Global stabilization of feedforward systems with exponentially unstable Jacobian linearization

The global stabilization of a class of feedforward systems having an exponentially unstable Jacobian linearization is achieved by a high-gain feedback saturated at a low level. The control law forces the derivatives of the state variables to small values along the closed-loop trajectories. This "slow control" design is illustrated with a benchmark example and its limitations are emphasized. © 1999 Elsevier Science B.V. All rights reserved.

Model-based control of thermoacoustic instabilities in partially premixed lean combustion - A design case study

Self-excited oscillation is becoming a major issue in low-emission, lean partially premixed combustion systems, and active control has been shown to be a feasible method to suppress such instabilities. A number of robust control methods are employed to obtain a feedback controller and it is observed that the robustness to system uncertainty is significantly better for a low complexity controller in spite of the norms being similar. Moreover, we demonstrate that closed-loop stability for such a complex system can be proved via use of the integral quadratic constraint method. Open- and closed-loop nonlinear simulations are provided. © 2013 Copyright Taylor and Francis Group, LLC.

What is the weakest topology in which feedback stability is robust?

Mathematical theorems in control theory are only of interest in so far as their assumptions relate to practical situations. The space of systems with transfer functions in ℋ∞, for example, has many advantages mathematically, but includes large classes of non-physical systems, and one must be careful in drawing inferences from results in that setting. Similarly, the graph topology has long been known to be the weakest, or coarsest, topology in which (1) feedback stability is a robust property (i.e. preserved in small neighbourhoods) and (2) the map from open-to-closed-loop transfer functions is continuous. However, it is not known whether continuity is a necessary part of this statement, or only required for the existing proofs. It is entirely possible that the answer depends on the underlying classes of systems used. The class of systems we concern ourselves with here is the set of systems that can be approximated, in the graph topology, by real rational transfer function matrices. That is, lumped parameter models, or those distributed systems for which it makes sense to use finite element methods. This is precisely the set of systems that have continuous frequency responses in the extended complex plane. For this class, we show that there is indeed a weaker topology; in which feedback stability is robust but for which the maps from open-to-closed-loop transfer functions are not necessarily continuous. © 2013 Copyright Taylor and Francis Group, LLC.

Predictive control for spacecraft rendezvous in an elliptical orbit using an FPGA

A field programmable gate array (FPGA)-based predictive controller for a spacecraft rendezvous manoeuvre is presented. A linear time varying prediction model is used to accommodate elliptical orbits, and a variable prediction horizon is used to facilitate finite time completion of manoeuvres. The resulting constrained optimisation problems are solved using a primal dual interior point algorithm. The majority of the computational demand is in solving a set of linear equations at each iteration of this algorithm. To accelerate this operation, a custom circuit is implemented, using a combination of Mathworks HDL Coder and Xilinx System Generator for DSP, and used as a peripheral to a MicroBlaze soft core processor. The system is demonstrated in closed loop by linking the FPGA with a simulation of the plant dynamics running in Simulink on a PC, using Ethernet. © 2013 EUCA.

Aberration correction for free space optical communications using rectangular zernike modal wavefront sensing

A time multiplexed rectangular Zernike modal wavefront sensor based on a nematic phase-only liquid crystal spatial light modulator and specially designed for a high power two-electrode tapered laser diode which is a compact and novel free space optical communication source is used in an adaptive beam steering free space optical communication system, enabling the system to have 1.25 GHz modulation bandwidth, 4.6° angular coverage and the capability of sensing aberrations within the system and caused by atmosphere turbulence up to absolute value of 0.15 waves amplitude and correcting them in one correction cycle. Closed-loop aberration correction algorithm can be implemented to provide convergence for larger and time varying aberrations. Improvement of the system signal-to-noise-ratio performance is achieved by aberration correction. To our knowledge, it is first time to use rectangular orthonormal Zernike polynomials to represent balanced aberrations for high power rectangular laser beam in practice. © 2014 IEEE.

Field programmable gate array based predictive control system for spacecraft rendezvous in elliptical orbits

Copyright © 2014 John Wiley & Sons, Ltd. Copyright © 2014 John Wiley & Sons, Ltd. Summary A field programmable gate array (FPGA) based model predictive controller for two phases of spacecraft rendezvous is presented. Linear time-varying prediction models are used to accommodate elliptical orbits, and a variable prediction horizon is used to facilitate finite time completion of the longer range manoeuvres, whilst a fixed and receding prediction horizon is used for fine-grained tracking at close range. The resulting constrained optimisation problems are solved using a primal-dual interior point algorithm. The majority of the computational demand is in solving a system of simultaneous linear equations at each iteration of this algorithm. To accelerate these operations, a custom circuit is implemented, using a combination of Mathworks HDL Coder and Xilinx System Generator for DSP, and used as a peripheral to a MicroBlaze soft-core processor on the FPGA, on which the remainder of the system is implemented. Certain logic that can be hard-coded for fixed sized problems is implemented to be configurable online, in order to accommodate the varying problem sizes associated with the variable prediction horizon. The system is demonstrated in closed-loop by linking the FPGA with a simulation of the spacecraft dynamics running in Simulink on a PC, using Ethernet. Timing comparisons indicate that the custom implementation is substantially faster than pure embedded software-based interior point methods running on the same MicroBlaze and could be competitive with a pure custom hardware implementation.

Comparison of different scheduling techniques for H-infinity controllers

Several approaches to designing schedule H-infinity control systems are compared. These include a controller switching approach and also parameter scheduling of an observer representation of the controller. They are illustrated by application to a Generic VSTOI. Aircraft Model (GVAM) supplied by The Royal Aerospace Establishment (RAE) at Bedford. The switched design has been tested on the simulator at RAE Bedford. The linear H-infinity designs make use of a loop-shaping followed by robust stabilisation to additive perturbations of a normalised coprime factorisation of the shaped plans. The different scheduling approaches are compared with respect to achieved robust stability levels. performance and complexity of implementation.