Probabilistic Robustness Analysis with Aerospace Applications

This thesis develops theoretical and computational methods for the robustness analysis of uncertain systems. The considered systems are linearized and depend rationally on random parameters with an associated probability distribution. The uncertainty is tackled by applying a polynomial chaos expansion (PCE), a series expansion for random variables similar to the well-known Fourier series for periodic time signals. We consider the linear perturbations around a system's operating point, i.e., reference trajectory, both from a probabilistic and worst-case point of view. A chief contribution is the polynomial chaos series expansion of uncertain linear systems in linear fractional representation (LFR). This leads to significant computational benefits when analyzing the probabilistic perturbations around a system's reference trajectory. The series expansion of uncertain interconnections in LFR further delivers important theoretical insights. For instance, it is shown that the PCE of rational parameter-dependent linear systems in LFR is equivalent to applying Gaussian quadrature for numerical integration. We further approximate the worst-case performance of uncertain linear systems with respect to quadratic performance metrics. This is achieved by approximately solving the underlying parametric Riccati differential equation after applying a polynomial chaos series expansion. The utility of the proposed probabilistic robustness analysis is demonstrated on the example of an industry-sized autolanding system for an Airbus A330 aircraft. Mean and standard deviation of the stochastic perturbations are quantified efficiently by applying a PCE to a linearization of the system along the nominal approach trajectory. Random uncertainty in the aerodynamic coefficients and mass parameters are considered, as well as atmospheric turbulence and static wind shear. The approximate worst-case analysis is compared with Monte Carlo simulations of the complete nonlinear model. The methods proposed throughout the thesis rapidly provide analysis results in good agreement with the Monte Carlo benchmark, at reduced computational cost

Alternatives for jet engine control

Research centered on basic topics in the modeling and feedback control of nonlinear dynamical systems is reported. Of special interest were the following topics: (1) the role of series descriptions, especially insofar as they relate to questions of scheduling, in the control of gas turbine engines; (2) the use of algebraic tensor theory as a technique for parameterizing such descriptions; (3) the relationship between tensor methodology and other parts of the nonlinear literature; (4) the improvement of interactive methods for parameter selection within a tensor viewpoint; and (5) study of feedback gain representation as a counterpart to these modeling and parameterization ideas

Survey of Optimal Control and Model Predictive Control with State Estimation and a Real Time Application

The optimal control and its limited version namely the model predictive control represent one of the most important nonlinear control alternatives nowadays. The success of them are also proven in many practical applications. These can provide for several industrial applications the optimal trajectory calculation as well as calculation of the real-time control signal. One successful version of this is Generalized Predictive Control (GPC). A big advantage of these control algorithms is that they solutions are able to take into account the limitations of the inputs, and the states. In some cases, it is important to know the mathematical model chosen and the complete state information. Otherwise, the model can be estimated during the operation. Our study shows through the control of the cathode heating of a high-power electron beam device the self-tuning adaptive control thus constructed. Using a suitable dynamic model and an extended Kalman estimator, we determine the estimated temperature of the two cathodes during operation and the saturation electron current, which ensures the maximum cathode life. The practical application was tested on a CTW 5/60 type electron gun

Guidance and control using model predictive control for low altitude real-time terrain following flight

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (p. 123-125).This thesis presents the design and implementation of a model predictive control based trajectory optimization method for Nap-of-the-Earth (NOE) flight. A NOE trajectory reference is generated over a subspace of the terrain. It is then inserted into the cost function and the resulting trajectory tracking error term is weighted for more precise longitudinal tracking than lateral tracking through the introduction of the TF/TA ratio. The TF/TA ratio, control effort penalties and MPC prediction horizon are tuned for this application via simulation and eigenvalue analysis for stability and performance. Steps are taken to reduce complexity in the optimization problem including perturbational linearization in the prediction model generation and the use of control basis functions which are analyzed for their trade-off between approximation of the optimal cost/solution and reduction of the optimization complexity. Obstacle avoidance including preclusion of ground collision is accomplished through the establishment of hard state constraints. These state constraints create a 'safe envelope' within which the optimal trajectory can be found. Results over a variety of sample terrains are provided to investigate the sensitivity of tracking performance to nominal velocities. The mission objective of low altitude and high speed was met satisfactorily without terrain or obstacle collision, however, methods to preclude or deal with infeasibility must be investigated as terrain severity (measured by commanded flight path angle) is increased past 30 degrees or speed is increased to and past 30 knots.by Tiffany Rae Lapp.S.M

