square plant with a constant matrix. We show that, for wide plants, the control input generated by RCAC lies in a time-invariant ‘input subspace’, which is equivalent to pre-compensating the plant with a constant matrix. On the other hand, for tall plants, we show that the controller update is driven by the output of the plant post-compensated with a constant matrix. Accordingly, in either case, signal boundedness properties of the closed-loop system are determined by the transmission zeros of the squared system, which we call the ‘subspace zeros’. To deal with NMP subspace zeros, we introduce a robustness modification, which prevents RCAC from cancelling the NMP subspace zeros.
    International Journal of Control 02/2015; 88(2). DOI:10.1080/00207179.2014.951690 · 1.14 Impact Factor
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    ABSTRACT: We compare four spacecraft attitude control laws that require no prior modeling of the spacecraft mass distribution. All four control laws are based on rotation matrices, which provide a singularity-free attitude representation and unwinding-free operation without discontinuous switching. We apply these control laws to motion-to-rest and motion-to-spin maneuvers. Simulation results are given to illustrate the robustness of the control laws to uncertainty in the spacecraft inertia. For motion-to-rest maneuvers about a principal axis with bounded torque, we compare the settling time of the inertia-free control laws with the time-optimal bang-bang control law operating under known inertia. We also investigate closed-loop performance in the presence of attitude-dependent torque disturbances, actuator nonlinearities, sensor noise, and actuator bias.
    Advances in Estimation, Navigation, and Spacecraft Control, Edited by Daniel Choukroun, Yaakov Oshman, Julie Thienel, Moshe Idan, 01/2015: chapter A Comparison of Nonlinear PI and PID Inertia-free Spacecraft Attitude Control Laws: pages 517-541; Springer Berlin Heidelberg., ISBN: 978-3-662-44784-0
  • Anna Prach, Ozan Tekinalp, Dennis S. Bernstein
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    ABSTRACT: One of the foundational principles of optimal control theory is that optimal control laws are propagated backward in time. For linear-quadratic control, this means that the solution of the Riccati equation must be obtained from backward integration from a final-time condition. These features are a direct consequence of the transversality conditions of optimal control, which imply that a free final state corresponds to a fixed final adjoint state [1], [2]. In addition, the principle of dynamic programming and the associated Hamilton-Jacobi-Bellman equation is an inherently backward-propagating methodology [3].
    IEEE control systems 01/2015; 35(2):78-93. DOI:10.1109/MCS.2014.2385252 · 3.39 Impact Factor
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    ABSTRACT: Control textbooks sometimes give the impression that amplification and phase shift are properties confined to asymptotically stable systems. For example, [1, p. 400] states that "Any system with a pole in the RHP is unstable; hence it would be impossible to determine its frequency response experimentally because the system would never reach a steady-state sinusoidal response for a sinusoidal input." This statement is correct in reference to an unstable plant operating in open loop but does not consider the case of an unstable plant operating inside a stabilized closed loop.
    IEEE control systems 12/2014; 34(6):86-141. DOI:10.1109/MCS.2014.2350591 · 3.39 Impact Factor
  • Matthew S. Hölzel, Dennis S. Bernstein
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    ABSTRACT: We present an elimination theory-based method for solving equality-constrained multivariable polynomial least-squares problems in system identification. While most algorithms in elimination theory rely upon Groebner bases and symbolic multivariable polynomial division algorithms, we present an algorithm which is based on computing the nullspace of a large sparse matrix and the zeros of a scalar, univariate polynomial.
    Automatica 10/2014; DOI:10.1016/j.automatica.2014.10.039 · 3.13 Impact Factor
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    Xin Zhou, Tulga Ersal, Jeffrey L Stein, Dennis S Bernstein
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    ABSTRACT: This paper introduces a method to estimate battery state of health (SoH) via health-relevant electrochemical features. Battery state of health estimation is a critical part of battery management because it allows for balancing the trade-off between maximizing performance and minimizing degradation. In this paper, a health-relevant electrochemical feature, the side reaction current density, is used as the indicator of battery SoH. An estimation algorithm is required due to the unavailability of the side reaction current density via noninvasive methods. In this paper, Retrospective-Cost Subsystem Identification (RCSI) is used to estimate the side reaction current density via identification of an unknown battery health subsystem that generates the side reaction current density. Simulation results are provided for constant current charge and discharge cycles with different C rates. A current profile for an electric vehicle (EV) going through Urban Dynamometer Driving Schedule (UDDS) cycles is also used as the excitation signal during estimation. The simulations show promising results in battery health dynamic identification and side reaction current density estimation with RCSI.
