M. Nabi

A finite-time convergent continuous time sliding mode controller for spacecraft attitude control

In this work a finite time convergent, continuous time sliding mode robust controller is proposed for attitude control of rigid spacecraft. The controller is designed with a new proposed fast terminal sliding mode (FTSM). Finite time reachability to the small neighborhood of sliding surface and faster finite time convergent of system states to equilibrium point is shown using a Lyapunov-type theorem. Simulation results show better convergent performance of the FTSM over terminal sliding mode controller (TSM).

Novel modeling and solution approach for repeated finite-element analysis of eddy-current systems

In this paper, we present an efficient modeling and computational scheme for a repeated solution of an eddy-current system with different values of the supply frequency as well as of the permeability and conductivity of the eddy-current region. The scheme is based on a general parametric expression obtained for the finite-element (FE) solution with the supply frequency, permeability, and conductivity as parameters. The algorithm allows for numerically efficient updating of the solution for different values of the parameters through the solution of a much smaller sparse linear system, instead of a repeated solution of the entire FE model. Moreover, if required, the solution can be computed only over a small region of interest, making the scheme ideally suited to many coupled-field problems. As an application, the scheme is applied to a typical bar-plate eddy-current system, excited by nonsinusoidal currents. The time variations of the magnetic field are computed as a superposition of responses computed for a number of harmonics. An a priori estimate for the difference between responses to two harmonics has been obtained, which can be used as a frequency-sensitivity measure to avoid computation of responses to all individual harmonics. The applicability of the approach to general transient excitations and further possible developments are identified.

Attitude control of magnetic actuated spacecraft using super-twisting algorithm with nonlinear sliding surface

The three-axis attitude control of magnetic actuated rigid spacecraft is considered in this paper. In the presented work, second order sliding mode control (2-SMC) with a nonlinear sliding surface is considered to generate continuous control with a finite time convergence property. The super-twisting control algorithm is considered for 2-SMC. The simulation results show that super-twisting based control with considered nonlinear sliding surface, is able to generate sufficient control torque, which results three-axis controllable spacecraft. Results show that controller steers the attitude trajectories to their nearest equilibrium. The robustness of controller is evaluated by subjecting cyclic disturbance torques, and inertia uncertainty.

AN EFFICIENT COMPUTATIONAL MODELING AND SOLUTION SCHEME FOR REPEATED FINITE ELEMENT ANALYSIS OF COMPOSITE DOMAINS WITH VARYING MATERIAL PROPERTY

Many engineering applications require efficient computation of the solution of the Poisson equation defined over one, two or three dimensions, representing a wide variety of physical systems. The most popular method used for this purpose is the finite element method (FEM). An important class of applications in modeling and simulation require repeated computation of the solution over a given geometry, for different values of the relevant material property in a region within the domain. They can arise in the areas of nondestructive testing and evaluation, field-control in electromagnetic applications, as well as computer-aided design of devices and systems. In this work, a linear algebraic study of the dependence of the coefficient (stiffness) matrix on the varying material property is used to develop a general expression of the finite element solution. Based on this, a novel modeling and simulation scheme is suggested which significantly reduces the computational cost of the repetitive solution stage, as well as the size of the numerical model to be stored. Numerical simulations are presented for a simple illustrative case and a few possible applications are suggested in different engineering fields.

Reduced Order Modeling of a Microgripper Using SVD-Second-Order Krylov Method

This article considers the problem of modeling of a three-dimensional microgripper system. It is described by partial differential equations and a discretization method is applied to obtain a very large-sized second-order ordinary differential equation model. A two-stage model reduction technique is proposed here. In the first stage, size of the model is reduced using SVD second-order Krylov method, which yields a second-order asymptotic stable model. But the size of this model is still relatively large and, in the next stage of reduction, pure SVD is applied to obtain a reasonably small model. The main reason for applying SVD second-order Krylov is to obtain a bound on the neglected dynamics, which can further be utilized as a bounded uncertainty on the reduced model. Results of the numerical implementations are presented and possible further extensions are identified.

