Showing papers by "Dennis S. Bernstein published in 2012"

Retrospective Cost Model Reference Adaptive Control for Nonminimum-Phase Systems

Abstract: DOI: 10.2514/1.57001 This paper presents a direct model reference adaptive controller for single-input/single-output discrete-time (and thus sampled-data) systems that are possibly nonminimum phase. The adaptive control algorithm requires knowledge of the nonminimum-phase zeros of the transfer function from the control to the output. This controller uses a retrospective performance, which is a surrogate measure of the actual performance, and a cumulative retrospective cost function, which is minimized by a recursive-least-squares adaptation algorithm. This paper develops the retrospective cost model reference adaptive controller and analyzes its stability.

Forward-integration Riccati-based output-feedback control of linear time-varying systems

Abstract: In applications involving time-varying systems, the state dynamics matrix is often not known in advance. To address this problem, this paper investigates the effectiveness of a forward-in-time Riccati-based control law. This approach is motivated by the fact that the optimal state estimator is based on a forward-in-time Riccati-based solution that does not require advance knowledge of the system dynamics. In this paper we show that a forward-in-time Riccati-based control law stabilizes the system if the dynamics of the quasi-dual system are asymptotically stable. This property holds if the closed-loop dynamics are symmetric, and, for some plants, is achieved by dynamics with sufficiently fast time variation. In addition, using a separation principal type result, we guarantee closed-loop stability in the case of output feedback.

Adaptive forward-propagating input reconstruction for nonminimum-phase systems

Abstract: Input reconstruction is a process where the inputs to a system are estimated using the measured system output, and possibly some modeling information from the system model. One way to achieve this goal is to invert the system model and cascade delays to guarantee that the inverse is proper. A standing issue in input reconstruction lies in the inversion of nonminimum-phase systems, since the inverse model is unstable. We consider two methods for achieving input reconstruction despite the presence of nonminimum-phase zeros. First, we develop an open-loop partial inversion of the system model using a finite number of frequency points, where the partial inverse is a finite impulse response model and therefore is guaranteed to be asymptotically stable. Second, we examine a closed-loop approach that uses an infinite impulse response model. We demonstrate both methods on several illustrative examples.

Noninvasive battery-health diagnostics using retrospective-cost identification of inaccessible subsystems

Abstract: Health management of Li-ion batteries depends on 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. This presents a problem of identification of inaccessible subsystems. To address this problem, we apply the retrospective-cost subsystem identification (RCSI) method. As a first step, this paper presents a simulation-based study that assumes as the truth model of the battery an electrochemistrybased battery charge/discharge model of Doyle, Fuller, and Newman, and later augmented with a battery-health model by Ramadass. First, this truth model is used to generate the data needed for the identification study. Next, the film-growth component of the battery-health model is assumed to be unknown, and the identification of this inaccessible subsystem is performed using RCSI. The results show that the subsystem identification method can identify the film growth quite accurately when the chemical reactions leading to film growth are consequential.

Retrospective Cost Adaptive Control of Spacecraft Attitude

Abstract: We apply retrospective cost adaptive control (RCAC) to spacecraft attitude control. First, we develop results for angular rate control. These results are then extended to attitude control. We examine two problems for each of the controllers. For both problems, the spacecraft has an arbitrary initial angular rate, and in the case of attitude control, an arbitrary initial attitude. The objective for the first problem is to bring the body to rest and to a specified attitude in the attitude control case. The second problem seeks to bring the spacecraft to spin about a specified body axis, which, in the case of attitude control, is inertially pointed. We first test the algorithm using an estimate of the spacecraft’s Markov parameters obtained from discretization of the linearized Euler’s and Poisson’s equations. Then, we limit the dependence on knowledge of the mass properties by removing inertia information from the Markov parameter. Finally, we test for robustness by scaling the Markov parameter and rotating the actuator matrix.

