### Browsing by Author "Bernstein, Dennis S."

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Item An Adaptive Digital Autopilot for Fixed-Wing Aircraft with Actuator Faults(2021-10-21) Lee, Joonghyun; Spencer, John; Paredes, Juan Augusto; Ravela, Sai; Bernstein, Dennis S.; Goel, AnkitThis paper develops an adaptive digital autopilot for a fixed-wing aircraft and compares its performance with a fixed-gain autopilot. The adaptive digital autopilot is constructed by augmenting the autopilot architecture implemented in PX4 flight stack with adaptive digital control laws that are updated using the retrospective cost adaptive control algorithm. In order to investigate the performance of the adaptive digital autopilot, the default gains of the fixed-gain autopilot are scaled down to degrade its performance. This scenario provides a venue for determining the ability of the adaptive digital autopilot to compensate for the detuned fixed-gain autopilot. Next, the performance of the adaptive autopilot is examined under failure conditions by simulating a scenario where one of the control surfaces is assumed to be stuck at an unknown angular position. The adaptive digital autopilot is tested in simulation, and the resulting performance improvements are examined.Item Adaptive Energy Control of Longitudinal Aircraft Dynamics(American Institute of Aeronautics and Astronautics, 2021-12-29) Anandakumar, Ashwin; Bernstein, Dennis S.; Goel, AnkitThe Total Energy Control System (TECS) is a method to control airplane longitudinal flight dynamics by regulating energy and energy balance. This multiple input, multiple output method accounts for the highly coupled nature of aircraft dynamics and allows for control of airspeed and altitude with a proportional-integral controller. This paper reviews the heuristic TECS control law and then validates it in a MATLAB simulation. Next, an adaptive TECS is designed by augmenting the fixed-gain controllers in a nominal TECS with retrospective cost optimization-based adaptive controllers. It is shown through simulations that adaptive augmentation improves the closed-loop performance and accelerates the tuning process.Item Euler's Equation via Lagrangian Dynamics with Generalized Coordinates(2022-12-22) Bernstein, Dennis S.; Goel, Ankit; Kouba, OmranEuler’s equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler’s equation in terms of generalized coordinates. This is done by parameterizing the angular velocity vector in terms of 3-2-1 and 3-1-3 Euler angles as well as Euler parameters, that is, unit quaternions.Item Experimental Flight Testing of a Fault-Tolerant Adaptive Autopilot for Fixed-Wing Aircraft(2022-10-24) Lee, Joonghyun; Spencer, John; Shao, Siyuan; Paredes, Juan Augusto; Bernstein, Dennis S.; Goel, AnkitThis paper presents an adaptive autopilot for fixed-wing aircraft and compares its performance with a fixedgain autopilot. The adaptive autopilot is constructed by augmenting the autopilot architecture with adaptive control laws that are updated using retrospective cost adaptive control. In order to investigate the performance of the adaptive autopilot, the default gains of the fixed-gain autopilot are scaled to degrade its performance. This scenario provides a venue for determining the ability of the adaptive autopilot to compensate for the degraded fixed-gain autopilot. Next, the performance of the adaptive autopilot is examined under failure conditions by simulating a scenario where one of the control surfaces is assumed to be stuck at an unknown angle. The adaptive autopilot is also tested in physical flight experiments under degraded-nominal conditions, and the resulting performance improvement is examined.Item Experimental Flight Testing of an Adaptive Autopilot with Parameter Drift Mitigation(2023-04-20) Chee, Yin Yong; Oveissi, Parham; Shao, Siyuan; Lee, Joonghyun; Paredes, Juan A.; Bernstein, Dennis S.; Goel, AnkitThis paper modifies an adaptive multicopter autopilot to mitigate instabilities caused by adaptive parameter drift and presents simulation and experimental results to validate the modified autopilot. The modified adaptive controller is obtained by including a static nonlinearity in the adaptive loop, updated by the retrospective cost adaptive control algorithm. It is shown in simulation and physical test experiments that the adaptive autopilot with proposed modifications can continually improve the fixed-gain autopilot as well as prevent the drift of the adaptive parameters, thus improving the robustness of the adaptive autopilot.Item Injection-Constrained State Estimation(AIAA, 2022-01-11) Goel, Ankit; Bernstein, Dennis S.In applications of state estimation involving data assimilation over a spatial region, it is often convenient, and sometimes necessary, to