Feedback Control of a Spacecraft Electro-dynamic Thruster

In this paper, the possibility of feedback servo control of a spacecraft thruster’s specific impulse by a boundary feedback system is theoretically considered. The motivation to introduce feedback control is two-fold. The first is to stabilize any inherent plasma instabilities and the second is regulate the output specific impulse of the thruster. Two cases are considered: Electro-thermal thrusters and Electro-dynamic thrusters. The chamber inlet temperature in the case of the electro-thermal thruster or the boundary electric field potential responsible for generation of the velocity of the plasma ions in the case of an electrodynamic thruster, are controlled by feedback so as to regulate the thruster's specific impulse. By introducing typical disturbances in the plasma ionization voltage, it is shown using a two-dimensional fluid model and a suitable boundary feedback law, where the chamber inlet temperature or applied boundary potential is proportional to the error in the specific impulse and the desired specific impulse, that the specific impulse of the thruster may be regulated and held constant. The robustness of the control system is numerically tested, by a two dimensional simulation model using McCormacks's method. The Navier-Stokes equations, including the magneto-hydrodynamic variables were discretized and simulated, using the explicit MacCormack method for a typical nozzle domain. The numerical results for the open and closed-loop velocity fields were obtained and the specific impulse was computed from these fields. It was thus shown that not only the stability of the plasma is realized but also that the specific impulse is regulated as desired

Finite state modeling of aeroelastic systems

A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils

Optimum Power Output Control of a Wind Turbine Rotor

© 2016 S. Wijewardana et al. An active and optimum controller is applied to regulate the power output from a wind turbine rotor. The controller is synthesized in two steps. The first step defines the equilibrium operation point and ensures that the desired equilibrium point is stable. The stability of the equilibrium point is guaranteed by a control law that is synthesized by applying the methodology of model predictive control (MPC). The method of controlling the turbine involves pitching the turbine blades. In the second step the blade pitch angle demand is defined. This involves minimizing the mean square error between the actual and desired power coefficient. The actual power coefficient of the wind turbine rotor is evaluated assuming that the blade is capable of stalling, using blade element momentum theory. This ensures that the power output of the rotor can be reduced to any desired value which is generally not possible unless a nonlinear stall model is introduced to evaluate the blade profile coefficients of lift and drag. The relatively simple and systematic nonlinear modelling and MPC controller synthesis approach adopted in this paper clearly highlights the main features on the controller that is capable of regulating the power output of the wind turbine rotor

Flutter and forced response of mistuned rotors using standing wave analysis

A standing wave approach is applied to the analysis of the flutter and forced response of tuned and mistuned rotors. The traditional traveling wave cascade airforces are recast into standing wave arbitrary motion form using Pade approximants, and the resulting equations of motion are written in the matrix form. Applications for vibration modes, flutter, and forced response are discussed. It is noted that the standing wave methods may prove to be more versatile for dealing with certain applications, such as coupling flutter with forced response and dynamic shaft problems, transient impulses on the rotor, low-order engine excitation, bearing motion, and mistuning effects in rotors

Mars Powered Descent Phase Guidance Design Based on Fixed-Time Stabilization Technique

This paper proposes a guidance scheme to achieve an autonomous precision landing on Mars and proposes a practical fixed-time stabilization theorem to analyze the robustness of the guidance. The proposed guidance is mainly based on the fixed-time stabilization method, and it can achieve the precision landing within a pre-defined time. This property enables the proposed guidance to outperform the finite-time stabilization technique which cannot handle uncertainties well and whose convergence time is dependent on initial states. Compared with the existing fixed-time stabilization theorem, the proposed practical fixed-time stabilization theorem can achieve a shorter convergence time and cope with unknown disturbances. When the Mars landing guidance is designed by this proposed theorem, the upper bound of the landing time and the maximum landing error subject to unknown disturbances can be calculated in advance. Theoretical proofs and Monte Carlo simulation results confirm the effectiveness of the proposed theorem and the proposed guidance. Furthermore, the efficacy of the proposed guidance with thrust limitations is also demonstrated by testing of 50 cases with a range of initial positions and velocities

Optimal Trajectory Synthesis for Spacecraft Asteroid Rendezvous

Several researchers are considering the plausibility of being able to rapidly launch a mission to an asteroid, which would fly in close proximity of the asteroid to deliver an impulse in a particular direction so as to deflect the asteroid from its current orbit. Planetary motion, in general, and the motion of asteroids, in particular, are subject to planetary influences that are characterised by a kind of natural symmetry, which results in an asteroid orbiting in a stable and periodic or almost periodic orbit exhibiting a number of natural orbital symmetries. Tracking and following an asteroid, in close proximity, is the subject of this paper. In this paper, the problem of synthesizing an optimal trajectory to a NEO such as an asteroid is considered. A particular strategy involving the optimization of a co-planar trajectory segment that permits the satellite to approach and fly alongside the asteroid is chosen. Two different state space representations of the Hill–Clohessy–Wiltshire (HCW) linearized equations of relative motion are used to obtain optimal trajectories for a spacecraft approaching an asteroid. It is shown that by using a state space representation of HCW equations where the secular states are explicitly represented, the optimal trajectories are not only synthesized rapidly but also result in lower magnitudes of control inputs which must be applied continuously over extended periods of time. Thus, the solutions obtained are particularly suitable for low thrust control of the satellites orbit which can be realized by electric thrusters

Feedback Control of LCOs and Transonic buzz, using the Nonlinear TSD Aerodynamics

In this paper a systematic method to suppress transonic buzz with feedback is presented. A trailing edge control surface in the form of part-span flap was used only to modify and control the unsteady aerodynamic loading on the wing. The flap rotation was used to provide feedback, which consisted of a weighted linear combination of the amplitudes of the principal modes of the structure, referred to as the control law. A linear, optimal feedback control law, that is synthesised systematically based on pseudo-spectral time domain analysis, may be used in principle, to assess its capacity to actively suppress the buzz in the transonic flow domain by using a servo-controlled control surface to modify the unsteady, nonlinear aerodynamic loads on the wing. Thus it is essential that a set of feasible control laws are first constructed. In this paper, this is done by applying the doublet-lattice method (DLM). Restrictions, such as near-zero structural damping in the flap mode, were imposed on the aeroelastic model to facilitate the occurrence of transonic buzz. The feasible set of control laws were then assessed using the nonlinear transonic small disturbance (TSD) theory and an optimum control is selected to suppress the buzz. The essential difference of the behaviour of the closed loop system in non-linear transonic flow, when compared to the applications of linear optimal control in linear potential flow, are presented and discussed