Retrospective Cost Adaptive Control with Error-Dependent Regularization for MIMO Systems with Uncertain Nonminimum-Phase Transmission Zeros

Abstract: In this paper we focus on retrospective cost adaptive control (RCAC), which is applicable to stabilization, command following, disturbance rejection, and model reference control problems for SISO and MIMO plants. RCAC uses limited modeling information, specifically, Markov parameters of the transfer function from the control input to the performance variable. Typically, a small number of Markov parameters are needed, for example, one Markov parameter usually suffices if the plant is minimum phase. If the plant is Lyapunov stable and nonminimum phase, then knowledge of the locations of the nonminimum-phase zeros is not needed as long as an error-dependent regularization term is used to weight the control effort. For plants that are both open-loop unstable and nonminimum phase, knowledge of the locations of the nonminimum-phase zeros may be needed. The goal of the present paper is to further investigate the effectiveness of the error-dependent regularization terms. Furthermore, we remove the intermediate step of reconstructing the retrospective controls and we directly update the controller. Next, we consider channelwise phase-matching conditions for MIMO plants. Finally, we investigate the role of zeros in MIMO nonsquare systems.

Adaptive control of uncertain Hammerstein systems with monotonic input nonlinearities using auxiliary nonlinearities

Abstract: We extend retrospective cost adaptive control (RCAC) to command following for uncertain Hammerstein systems. We assume that only one Markov parameter of the linear plant is known and that the input nonlinearity is monotonic but otherwise unknown. Auxiliary nonlinearities are used within RCAC to account for the effect of the input nonlinearity.

Retrospective-Cost Adaptive Control of Uncertain Hammerstein-Wiener Systems with Memoryless and Hysteretic Nonlinearities

Abstract: We apply retrospective cost adaptive control (RCAC) with auxiliary nonlinearities to a command-following problem for uncertain Hammerstein-Wiener systems with memoryless and hysteretic nonlinearities. The only required modeling information of the linear plant is a single Markov parameter. To account for the nonlinearities, RCAC uses auxiliary nonlinearities that reflect the monotonicity properties of the nonlinearity. Various memoryless nonlinearities such as deadband, cubic, and saturation are considered. The hysteresis nonlinearity is modeled using the Prandtl-Ishlinskii model.

FIR-based phase matching for robust Retrospective-Cost Adaptive Control

Abstract: In this paper we develop frequency-domain methods for approximating IIR plants with FIR transfer functions. The underlying goal is to increase the performance and robustness of Retrospective-Cost Adaptive Control (RCAC), which is applicable to MIMO possibly nonminimum-phase (NMP) plants without the need to know the locations of the NMP zeros. The only required modeling information is an FIR approximation of the plant, which may be based on a limited number of Markov parameters, or possibly noisy frequency response data. In this paper we investigate the resulting phase mismatch between the true plant and the FIR approximation obtained through linear and nonlinear approximation methods. We consider degradation in the phase mismatch due to uncertainty in the frequency response data.

Adaptive Control of Uncertain Linear Systems With Uncertain Hysteretic Input Nonlinearities

Abstract: We apply retrospective cost adaptive control (RCAC) with auxiliary nonlinearities to a command-following problem for uncertain Hammerstein systems with rate-dependent hysteretic input nonlinearities. The only required modeling information of the linear plant is a single Markov parameter. To account for the hysteretic input nonlinearity, RCAC uses auxiliary nonlinearities that reflect the monotonicity properties of the input nonlinearity. The hysteresis nonlinearity is modeled using the rate-dependent Prandtl-Ishlinskii model.Copyright © 2012 by ASME

Broadband Disturbance Rejection Using Retrospective Cost Adaptive Control

Abstract: We apply retrospective cost adaptive control (RCAC) to a broadband disturbance rejection problem under limited modeling information and assuming that the performance variable is measured The goal is to compare the asymptotic performance (that is, after convergence of the controller) of the adaptive controller with the performance of discrete-time LQG controller, which uses complete modeling information but does not require a measurement of the performance variable For RCAC we assume that the first nonzero Markov parameter of the plant is known We show that if the plant zeros are also known, the retrospective cost can be modified to recover the high-control-authority LQG performanceCopyright © 2012 by ASME

