arXiv subjects

Jamshed Riaz

Publications and source records attributed to Jamshed Riaz.

8 recordsLinked to original sources

arXiv2025

Geometrization of Higher-Order Linear Control Laws for Attitude Control on $\mathsf{SO(3)}$

This paper presents a theoretical framework for analyzing the stability of higher-order geometric nonlinear control laws for attitude control on the Special Orthogonal Group $\mathrm{SO(3)}$. In particular, the paper extends existing results on the analysis of PID-type geometric nonlinear control laws to more general higher-order dynamic state-feedback compensators on $\mathrm{SO(3)}$. The candidate Lyapunov function is motivated by quadratic Lyapunov functions of the form $V(x)=x^{\top}Px$ typically considered in the analysis of linear time-invariant (LTI) systems. The stability analysis is carried out in two steps. In the first step, a sufficient condition is obtained for the positive definiteness of the candidate Lyapunov function, and a necessary and sufficient condition for the negative definiteness of the corresponding Lyapunov rate. These conditions ensure that the desired equilibrium is almost globally asymptotically stable (AGAS). In the second step, a convex relaxation of the proposed conditions is used to obtain sufficient conditions in the form of linear matrix inequalities (LMIs). Overall, the approach is motivated by the widespread use of LMI-based analysis and design tools for LTI systems. To reduce conservatism, matrix gains are considered for the controller gains as well as the Lyapunov function coefficients. The applicability of the approach to practical problems is illustrated by designing and analyzing a 21-state geometric nonlinear attitude control law for a multicopter.

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arXiv2024

Rigid-Body Attitude Control on $\mathsf{SO(3)}$ using Nonlinear Dynamic Inversion

This paper presents a cascaded control architecture, based on nonlinear dynamic inversion (NDI), for rigid body attitude control. The proposed controller works directly with the rotation matrix parameterization, that is, with elements of the Special Orthogonal Group $\mathsf{SO(3)}$, and avoids problems related to singularities and non-uniqueness which affect other commonly used attitude representations such as Euler angles, unit quaternions, modified Rodrigues parameters, etc. The proposed NDI-based controller is capable of imposing desired linear dynamics of any order for the outer attitude loop and the inner rate loop, and gives control designers the flexibility to choose higher-order dynamic compensators in both loops. In addition, sufficient conditions are presented in the form of linear matrix inequalities (LMIs) which ensure that the outer loop controller renders the attitude loop almost globally asymptotically stable (AGAS) and the rate loop globally asymptotically stable (GAS). Furthermore, the overall cascaded control architecture is shown to be AGAS in the case of attitude error regulation. Lastly, the proposed scheme is compared with an Euler angles-based NDI scheme from literature for a tracking problem involving agile maneuvering of a multicopter in a high-fidelity nonlinear simulation.

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arXiv2024

Nonlinear Control Allocation: A Learning Based Approach

Modern aircraft are designed with redundant control effectors to cater for fault tolerance and maneuverability requirements. This leads to aircraft being over-actuated and requires control allocation schemes to distribute the control commands among control effectors. Traditionally, optimization-based control allocation schemes are used; however, for nonlinear allocation problems, these methods require large computational resources. In this work, an artificial neural network (ANN) based nonlinear control allocation scheme is proposed. The proposed scheme is composed of learning the inverse of the control effectiveness map through ANN, and then implementing it as an allocator instead of solving an online optimization problem. Stability conditions are presented for closed-loop systems incorporating the allocator, and computational challenges are explored with piece-wise linear effectiveness functions and ANN-based allocators. To demonstrate the efficacy of the proposed scheme, it is compared with a standard quadratic programming-based method for control allocation.

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arXiv2023

Modelling, Simulation, and Control of a Flexible Space Launch Vehicle

Modern Space Launch Vehicles (SLVs), being slender in shape and due to the use of lightweight materials, are generally flexible in nature. This structural flexibility, when coupled with sensor and actuator dynamics, can adversely affect the control of SLV, which may lead to vehicle instability and, in the worst-case scenario, to structural failure. This work focuses on modelling and simulation of rigid and flexible dynamics of an SLV and its interactions with the control system. SpaceX's Falcon 9 has been selected for this study. The flexible modes are calculated using modal analysis in Ansys. High-fidelity nonlinear simulation is developed which incorporates the flexible modes and their interactions with rigid degrees of freedom. Moreover, linearized models are developed for flexible body dynamics, over the complete trajectory until the first stage's separation. Using classical control methods, attitude controllers, that keep the SLV on its desired trajectory, are developed, and multiple filters are designed to suppress the interactions of flexible dynamics. The designed controllers along with filters are implemented in the nonlinear simulation. Furthermore, to demonstrate the robustness of designed controllers, Monte-Carlo simulations are carried out and results are presented.

