### Browsing by Author "Goel, Ankit"

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Item Adaptive Backstepping Control of a Bicopter in Pure Feedback Form with Dynamic Extension(2024-02-06) Delgado, Jhon Manuel Portella; Mirtaba, Mohammad; Goel, AnkitThis paper presents a model-based, adaptive, nonlinear controller for the bicopter stabilization and trajectory-tracking problem. The nonlinear controller is designed using the backstepping technique. Due to the non-invertibility of the input map, the bicopter system is first dynamically extended. However, the resulting dynamically extended system is in the pure feedback form with the uncertainty appearing in the input map. The adaptive backstepping technique is then extended and applied to design the controller. The proposed controller is validated in simulation for a smooth and nonsmooth trajectory-tracking problem.Item Adaptive Combustion Regulation in Solid Fuel Ramjet(AIAA, 2024-01-04) Oveissi, Parham; Goel, Ankit; Tumuklu, Ozgur; Hanquist, Kyle M.Control of the combustion process under hypersonic conditions remains a challenging problem. In this paper, we investigate the application of a data-driven, learning-based control technique to regulate a combustion process evolving inside a solid fuel ramjet to regulate the generated thrust under unknown operating conditions. A computational model to simulate the combustion dynamics is developed by combining compressible flow theory with equilibrium chemistry. The computational model is simulated to ascertain the combustion dynamics' stability and establish the engine's operational envelope. Based on retrospective cost optimization, an online learning controller is then integrated with the computational model to regulate the generated thrust. Numerical simulation results are presented to demonstrate the robustness of the adaptive control system.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 Adaptive Nonlinear Control of a Bicopter with Unknown Dynamics(2023-05-05) Delgado, Jhon Manuel Portella; Goel, AnkitThis paper presents an adaptive input-output linearization controller with a finite-time convergent parameter estimator for the multicopter trajectory following problem. The controller is constructed by augmenting the input-output linearizing controller based on a dynamically extended multicopter model with a parameter estimator with finite-time convergence properties. Unlike control systems based on the time separation principle to separate the translational and rotational dynamics, the proposed technique is applied to design a controller for the full nonlinear dynamics of the system to obtain desired transient performance. The proposed controller is validated in simulation for a smooth and nonsmooth trajectory following problem.Item An Adaptive PID Autotuner for Multicopters with Experimental Results(2021-09-27) Spencer, John; Lee, Joonghyun; Paredes, Juan Augusto; Goel, Ankit; Bernstein, DennisThis paper develops an adaptive PID autotuner for multicopters, and presents simulation and experimental results. The autotuner consists of adaptive digital control laws based on retrospective cost adaptive control implemented in the PX4 flight stack. A learning trajectory is used to optimize the autopilot during a single flight. The autotuned autopilot is then compared with the default PX4 autopilot by flying a test trajectory constructed using the second-order Hilbert curve. In order to investigate the sensitivity of the autotuner to the quadcopter dynamics, the mass of the quadcopter is varied, and the performance of the autotuned and default autopilot is compared. It is observed that the autotuned autopilot outperforms the default autopilot.Item Circumventing Unstable Zero Dynamics in Input-Output Linearization of Longitudinal Flight Dynamics(AIAA, 2024-01-04) Delgado, Jhon M. Portella; Goel, AnkitIn this paper, we consider the problem of input-output linearization of the longitudinal flight dynamics. In longitudinal flight dynamics, inputs are typically thrust and elevator deflection whereas the outputs are the velocity and the flight path angle. An input-output linearization-based controller can be designed to render the multi-input, multi-output system linear; however, the resulting zero dynamics turns out to be unstable. In this work, we remove the zero dynamics from the closed-loop dynamics by considering an additional output. Although the additional output makes the system tall, which, in general, means that the input-to-output dynamics can not be linearized, we show that in the case of longitudinal flight dynamics, linearization is possible due to special geometric properties of the nonlinear terms.Item Computing Invariant Zeros of a Linear System Using State-Space Realization(2023-07-28) Delgado, Jhon Manuel Portella; Goel, AnkitIt is well known that zeros and poles of a single-input, single-output system in the transfer function form are the roots of the transfer function’s numerator and the denominator polynomial, respectively. However, in the state-space form, where the poles are a subset of the eigenvalue of the dynamics matrix and thus can be computed by solving an eigenvalue problem, the computation of zeros is a non-trivial problem. This paper presents a realization of a linear system that allows the computation of invariant zeros by solving a simple eigenvalue problem. The result is valid for square multi-input, multi-output (MIMO) systems, is unaffected by lack of observability or controllability, and is easily extended to wide MIMO systems. Finally, the paper illuminates the connection between the zero-subspace form and the normal form to conclude that zeros are the poles of the system’s zero dynamics.