confine the state correction to a prescribed subspace of the state space that corresponds to the measurement location. This is the injection-constrained state-estimation problem, where the injection of the output-error is constrained to a specified subspace of the state space. Unlike full-state output-error injection, which is the dual of static full-state feedback, constrained output-error injection is the dual of static output feedback. To address the injection-constrained state-estimation problem, this paper develops the injectionconstrained unscented Kalman filter (IC-UKF) and the injection-constrained retrospective cost filter (IC-RCF). The performance of these filters is evaluated numerically for linear and nonlinear state-estimation problems in order to compare their accuracy and determine their suboptimality relative to full-state output-error injection. As a benchmark test case, IC-UKF and IC-RCF are applied to the viscous Burgers equation for state and parameter estimation.Item On the Accuracy of the One-step UKF and the Two-step UKF(2022-08-18) Goel, Ankit; Bernstein, Dennis S.The most accurate version of the unscented Kalman filter (UKF) involves the construction of two ensembles. To reduce computational cost, however, UKF is often implemented without the second ensemble. This simplification comes at a price, however, since, for linear systems, the one-step variation of the two-step UKF does not specialize to the classical Kalman filter, with an associated loss of accuracy. This paper remedies this drawback by developing a modified one-step UKF that recovers the classical Kalman filter for linear systems. Numerical examples show that the modified one-step UKF also recovers the accuracy of the two-step UKF in nonlinear systems with linear outputs.Item On the Lack of Robustness of Observers for Systems with Uncertain, Unstable Dynamics(IEEE, 2023-07-03) Kamaldar, Mohammadreza; Goel, Ankit; Islam, S. A. U.; Bernstein, Dennis S.We consider the robustness of state estimation for linear, time-invariant systems. Since state estimation is dual to full-state feedback, it may be expected that stability of the error dynamics depends continuously on perturbations of the dynamics matrix. This paper shows, however, that, if the system dynamics are unstable, then—regardless of how the filter gain is chosen—there always exist arbitrarily small perturbations of the system dynamics that give rise to unbounded state-estimation error. Since this phenomenon cannot occur in full-state feedback control, this result reveals a surprising break-down in the duality between estimation and control.Item Retrospective Cost-based Extremum Seeking Control with Vanishing Perturbation for Online Output Minimization(2024-02-06) Paredes, Juan A.; Delgado, Jhon Manuel Portella; Bernstein, Dennis S.; Goel, AnkitExtremum seeking control (ESC) constitutes a powerful technique for online optimization with theoretical guarantees for convergence to the neighborhood of the optimizer under well-understood conditions. However, ESC requires a nonconstant perturbation signal to provide persistent excitation to the target system to yield convergent results, which usually results in steady state oscillations. While certain techniques have been proposed to eliminate perturbations once the neighborhood of the minimizer is reached, system modifications and environmental perturbations can suddenly change the minimizer and nonconstant perturbations would once more be required to convergence to the new minimizer. Hence, this paper develops a retrospective cost-based ESC(RC/ESC) technique for online output minimization with a vanishing perturbation, that is, a perturbation that becomes zero as time increases independently from the state of the controller or the controlled system. The performance of the proposed algorithm is illustrated via numerical examples.Item Vibrational Stabilization of the Kapitza Pendulum Using Model Predictive Control with Constrained Base Displacement(IEEE, 2023-07-03) Ahrazoğlu, M. Akif; Islam, Syed Aseem Ul; Goel, Ankit; Bernstein, Dennis S.It is well known that, for some systems, stabilization can be achieved by open-loop control in the form of high-frequency vibrations. Vibrational control is attractive since it requires no sensors. On the other hand, however, vibrational control requires careful selection of the frequency and amplitude of the input. The present paper is aimed at understanding the robustness of vibrational control and the required control effort by applying nonlinear model predictive control to the classical Kapitza pendulum. A numerical investigation shows that closed-loop control using nonlinear model predictive control is significantly more efficient than open-loop vibrational control with respect to signal power.