    ASME Dynamic Systems and Control Conference, San Antonio, TX; 10/2014
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    ABSTRACT: We present a numerical investigation of the performance of retrospective cost adaptive control (RCAC) for spacecraft attitude control using control-moment-gyroscopes (CMG). The setup consists of three orthogonally mounted CMG's that are velocity commanded without the use of a steering law. RCAC is applied in a decentralized architecture; each CMG is commanded by an independent RCAC control laws. This architecture simplifies the required modeling information and treats the axis-coupling effects as unmodeled disturbances. A rotation-matrix parameterization of attitude is used to implement a dynamic compensator with state feedback. The adaptive controller is able to complete various slew and spin maneuvers using limited information about the mass-distribution of the spacecraft.
    American Control Conference (ACC), 2014, Portland, OR, USA; 06/2014
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    Mohammad Al Janaideh, Dennis S. Bernstein
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    ABSTRACT: We investigate a NARMAX controller structure involving hysteretic nonlinearities. A weighted combination of backlash nonlinearities constitutes a Prandtl-Ishlinskii hysteresis model. The rationale for using a Prandtl-Ishlinskii NARMAX (PIN) controller is due to the fact that the describing function of a backlash nonlinearity has both gain and phase shift. By combining backlash nonlinearities into a NARMAX control law it is reasonable to expect that arbitrary gain and phase shift can be attained by adaptively updated controller coefficients.
    2014 American Control Conference - ACC 2014; 06/2014
  • Anna Prach, Ozan Tekinalp, Dennis S. Bernstein
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    ABSTRACT: Feedback control of linear time-varying systems arises in numerous applications. In this paper we numerically investigate and compare the performance of two heuristic techniques. The first technique is the frozen-time Riccati equation, which is analogous to the state-dependent Riccati equation, where the instantaneous dynamics matrix is used within an algebraic Riccati equation solved at each time step. The second technique is the forward-propagating Riccati equation, which solves the differential algebraic Riccati equation forward in time rather than backward in time as in optimal control. Both techniques are heuristic and suboptimal in the sense that neither stability nor optimal performance is guaranteed. To assess the performance of these methods, we construct Pareto efficiency curves that illustrate the state and control cost tradeoffs. Three examples involving periodically time-varying dynamics are considered, including a second-order exponentially unstable Mathieu equation, a fourth-order rotating disk with rigid body unstable modes, and a 10th-order parametrically forced beam with exponentially unstable dynamics. The first two examples assume full-state feedback, while the last example uses a scalar displacement measurement with state estimation performed by a dual Riccati technique.
    2014 American Control Conference - ACC 2014; 06/2014
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    Mohammad Al Janaideh, Dennis S. Bernstein
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    ABSTRACT: We apply retrospective cost adaptive control (RCAC) to a command-following problem for uncertain Hammerstein systems with Duhem hysteresis nonlinearities. The only required modeling information of the linear plant is a single Markov parameter. We numerically investigate the sense in which RCAC achieves internal model control. The properties of the asymptotic controller are analyzed by using phase shift calculations.
    2014 American Control Conference - ACC 2014; 06/2014
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    ABSTRACT: Retrospective cost model refinement is applied to on-board identification of a linearized aircraft model, and it is shown that with altitude and airspeed measurements, the aircraft stability derivatives can be estimated. These estimates are then compared to the nominal values at the same flight condition. The comparison between identified and nominal stability derivatives provides a fault signature. We also describe a methodology for updating the flight envelope based on identified stability derivatives.