Adaptive Decentralized Noise and Vibration Control With Conflicting Performance Objectives

Abstract: Decentralized control is a longstanding challenge in systems theory A decentralized controller may consist of multiple local controllers, connected to disjoint or overlapping sets of sensors and actuators, and where each local controller has limited ability to communicate directly with the remaining local controllers and, in addition, may lack global knowledge of the plant and operation of the remaining local controllers In the present paper we apply adaptive control to investigate the ability of the local controllers to cooperate globally despite uncertainty, communication constraints, and possibly conflicting performance objectives The approach we apply in this paper is based on retrospective cost adaptive control (RCAC) The development of RCAC assumes a centralized controller structure; the goal of the present paper is to investigate the stability and performance of RCAC in a decentralized settingCopyright © 2012 by ASME

Sensor-to-sensor identification for the SOFIA testbed

Abstract: In many system identi cation applications, only output measurements are available for constructing empirical models. In these cases, sensor-to-sensor identi cation (S2SID) can be used. In the SISO case, one measurement is designated as the pseudo-input, while another measurement is designated as the pseudo-output. Identi cation between the pseudoinput and pseudo-output results in the construction of a pseudo transfer function (PTF). In the present paper we apply S2SID to data obtained from the NASA SOFIA (Stratospheric Observatory for Infrared Astronomy) testbed. The objective of this work is to determine whether linear PTF models can approximate the relationship between di erent sensor measurements. The identi cation of such models can potentially be used in practice to detect faults or changes in a structure.

Retrospective-Cost-Based Adaptive State Estimation and Input Reconstruction for a Maneuvering Aircraft with Unknown Acceleration

Abstract: A method is presented to obtain state estimates for a possibly nonminimum-phase system in the presence of unknown harmonic inputs. The method estimates the states and reconstructs the unknown harmonic input. An adaptive feedback model injects an input into the estimator such that the error between the estimator output and the actual output converges to zero despite the presence of the unknown harmonic input. Using input reconstruction based on a retrospective cost, the unknown harmonic input is reconstructed. Using the reconstructed input, the parameters of the adaptive feedback system are updated using recursive least squares. Results are presented for a rigid body, a damped rigid body, and a 2D missile with a three-loop autopilot topology.

Inertia-free spacecraft attitude control with control moment gyroscope actuation

Abstract: We extend the inertia-free continuous control law for spacecraft attitude tracking derived in prior work to the case of three single-axis control moment gyroscopes with spherical gyro wheels. These CMGs are assumed to be mounted in a known and linearly independent con guration with an arbitrary and unknown orientation relative to the spacecraft principal axes. We demonstrate the performance of the modi ed control laws for rest-to-rest, motionto-rest and spin maneuvers without the need for a seperate steering algorithm.

Forward-integration Riccati-based feedback control of magnetically actuated spacecraft

Abstract: We apply the forward-integration Riccati-based feedback controller developed in prior work to a magnetically actuated spacecraft for the cases of both inertial and nadir pointing. The spacecraft is assumed to be in low-Earth orbit and actuated by only three orthogonal electromagnetic actuators. We assume no advance knowledge of the magnetic eld, and thus make no periodicity assumptions, instead relying only on measurements that are available at the current time. We simulate the spacecraft attitude with actuator saturation, noisy magnetic measurements, and without rate feedback. The simulations are based on the International Geomagnetic Reference Field model of the magnetic eld.

Forward-integration Riccati-based feedback control for spacecraft rendezvous maneuvers on elliptic orbits

Abstract: We apply the forward-integrating Riccati-based feedback controller, which has been developed in our previous work for stabilization of time-varying systems, to a maneuvering spacecraft in an elliptic orbit around the Earth. We simulate rendezvous maneuvers on Molniya and Tundra orbits. We demonstrate that the controller performs well under thrust constraints, in the case where the spacecraft can thrust in only the orbital tangential direction, in the case where the thrusters may operate only intermittently due to faults or power availability, with thrust direction errors, and, finally, in an output feedback configuration where only relative position measurements are available.