An indirect adaptive neuro-fuzzy speed control of induction motors

This paper presents an indirect adaptive system based on neuro-fuzzy approximators for the speed control of induction motors. The uncertainty including parametric variations, the external load disturbance and unmodeled dynamics is estimated and compensated by designing neuro-fuzzy systems. The contribution of this paper is presenting a stability analysis for neuro-fuzzy speed control of induction motors. The online training of the neuro-fuzzy systems is based on the Lyapunov stability analysis and the reconstruction errors of the neuro-fuzzy systems are compensated in order to guarantee the asymptotic convergence of the speed tracking error. Moreover, to improve the control system performance and reduce the chattering, a PI structure is used to produce the input of the neuro-fuzzy systems. Finally, simulation results verify high performance characteristics and robustness of the proposed control system against plant parameter variation, external load and input voltage disturbance

Path controller implementation for airborne wind energy systems

The implementation of a path controller to a two-line kite model is presented. Within the first chapter, an introduction to Airborne Wind Energy systems and the discussion of some typical control methods can be found. The following chapter deals with the mathematical model of a two line kite. This model considers a kite-surf size kite that can be controlled via two equal tethers. Some thoughts and explanations on the model are included. Thereafter, an open loop control law capable of allowing figure of eight trajectories is defined. Accordingly, an analytical expression for such figure of eight orbits is presented. Some insight on Floquet theory is required in order to properly understand the physics behind periodic orbits. A general purpose predictor-corrector algorithm for periodic orbit propagation determines a set of feasible initial conditions that yield a periodic orbit for a given control law. By means of this tool, it is possible to obtain a periodic orbit applying the control law that has been previously defined. A discussion on such orbit is included, together with its stability analysis. At this point, it is of interest to perform a parametric analysis with the aim of understanding how the stability and the trajectory respond to variations in the control law. Finally the path controller scheme is presented in the form of an optimal control problem. The latter selection was triggered by the failure in implementing a proportional-derivative runtime controller. The results of the project are a deep understanding on the kite sensitivity to variation of tether lengths, i.e. their controls, together with a controller capable of determining optimal control laws for any given desired target path.Ingeniería Aeroespacial (Plan 2010

Do muscle synergies reduce the dimensionality of behavior?

The muscle synergy hypothesis is an archetype of the notion of Dimensionality Reduction (DR) occurring in the central nervous system due to modular organisation. Towards validating this hypothesis, it is however important to understand if muscle synergies can reduce the state-space dimensionality while suitably achieving task control. In this paper we present a scheme for investigating this reduction, utilising the temporal muscle synergy formulation. Our approach is based on the observation that constraining the control input to a weighted combination of temporal muscle synergies instead constrains the dynamic behaviour of a system in trajectory-specific manner. We compute this constrained reformulation of system dynamics and then use the method of system balancing for quantifying the DR; we term this approach as Trajectory Specific Dimensionality Analysis (TSDA). We then use this method to investigate the consequence of minimisation of this dimensionality for a given task. These methods are tested in simulation on a linear (tethered mass) and a nonlinear (compliant kinematic chain) system; dimensionality of various reaching trajectories is compared when using idealised temporal synergies. We show that as a consequence of this Minimum Dimensional Control (MDC) model, smooth straight-line Cartesian trajectories with bell-shaped velocity profiles are obtained as the solution to reaching tasks in both of the test systems. We also investigate the effect on dimensionality due to adding via-points to a trajectory. The results indicate that a synergy basis and trajectory-specific DR of motor behaviours results from usage of muscle synergy control. The implications of these results for the synergy hypothesis, optimal motor control, developmental skill acquisition and robotics are then discussed

Deep learning control for digital feedback systems: Improved performance with robustness against parameter change

Training data for a deep learning (DL) neural network (NN) controller are obtained from the input and output signals of a conventional digital controller that is designed to provide the suitable control signal to a specified plant within a feedback digital control system. It is found that if the DL controller is sufficiently deep (four hidden layers), it can outperform the conventional controller in terms of settling time of the system output transient response to a unit-step reference signal. That is, the DL controller introduces a damping effect. Moreover, it does not need to be retrained to operate with a reference signal of different magnitude, or under system parameter change. Such properties make the DL control more attractive for applications that may undergo parameter variation, such as sensor networks. The promising results of robustness against parameter changes are calling for future research in the direction of robust DL control

Analysis and structural design of on-line process optimization systems.

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