Original article: Nonlinearity-aware sub-model combination in trajectory based methods for nonlinear Mor

Trajectory based methods approximate nonlinear dynamical systems by superposition of dimensionally reduced linear systems. The linear systems are obtained by linearisations at multiple points along a state-trajectory. They are combined in a weighted sum and the combinations are switched appropriately to approximate the dynamic behaviour of the nonlinear system. Weights assigned at a specimen point on the trajectory generally depend on the euclidean distance to the linearisation points. In this work, limitations of the conventional weight-assignment scheme are pointed out. It is shown that the procedure is similar across all nonlinearities, and hence ignores the nonlinear vector field curvature for superposition. Additionally, it results in an inadequate assessment of the linear systems when they are equidistant from the specimen point. An improved method for weight-assignment, which uses state-velocities in addition to state-positions is proposed. The method naturally takes into account the system nonlinearity and is hence called Nonlinearity-aware Trajectory Piece-wise Linear (Ntpwl) method. Further, a computationally efficient procedure for estimating the state-velocity is introduced. The new strategy is illustrated and assessed with the help of case studies and it is shown that the Ntpwl model substantially improves the approximation of the nonlinear systems considered. Increased robustness to training and negligible stretching of the computational resources is also obtained.

Modelling and simulation strategy for parametric transient electromagnetic simulations

This paper presents an efficient two-step reduction strategy for parametric transient electromagnetic simulations. The first step involves the conversion of a large system of parametrised differential algebraic equations (PDAEs), obtained after finite element (FE) discretisation into a significantly smaller system of ordinary differential equations, while symbolically preserving the parameters. The parametric ODE (PODE) model so obtained, having an affine parametric dependence can be further reduced using system theoretic parametric model order reduction strategies. In this work, two techniques of achieving such reductions are presented: aggregate projection matrix approach and multi-dimensional moment matching. Both these methods result in symbolic retention of parameters in the reduced model. The transient electromagnetic simulations corresponding to different values of the parameters can then be carried out in the reduced space at a drastically reduced computational cost. However, it was observed that ...

Piece-wise Quasi-linear Approximation for Nonlinear Model Reduction

The trajectory piece-wise linear (TPWL) method is a popular technique for nonlinear model order reduction (MOR). Though widely studied, it has primarily been restricted to applications modeled by nonlinear systems with linear input operators. This paper is an effort to bridge this gap. We illustrate problems in the TPWL method in creating reduced order models for nonlinear systems with nonlinear input operators. We also propose a solution based on a quasi-linear formulation of the nonlinear system at approximation points. This results in a method for nonlinear MOR, called the trajectory piece-wise quasi-linear (TPWQ) method. TPWQ is formulated, numerically validated and a new technique to reduce the computational costs associated with simulating the quasi-linear systems is also demonstrated.

A control law for a nonlinear heat conduction problem on nontrivial domains using FEM

A modeling and control strategy is presented for a nonlinear problem of heating a domain of nontrivial geometry from an arbitrary initial to another arbitrary desired temperature profile. A large dynamic model of the nonlinear heat equation is obtained through finite element (FE), which is reduced using proper orthogonal decomposition. Finally, a nonlinear control law is proposed for the control problem and its stability proved through Lyapunov analysis. Results of numerical implementation are presented and possible extensions identified.

Re-entry trajectory optimization for space shuttle using Sine-Cosine Algorithm

The re-entry phase of the reusable launch vehicle (RLV) is a challenging optimal control problem because of its high nonlinearity and numerical sensitivity. In this paper, a recently proposed metaheuristic optimization algorithm, Sine-Cosine Algorithm(SCA) is employed to solve the re-entry trajectory problem for space shuttle vehicle. A cost function which maximizes the cross range along with satisfying certain boundary conditions is selected for the problem. Control inputs are parameterized with defined ranges for the implementation of SCA to solve the optimal control problem. The results demonstrate the optimal trajectory. The results obtained show efficiency and applicability of SCA for solving the trajectory optimal control problem.