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 Improving Forecasting Ability of GITM using Data-driven Model Refinement(2022-11-21) Ponder, Brandon M.; Ridley, Aaron J.; Goel, Ankit; Bernstein, D. S.At altitudes below about 600 km, satellite drag is one of the most important and variable forces acting on a satellite. Neutral mass density predictions in the upper atmosphere are therefore critical for (1) designing satellites; (2) performing adjustments to stay in an intended orbit; and (3) collision avoidance maneuver planning. Density predictions have a great deal of uncertainty, including model biases and model misrepresentation of the atmospheric response to energy input. These may stem from inaccurate approximations of terms in the Navier-Stokes equations, unmodeled physics, incorrect boundary conditions, or incorrect parameterizations. Two commonly parameterized source terms are the thermal conduction and eddy diffusion. Both are critical components in the transfer of the heat in the thermosphere. Determining how well the major constituents ($N_2$, $O_2$, $O$) are as heat conductors will have effects on the temperature and mass density changes from a heat source. This work shows the effectiveness of using the retrospective cost model refinement (RCMR) technique at removing model bias caused by different sources within the Global Ionosphere Thermosphere Model (GITM). Numerical experiments, Challenging Minisatellite Payload (CHAMP) and Gravity Recovery and Climate Experiment (GRACE) data during real events are used to show that RCMR can compensate for model bias caused by both inaccurate parameterizations and drivers. RCMR is used to show that eliminating model bias before a storm allows for more accurate predictions throughout the storm.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 Learning-based Adaptive Gust Mitigation with Oscillating Wings(ARC, 2023-01-19) Poudel, Naresh; Trivedi, Arjun; Oveissi, Parham; Yu, Meilin; Goel, Ankit; Hrynuk, John T.This paper investigates the application of a learning-based adaptive controller to mitigate the effect of gust on the lift generated by an airfoil in an unsteady flow environment. A high-order accurate CFD model is used to model the unsteady flow over a pitching airfoil. Open-loop simulations of the CFD model are used to ascertain feasible lift commands. The learning-based adaptive controller is based on the retrospective cost adaptive control (RCAC). First, RCAC is used to regulate the lift coefficient of the airfoil in a nominal case without gust. Next, the effect of the hyperparameters of the adaptive control on the closed-loop performance is investigated. Finally, we used RCAC to regulate the lift coefficient and mitigated the effect of gust on the airfoil.Item Learning-based Adaptive Thrust Regulation of Solid Fuel Ramjet(ARC, 2023-01-19) Oveissi, Parham; Trivedi, Arjun; Goel, Ankit; Tumuklu, Ozgur; Hanquist, Kyle M.; Farahmandi, Alireza; Philbrick, DouglasThis paper uses retrospective cost adaptive control to regulate the thrust generated by a solid fuel ramjet engine. A one-dimensional quasi-static model based on the conservation of mass, momentum, and energy, along with a simplified regression model for solid fuel combustion, is used to model the solid fuel ramjet engine. We use the SFRJ model in open-loop simulations to establish the operational envelope of the engine. Then, RCAC is tuned to regulate the thrust produced by the engine in nominal and off-nominal operating conditions. The performance of the adaptive controller is compared with a fixed-gain controller optimized by RCAC under nominal operating conditions. In each case, it is observed that the RCAC significantly improves the transient performance.Item MIMO Input-Output Linearization with Applications for Longitudinal Flight Dynamics(2022-05-12) Delgado, Jhon Manuel Portella; Goel, AnkitThis paper presents an extension of the input-output linearization method for nonsquare systems with more outputs than inputs. Unlike the square systems and nonsquare systems with fewer outputs than inputs, which can be completely linearized, we consider the problem of linearizing nonsquare systems with more outputs than inputs. In particular, the system is linearized by decomposing the state using a diffeomorphism, which is chosen such that the output of the system is a linear combination of the outputs of integrator chains, and the input of the system is chosen to cancel the nonlinearities using feedback linearization. In the case of nonsquare systems with more outputs than inputs, we observe that the resulting linear system can be stabilized even though it is uncontrollable at all times. This apparent contradiction is due to the switching behavior in the control action. We apply the input-output linearization method to linearize the longitudinal aircraft dynamics and demonstrate asymptotic stability of the closed-loop system despite the switching behavior.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 Attitude Filtering with Noisy Measurements and Unknown Gyro Bias(2024-01-23) Oveissi, Parham; Goel, AnkitAttitude filtering is a critical technology with applications in diverse domains such as aerospace engineering, robotics, computer vision, and augmented reality. Although attitude filtering is a particular case of the state estimation problem, attitude filtering is uniquely challenging due to the special geometric structure of the attitude parameterization. This paper presents a novel data-driven attitude filter, called the retrospective cost attitude filter (RCAF), for the SO(3) attitude representation. Like the multiplicative extended Kalman filter, RCAF uses a multiplicative correction signal, but instead of computing correction gains using Jacobians, RCAF computes the corrective signal using retrospective cost optimization and measured data. The RCAF filter is validated numerically in a scenario with noisy attitude measurements and noisy and biased rate-gyro measurements.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.