    2014 American Control Conference - ACC 2014; 06/2014
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    ABSTRACT: We apply retrospective cost adaptive control (RCAC) to a linearized aircraft dynamics with an unknown transition to nonminimum-phase (NMP) dynamics. In prior work, RCAC was used for command-following with unknown NMP zeros. In this work we extend those results to command following for cases where the dynamics transition from minimum-phase to NMP. We use system identification techniques to identify the NMP zero, and use this information in RCAC. We consider both full-state feedback and output feedback, and in both cases we follow step commands with transitioning dynamics. We first consider the case where RCAC is unaware of the change and NMP zero identification is unavailable to RCAC. We then assume that NMP zero information is available to RCAC from system identification.
    2014 American Control Conference - ACC 2014; 06/2014
  • Source
    Jin Yan, Dennis S. Bernstein
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    ABSTRACT: We augment retrospective cost adaptive control (RCAC) with auxiliary nonlinearities to address a command-following problem for uncertain Hammerstein systems with possibly non-monotonic input nonlinearities. We assume that only one Markov parameter of the linear plant is known and that the input nonlinearity is uncertain. Auxiliary nonlinearities are used within RCAC to create a globally non-decreasing composite input nonlinearity. The required modelling information for the input nonlinearity includes the intervals of monotonicity as well as values of the nonlinearity that determine overlapping segments of the range of the nonlinearity within each interval of monotonicity.
    International Journal of Control 03/2014; 87(3). DOI:10.1080/00207179.2013.842264 · 1.14 Impact Factor
  • M. Al Janaideh, D. S. Bernstein
    Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering 01/2014; 229(2):149-157. DOI:10.1177/0959651814551660 · 0.78 Impact Factor
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    ABSTRACT: This paper proposes a differential inflation scheme and applies this technique to driver estimation for the Global Ionosphere–Thermosphere Model (GITM) using the Ensemble Adjustment Kalman Filter (EAKF), which is a part of the Data Assimilation Research Testbed (DART). Driver estimation using EAKF is first demonstrated on a linear example and then applied to GITM. The Challenging Minisatellite Payload (CHAMP) neutral mass density measurements are assimilated into a biased version of GITM, and the solar flux index, F10.7, is estimated. Although the estimate of F10.7 obtained using DART does not converge to the measured values, the converged values are shown to drive the GITM output close to CHAMP measurements. In order to prevent the ensemble spread from converging to zero, the state and driver estimates are inflated. In particular, the F10.7 estimate is inflated to have a constant variance. It is shown that EAKF with differential inflation reduces the model bias from 73% down to 7% along the CHAMP satellite path when compared to the biased GITM output obtained without using data assimilation. The Gravity Recovery and Climate Experiment (GRACE) density measurements are used to validate the data assimilation performance at locations different from measurement locations. It is shown that the bias at GRACE locations is decreased from 76% down to 52% as compared to not using data assimilation, showing that model estimation of the thermosphere is improved globally.
    Journal of Atmospheric and Solar-Terrestrial Physics 11/2013; 104:126-136. DOI:10.1016/j.jastp.2013.08.016 · 1.75 Impact Factor
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    Khaled F. Aljanaideh, Dennis S. Bernstein
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    ABSTRACT: In this paper, we present a technique for estimating the input nonlinearity of a Hammerstein system by using multiple orthogonal ersatz nonlinearities. Theoretical analysis shows that by replacing the unknown input nonlinearity by an ersatz nonlinearity, the estimates of the Markov parameters of the plant are correct up to a scalar factor, which is related to the inner product of the true input nonlinearity and the ersatz nonlinearity. These coefficients are used to construct and estimate the true nonlinearity represented as an orthogonal basis expansion. We demonstrate this technique by using a Fourier series expansion as well as orthogonal polynomials. We show that the kernel of the inner product associated with the orthogonal basis functions must be chosen to be the density function of the input signal.
