Active Flutter Suppression of a Two-Dimensional Airfoil with Actuator Saturation

This paper presents a systematic methodology to evaluate the feasibility of suppressing airplane flutter instabilities through the actively controlled closed-loop actuation of control surfaces in presence of actuator deflection constraints. When active flutter suppression proves to be feasible, the methodology synthesizes a preliminary feedback law able to augment flutter stability of the aeroelastic model under investigation. If active flutter suppression proves to be not viable due to the physical limitations imposed by actuator deflection saturation, the methodology can be employed in a parametric manner to define the actuator performance requirements that would take to implement active flutter suppression. The theoretical background of the methodology is presented and its implementation is validated employing the generic twodimensional wing section of Theodorsen

Autonomous thruster failure recovery on underactuated spacecraft using model predictive control

Thruster failures historically account for a large percentage of failures that have occurred on orbit. These failures are typically handled through redundancy, however, with the push to using smaller, less expensive satellites in clusters or formations there is a need to perform thruster failure recovery without additional hardware. This means that a thruster failure may cause the spacecraft to become underactuated, requiring more advanced control techniques. A model of a thruster-controlled spacecraft is developed and analyzed with a nonlinear controllability test, highlighting several challenges including coupling, nonlinearities, severe control input saturation, and nonholonomicity. Model Predictive Control (MPC) is proposed as a control technique to solve these challenges. However, the real-time, online implementation of MPC brings about many issues. A method of performing MPC online is described, implemented and tested in simulation as well as in hardware on the Synchronized Position-Hold, Engage, Reorient Experimental Satellites (SPHERES) testbed at the Massachusetts Institute of Technology (MIT) and on the International Space Station (ISS). These results show that MPC provided improved performance over a simple path planning technique

On the Decidability of Reachability in Linear Time-Invariant Systems

We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by boolean combinations of linear inequalities. Decidability of the version of the reachability problem in which control sets are affine subspaces of $\mathbb{R}^n$ is a fundamental result in control theory. Our first result is that reachability is undecidable if the set of controls is a finite union of affine subspaces. We also consider versions of the reachability problem in which (i)~the set of controls consists of a single affine subspace together with the origin and (ii)~the set of controls is a convex polytope. In these two cases we respectively show that the reachability problem is as hard as Skolem's Problem and the Positivity Problem for linear recurrence sequences (whose decidability has been open for several decades). Our main contribution is to show decidability of a version of the reachability problem in which control sets are convex polytopes, under certain spectral assumptions on the transition matrix

Constrained control using convex optimization

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1997.Includes bibliographical references (p. 113-121).by John Marc Shewchun.M.S

Digital repetitive control under varying frequency conditions

Premi extraordinari doctorat curs 2011-2012, àmbit d’Enginyeria IndustrialThe tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area and Repetitive Control has proven to be an efficient way to face this topic; however, in some applications the period of the signal to be tracked/rejected changes in time or is uncertain, which causes and important performance degradation in the standard repetitive controller. This thesis presents some contributions to the open topic of repetitive control working under varying frequency conditions. These contributions can be organized as follows: One approach that overcomes the problem of working under time varying frequency conditions is the adaptation of the controller sampling period, nevertheless, the system framework changes from Linear Time Invariant to Linear Time-Varying and the closed-loop stability can be compromised. This work presents two different methodologies aimed at analysing the system stability under these conditions. The first one uses a Linear Matrix Inequality (LMI) gridding approach which provides necessary conditions to accomplish a sufficient condition for the closed-loop Bounded Input Bounded Output stability of the system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability conditions. Both methodologies yield a frequency variation interval for which the system stability can be assured. Although several approaches exist for the stability analysis of general time-varying sampling period controllers few of them allow an integrated controller design which assures closed-loop stability under such conditions. In this thesis two design methodologies are presented, which assure stability of the repetitive control system working under varying sampling period for a given frequency variation interval: a mu-synthesis technique and a pre-compensation strategy. On a second branch, High Order Repetitive Control (HORC) is mainly used to improve the repetitive control performance robustness under disturbance/reference signals with varying or uncertain frequency. Unlike standard repetitive control, the HORC involves a weighted sum of several signal periods. With a proper selection of the associated weights, this high order function offers a characteristic frequency response in which the high gain peaks located at harmonic frequencies are extended to a wider region around the harmonics. Furthermore, the use of an odd-harmonic internal model will make the system more appropriate for applications where signals have only odd-harmonic components, as in power electronics systems. Thus an Odd-harmonic High Order Repetitive Controller suitable for applications involving odd-harmonic type signals with varying/uncertain frequency is presented. The open loop stability of internal models used in HORC and the one presented here is analysed. Additionally, as a consequence of this analysis, an Anti-Windup (AW) scheme for repetitive control is proposed. This AW proposal is based on the idea of having a small steady state tracking error and fast recovery once the system goes out of saturation. The experimental validation of these proposals has been performed in two different applications: the Roto-magnet plant and the active power filter application. The Roto-magnet plant is an experimental didactic plant used as a tool for analysing and understanding the nature of the periodic disturbances, as well as to study the different control techniques used to tackle this problem. This plant has been adopted as experimental test bench for rotational machines. On the other hand, shunt active power filters have been widely used as a way to overcome power quality problems caused by nonlinear and reactive loads. These power electronics devices are designed with the goal of obtaining a power factor close to 1 and achieving current harmonics and reactive power compensation.Award-winningPostprint (published version

Control of Ocean Wave Energy Converters with Finite Stroke

In the design of ocean wave energy converters, proper control design is essential for the maximization of power generation performance. However, in practical applications, this control must be undertaken in the presence of stroke saturation and model uncertainty. In this dissertation, we address these challenges separately. To address stroke saturation, a nonlinear control design procedure is proposed, which guarantees to keep the stroke within its limits. The technique exploits the passivity of the wave energy converter to guarantee closed-loop stability. The proposed technique consists of three steps: 1) design of a linear feedback controller using multi-objective optimization techniques; 2) augmentation of this design with an extra input channel that adheres to a closed-loop passivity condition; and 3) design of an outer, nonlinear passive feedback loop that controls this augmented input in such a way as to ensure stroke limits are maintained. The discrete-time version of this technique is also presented. To address model uncertainty, in particular we consider the nonlinear viscosity drag effect as the model uncertainty. This robust control design problem can be regarded as a multi-objective optimization problem, whose primary objective is to optimize the nominal performance, while the second objective is to robustly stabilize the closed-loop system. The robust stability constraint can be posed using the concept of circle criterion. Because this optimization is non-convex, Loop Transfer Recovery methods are used to solve for sub-optimal solutions to the problem. These techniques are demonstrated in simulation, for arrays of buoy-type wave energy converters.PHDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163263/1/waynelao_1.pd