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arXiv2023

Robust Stability Analysis of a Class of LTV Systems

Many physical systems are inherently time-varying in nature. When these systems are linearized around a trajectory, generally, the resulting system is Linear Time-Varying (LTV). LTV systems describe an important class of linear systems and can be thought of as a natural extension of LTI systems. However, it is well known that, unlike LTI systems, the eigenvalues of an LTV system do not determine its stability. In this paper, the stability conditions for a class of LTV systems are derived. This class is composed of piecewise LTV systems, i.e. LTV systems that are piecewise linear in time. Sufficient conditions of stability are derived in the form of linear matrix inequalities (LMIs) by using the Lyapunov stability criterion. The feasibility of LMIs guarantees the stability of a given piecewise LTV system. Furthermore, uncertain piecewise LTV systems with scalar parametric uncertainty are also considered. Sufficient conditions for robust stability of this case are also presented, which come out to be quasi-LMIs, which can be optimized using a bisection algorithm to find the bounds of uncertainty for which the system is stable. The proposed method is applied to the problem of pitch angle control of a space launch vehicle, and the results are presented.

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arXiv2022

Reconfigurable Control of a Class of Multicopters

In this paper, a reconfigurable control scheme for a generalized class of multicopters is presented to overcome single or multiple rotor failures. In a multicopter, the rotor failure heavily affects its dynamics and thus its controllability. Limited controllability leads to limited or no reconfigurability. \emph{Available Control Authority Index} has been recently developed \cite{Du2015} as a measure of controllability of multicopters. In this work, the notion of \emph{Available Reduced-Control Authority Index} (ArCAI) is introduced, which shows that in some uncontrollable failures it is still possible to control reduced set of states. Based on this notion, a reconfigurable control scheme is presented, which comprises a \emph{Nonlinear Dynamic Inversion} based baseline control law, a constrained control allocation scheme along with some modifications to incorporate reconfiguration, and a simplified fault detection and isolation technique. Simulation results for a commonly used configuration of Hexacopter are presented in the presence of single and multiple rotor failures.

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arXiv2021

Airfoil's Aerodynamic Coefficients Prediction using Artificial Neural Network

Figuring out the right airfoil is a crucial step in the preliminary stage of any aerial vehicle design, as its shape directly affects the overall aerodynamic characteristics of the aircraft or rotorcraft. Besides being a measure of performance, the aerodynamic coefficients are used to design additional subsystems such as a flight control system, or predict complex dynamic phenomena such as aeroelastic instability. The coefficients in question can either be obtained experimentally through wind tunnel testing or, depending upon the accuracy requirements, by numerically simulating the underlying fundamental equations of fluid dynamics. In this paper, the feasibility of applying Artificial Neural Networks (ANNs) to estimate the aerodynamic coefficients of differing airfoil geometries at varying Angle of Attack, Mach and Reynolds number is investigated. The ANNs are computational entities that have the ability to learn highly nonlinear spatial and temporal patterns. Therefore, they are increasingly being used to approximate complex real-world phenomenon. However, despite their significant breakthrough in the past few years, ANNs' spreading in the field of Computational Fluid Dynamics (CFD) is fairly recent, and many applications within this field remain unexplored. This study thus compares different network architectures and training datasets in an attempt to gain insight as to how the network perceives the given airfoil geometries, while producing an acceptable neuronal model for faster and easier prediction of lift, drag and moment coefficients in steady state, incompressible flow regimes. This data-driven method produces sufficiently accurate results, with the added benefit of saving high computational and experimental costs.

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arXiv2021

Robust Stability Analysis of an Uncertain Aircraft Model with Scalar Parametric Uncertainty

A robust controller is specified, and the stability bounds of the uncertain closed-loop system are determined using the small gain, circle, positive real, and Popov criteria. A graphical approach is employed in order to demonstrate the ease with which the above robustness tests can be carried out on a problem of practical interest. A significant improvement in stability bounds is observed as the analysis moves from the small gain test to the circle, positive real, and Popov tests. In particular, small gain analysis results in the most conservative robust stability bounds, while Popov analysis yields significantly less conservative bounds. This is because traditional small gain type tests allow the uncertainty to be arbitrarily time-varying, whereas Popov analysis restricts the uncertainty to be constant, real parametric uncertainty. Therefore, the results reported here indicate the conservatism associated with small gain analysis, and the effectiveness of Popov analysis, in gauging robust stability in the presence of constant, real parametric uncertainty.

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