Retrospective-Cost-Based Adaptive State Estimation and Input Reconstruction for the Global Ionosphere-Thermosphere Model

Abstract: We consider the problem of estimating the unknown solar driver F10.7 and physical states in the ionosphere and thermosphere using retrospective cost adaptive state estimation (RCASE). We interface RCASE with the Global Ionosphere Thermosphere Model (GITM) to demonstrate state estimation and F10.7 input reconstruction. We further examine the various factors that affect F10.7 estimation including saturation limits, initial estimates, and RCASE tuning parameters.

Robust sampled-data adaptive control of the Rohrs counterexamples

Abstract: We revisit the Rohrs counterexamples within the context of sampled-data adaptive control. In particular, retrospective cost adaptive control (RCAC) is applied to the sampled continuous-time plant with unmodeled high-frequency dynamics, which involves nonminimum-phase (NMP) sampling zeros. It is shown that, without knowledge of these NMP zeros, RCAC stabilizes the uncertain plant and asymptotically follows the sinusoidal command.

Sensor-to-sensor identification of Hammerstein systems

Abstract: Traditional system identification uses measurements of the inputs, but when these measurements are not available, alternative methods, such as blind identification, output-only identification, or operational modal analysis, must be used. Yet another method is sensor-to-sensor identification (S2SID), which estimates pseudo transfer functions whose inputs are outputs of the original system. A special case of S2SID is transmissibility identification. Since S2SID depends on cancellation of the input, this approach does not extend to nonlinear systems. However, in the present paper we show that, for the case of a two-output Hammerstein system, the least-squares estimate of the PTF is consistent, that is, asymptotically correct, despite the presence of the nonlinearities.

Sensor-Only System Identification for Structural Health Monitoring of Advanced Aircraft

Abstract: Environmental conditions, cyclic loading, and aging contribute to structural wear and degradation, and thus potentially catastrophic events. The challenge of health monitoring technology is to determine incipient changes accurately and efficiently. This project addresses this challenge by developing health monitoring techniques that depend only on sensor measurements. Since actively controlled excitation is not needed, sensor-to-sensor identification (S2SID) provides an in-flight diagnostic tool that exploits ambient excitation to provide advance warning of significant changes. S2SID can subsequently be followed up by ground testing to localize and quantify structural changes. The conceptual foundation of S2SID is the notion of a pseudo-transfer function, where one sensor is viewed as the pseudo-input and another is viewed as the pseudo-output, is approach is less restrictive than transmissibility identification and operational modal analysis since no assumption is made about the locations of the sensors relative to the excitation.

Retrospective-Cost Adaptive Control of Uncertain Hammerstein Systems Using a NARMAX Controller Structure

Abstract: We apply an extension of retrospective cost adaptive control (RCAC) to a commandfollowing problem for uncertain Hammerstein systems. In particular, RCAC with a NARMAX controller strucuture is applied to linear systems cascaded with input nonlinearities. We assume that one Markov parameter of the linear plant is known. RCAC also uses knowledge of the monotonicity properties of the input nonlinearity. The goal is to determine whether RCAC with a NARMAX controller structure can improve the command-following performance compared to the linear RCAC controller.

Actuator Saturation in Individual Blade Control of Rotorcraft

Abstract: The e ect of actuator saturation on the vibration and noise reduction capabilities of actively controlled trailing-edge aps and micro aps is examined. A new approach to handling actuator saturation in the HHC algorithm is developed based on constrained nonlinear optimization techniques. The performance of this approach in reducing vibrations and noise is compared to three existing approaches at various ight conditions. The results indicate that truncating or scaling the optimal ap/micro ap de ection can signi cantly compromise the vibration or noise reduction performance. By comparison, the auto-weighting approach and the new optimization based approach yield far better performance. However, the optimization approach takes less computational time and performs better in the case of multiple control surfaces as it utilizes all of them to the maximum possible extent.

