Andrew Packard

Anti-windup controller design using linear parameter-varying control methods

In this paper, we seek to provide a systematic anti-windup control synthesis approach for systems with actuator saturation within a linear parameter-varying (LPV) design framework. The closed-loop induced L2 gain control problem is considered. Different from conventional two-step anti-windup design approaches, the proposed scheme directly utilizes saturation indicator parameters to schedule accordingly the parameter-varying controller. Hence, the synthesis conditions are formulated in terms of linear matrix inequalities (LMIs) that can be solved very efficiently. The resulting gain-scheduled controller is non-linear in general and would lead to graceful performance degradation in the presence of actuator saturation non-linearities and linear performance recovery. An aircraft longitudinal dynamics control problem with two input saturation non-linearities is used to demonstrate the effectiveness of the proposed LPV anti-windup scheme.

Control Applications of Sum of Squares Programming

We consider nonlinear systems with polynomial vector fields and pose two classes of system theoretic problems that may be solved by sum of squares programming. The first is disturbance analysis using three different norms to bound the reachable set. The second is the synthesis of a polynomial state feedback controller to enlarge the provable region of attraction. We also outline a variant of the state feedback synthesis for handling systems with input saturation. Both classes of problems are demonstrated using two-state nonlinear systems.

Assessment of Aircraft Flight Controllers Using Nonlinear Robustness Analysis Techniques

The current practice to validate flight control laws relies on applying linear analysis tools to assess the closed loop stability and performance characteristics about many trim conditions. Nonlinear simulations are used to provide further confidence in the linear analyses and also to uncover dynamic characteristics, e.g. limit cycles, which are not revealed by the linear analysis. This chapter reviews nonlinear analysis techniques which can be applied to systems described by polynomial dynamic equations. The proposed approach is to approximate the aircraft dynamics using polynomial models. Nonlinear analyses can then be solved using sum-of-squares optimization techniques. The applicability of these methods is demonstrated with nonlinear analyses of an F/A-18 aircraft and NASA’s Generic Transport Model aircraft. These nonlinear analysis techniques can fill the gap between linear analysis and nonlinear simulations and hence used to provide additional confidence in the flight control law performance.

Uncertain Model Set Calculation from Frequency Domain Data

Uncertainty models play a central role in the robust control framework. The uncertainty models and their structure determine the design trade off between performance and robustness of the closed-loop system. Therefore, given a nominal multivariable model of the system, a set of multivariable frequency response measurements, and model structure, it is desirable to generate a correspondingmodel set which tightly over bounds the given data.We show that computation of themodel set for a given structure, which is consistent with the data, can be formulated as a linear matrix inequality feasibility problem. Formulas are derived which allow comparison between model structures to assess the relative size of the each model set. The proposed algorithms are applied to the lateral-directional axis of a radio-controlled aircraft developed by NASA Langley researchers.

Control system analysis in nonlinear flight regimes

Coupling of the Reynolds-averaged Navier-Stokes equations, rigid-body dynamics, and an optimal state feedback control law is demonstrated with a twodimensional, two degree-of-freedom airfoil case. The application problem controls the altitude of an airfoil in subsonic flow with a magnitude and rate-limited applied couple. The applied pitch couple is computed using feedback of both attitude and altitude, vertical and angular velocities and integrated altitude error. Comparison of the trajectories showed a longer settling time and slight overshoot for the nonlinear simulation when compared to a linear plant model.

Tracking transience: a method for dynamic monitoring of biological events in Arabidopsis thaliana biosensors

AbstractMain conclusionThe activation and level of expression of an endogenous, stress-responsive biosensor (bioreporter) can be visualized in real-time and non-destructively using highly accessible equipment (fluorometer). Biosensor output can be linked to computer-controlled systems to enable feedback-based control of a greenhouse environment. Today’s agriculture requires an ability to precisely and rapidly assess the physiological stress status of plants in order to optimize crop yield. Here we describe the implementation and utility of a detection system based on a simple fluorometer design for real-time, continuous, and non-destructive monitoring of a genetically engineered biosensor plant. We report the responses to heat stress of Arabidopsis thaliana plants expressing a Yellow Fluorescent Protein bioreporter under the control of the DREB2A temperature-sensing promoter. Use of this bioreporter provides the ability to identify transient and steady-state behavior of gene activation in response to stress, and serves as an interface for novel experimental protocols. Models identified through such experiments inform the development of computer-based feedback control systems for the greenhouse environment, based on in situ monitoring of mature plants. More broadly, the work here provides a basis for informing biologists and engineers about the kinetics of bioreporter constructs, and also about ways in which other fluorescent protein constructs could be integrated into automated control systems.

Consistent Chemical Mechanism from Collaborative Data Processing

Numerical tool of Process Informatics Model (PrIMe) is mathematically rigorous and numerically efficient approach for analysis and optimization of chemical systems. It handles heterogeneous data and is scalable to a large number of parameters. The Boundto-Bound Data Collaboration module of the automated data-centric infrastructure of PrIMe was used for the systematic uncertainty and data consistency analyses of the H2/CO reaction model (73/17) and 94 experimental targets (ignition delay times). The empirical rule for evaluation of the shock tube experimental data is proposed. The initial results demonstrate clear benefits of the PrIMe methods for an evaluation of the kinetic data quality and data consistency and for developing predictive kinetic models.