    ASME 2013 Dynamic Systems and Control Conference; 10/2013
  • Source
    Xin Zhou, Tulga Ersal, Jeffrey L. Stein, Dennis S. Bernstein
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    ABSTRACT: Health management of Li-ion batteries requires knowledge of certain battery internal dynamics (e.g., lithium consumption and film growth at the solid-electrolyte interface) whose inputs and outputs are not directly measurable with noninvasive methods. Therefore, identification of those dynamics can be classified as an inaccessible subsystem identification problem. To address this problem, the retrospective-cost subsystem identification (RCSI) method is adopted in this paper. Specifically, a simulation-based study is presented that represents the battery using an electrochemistry-based battery charge/discharge model of Doyle, Fuller, and Newman augmented with a battery-health model by Ramadass. The solid electrolyte interface (SEI) film growth portion of the battery-health model is defined as the inaccessible subsystem to be identified using RCSI. First, it is verified that RCSI with a first-order subsystem structure can accurately estimate the film growth when noise or modeling errors are ignored. Parameter convergence issues are highlighted. Second, allowable input and output noise levels for desirable film growth tracking performance are determined by studying the relationship between voltage change and film growth in the truth model. The performance of RCSI with measurement noise is illustrated. The results show that RCSI can identify the film growth within 1.5% when the output measurement noise level is comparable to the change in output voltage between successive cycles due to film growth, or when the input measurement noise is comparable to the difference in current that results in a difference in voltage that is the same as the voltage change between successive cycles. Finally, the sensitivity of the performance of RSCI to initial condition errors in the battery charge/discharge model is investigated. The results show that when the initial conditions have an error of 1%, the identified results change by 7%. These results will help with selecting the appropriate sensors for the experiments with the hardware.
    Dynamic Systems and Control Conference, Palo Alto, CA; 10/2013
  • Source
    Jin Yan, Davi Antônio dos Santos, Dennis S. Bernstein
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    ABSTRACT: This paper applies retrospective cost adaptive control (RCAC) to command following in the presence of multivariable convex input saturation constraints. To account for the saturation constraint, we use convex optimization to minimize the quadratic retrospective cost function. The use of convex optimization bounds the magnitude of the retrospectively optimized input and thereby influences the controller update to satisfy the control bounds. This technique is applied to a tiltrotor with constraints on the total thrust magnitude and inclination of the rotor plane.
    ASME 2013 Dynamic Systems and Control Conference; 10/2013

Publication Stats

9k Citations
456.19 Total Impact Points

Institutions

  • 1992–2015
    • University of Michigan
      • Department of Aerospace Engineering
      Ann Arbor, Michigan, United States
    • Arizona State University
      • Department of Mechanical Engineering
      Tempe, AZ, United States
  • 1992–2013
    • Concordia University–Ann Arbor
      Ann Arbor, Michigan, United States
  • 2011
    • University of Kentucky
      • Department of Mechanical Engineering
      Lexington, KY, United States
  • 2009
    • Indian Institute of Technology Madras
      Chennai, Tamil Nādu, India
    • Palo Alto Research Center
      Palo Alto, California, United States
    • University of Hawaiʻi at Mānoa
      • Department of Mechanical Engineering
      Honolulu, HI, United States
    • The American Institute of Aeronautics and Astronautics
      Reston, Virginia, United States
  • 2008
    • Federal University of Minas Gerais
      • The Electrical Engineering Graduate Program
      Cidade de Minas, Minas Gerais, Brazil
    • Syracuse University
      • Department of Mechanical and Aerospace Engineering
      Syracuse, NY, United States
  • 1998–2007
    • Air Force Research Laboratory
      Washington, Washington, D.C., United States
  • 2006
    • National University of Science and Technology
      Islāmābād, Islāmābād, Pakistan
  • 1998–2005
    • Indian Institute of Technology Ropar
      Rūpar, Punjab, India
  • 2003
    • Vehicle Control Technologies, Inc.
      Reston, Virginia, United States
  • 2000
    • Honeywell
      Morristown, New Jersey, United States
  • 1995–1999
    • Georgia Institute of Technology
      • School of Aerospace Engineering
      Atlanta, GA, United States
    • Butler University
      Indianapolis, Indiana, United States
  • 1992–1994
    • Virginia Polytechnic Institute and State University
      • Department of Computer Science
      Blacksburg, VA, United States
  • 1988–1994
    • Florida Institute of Technology
      • Department of Mechanical and Aerospace Engineering
      Melbourne, FL, United States
  • 1984–1992
    • Harris Corporation
      Melbourne, Florida, United States
  • 1983–1992
    • Massachusetts Institute of Technology
      • Department of Aeronautics and Astronautics
      Cambridge, MA, United States