A Comparison of Nonlinear PI and PID Inertia-Free Spacecraft Attitude Control Laws

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.

Poincaré recurrence and output reversibility in linear dynamical systems

Abstract: Reversibility of dynamical processes arises in many physical dynamical systems. For example, lossless Newtonian and Hamiltonian mechanical systems exhibit trajectories that can be obtained by time going forward and backward, providing an example of time symmetry that arises in natural sciences. Another example of such time symmetry is the phenomenon known as Poincare recurrence wherein the dynamical system exhibits trajectories that return infinitely often to neighborhoods of their initial conditions. In this paper, we study output reversibility in linear dynamical systems, that is, the backward recoverability of the system output while time is going forward. Specifically, we provide necessary and sufficient conditions for output reversibility in terms of the spectrum of the system dynamics. In addition, we provide sufficient conditions for the absence of output reversibility. Furthermore, we establish that no system trajectory can retrace its time history backwards with time going forward which is also natural in light of the uniqueness of solutions to linear dynamical systems. Finally, we draw connections between output reversibility and Poincare recurrence.

Adaptive Control of a Seeker-Guided 2D Missile with Unmodeled Aerodynamics

Abstract: In this paper we apply extensions of retrospective cost adaptive control (RCAC) to a 2D missile model considered in prior papers as a benchmark test of adaptive control methods. The dynamics of the missile are highly nonlinear, and instantaneous linearizations are nonminimum phase due to nose sensing and tail actuation. The results that we present in this paper show that the RCAC controller provides results that are comparable to a highly tuned autopilot based on aerodynamic modeling, whereas the RCAC controller uses no knowledge of the missile’s aerodynamics. These results significantly improve the results obtained on the same problem using an earlier version of RCAC, presented at the 2010 GNC.

Setpoint control of the uncertain electromagnetically controlled oscillator

Abstract: We apply an extension of retrospective cost adaptive control (RCAC) to a command-following problem for the uncertain electromagnetically controlled oscillator (ECO). We assume that an estimate of the first Markov parameter of the discretized and linearized plant is known, but RCAC does not require knowledge of the inertia, damping, or stiffness of the plant. RCAC uses a setpoint feedback path and an auxiliary nonlinearity to stabilize the unstable ECO at the commanded equilibria.© 2012 ASME

Adaptive Control of the Air and EGR Flow System in a Diesel Engine

Abstract: We apply retrospective cost adaptive control (RCAC) to command-following and disturbance-rejection problems for a diesel engine model. The engine is a multi-input, multi-output system with strong static and dynamic interactions, nonlinearities, uncertainties and nonminimum phase characteristics. We demonstrate that RCAC is effective for both the linearized and nonlinear engine models provided that two Markov parameters of the linearized engine plant model are known, either analytically or through system identification. For the command-following and disturbance-rejection problems, we consider the case when the disturbance is harmonic but otherwise unknown, and while the command signal is harmonic and known but no advance knowledge of its spectrum is assumed to be available.Copyright © 2012 by ASME

A Frictionless Bristle-Based Friction Model That Exhibits Hysteresis and Stick-Slip Behavior ✩

Abstract: We investigate the origins of stick-slip friction by developing an asperitybased friction model based on the frictionless and lossless contact between a body and a row of rigid, rotating bristles attached to the ground by torsional springs and dashpots. This model exhibits hysteresis and quasi-stick-slip friction. The hysteretic energy-dissipation mechanism is the sudden release of the compressed bristles, after which the bristles oscillate and the stored energy is dissipated by the dashpot. The discontinuous rotating bristle model is an approximation of the rotating bristle model that exhibits exact stickslip and hysteresis. We derive a single-state formulation of the discontinuous rotating bristle model and investigate similarities to the LuGre model.