Stochastic disturbance rejection in model predictive control by randomized algorithms

In this paper we consider model predictive control with stochastic disturbances and input constraints. We present an algorithm which can solve this problem approximately but with arbitrary high accuracy. The optimization at each time step is a closed loop optimization and therefore takes into account the effect of disturbances over the horizon in the optimization. Via an example it is shown that this gives a clear improvement of performance although at the expense of a large computational effort

Optimal control of linear, stochastic systems with state and input constraints

In this paper we extend the work presented in our previous papers (2001) where we considered optimal control of a linear, discrete time system subject to input constraints and stochastic disturbances. Here we basically look at the same problem but we additionally consider state constraints. We discuss several approaches for incorporating state constraints in a stochastic optimal control problem. We consider in particular a soft-constraint on the state constraints where constraint violation is punished by a hefty penalty in the cost function. Because of the stochastic nature of the problem, the penalty on the state constraint violation can not be made arbitrary high. We derive a condition on the growth of the state violation cost that has to be satisfied for the optimization problem to be solvable. This condition gives a link between the problem that we consider and the well known $H_\infty$ control problem

User's manual for XTRAN2L (version 1.2): A program for solving the general-frequency unsteady transonic small-disturbance equation

The development, use and operation of the XTRAN2L program that solves the two dimensional unsteady transonic small disturbance potential equation are described. The XTRAN2L program is used to calculate steady and unsteady transonic flow fields about airfoils and is capable of performing self contained transonic flutter calculations. Operation of the XTRAN2L code is described, and tables defining all input variables, including default values, are presented. Sample cases that use various program options are shown to illustrate operation of XTRAN2L. Computer listings containing input and selected output are included as an aid to the user

Aeroelastic analysis of wings using the Euler equations with a deforming mesh

Modifications to the CFL3D three dimensional unsteady Euler/Navier-Stokes code for the aeroelastic analysis of wings are described. The modifications involve including a deforming mesh capability which can move the mesh to continuously conform to the instantaneous shape of the aeroelastically deforming wing, and including the structural equations of motion for their simultaneous time-integration with the governing flow equations. Calculations were performed using the Euler equations to verify the modifications to the code and as a first step toward aeroelastic analysis using the Navier-Stokes equations. Results are presented for the NACA 0012 airfoil and a 45 deg sweptback wing to demonstrate applications of CFL3D for generalized force computations and aeroelastic analysis. Comparisons are made with published Euler results for the NACA 0012 airfoil and with experimental flutter data for the 45 deg sweptback wing to assess the accuracy of the present capability. These comparisons show good agreement and, thus, the CFL3D code may be used with confidence for aeroelastic analysis of wings

Feedback model predictive control by randomized algorithms

In this paper we present a further development of an algorithm for stochastic disturbance rejection in model predictive control with input constraints based on randomized algorithms. The algorithm presented in our work can solve the problem of stochastic disturbance rejection approximately but with high accuracy at the expense of a large computational effort. The algorithm described here uses a predefined controller structure in the optimization and it is significantly less computationally demanding but with a price of some performance loss. Via an example it is shown that the algorithm gives considerable reduction in the computational time and that performance loss is rather small compared to the algorithm in our earlier work

Steady and unsteady transonic small disturbance analysis of realistic aircraft configurations

A transonic unsteady aerodynamic and aeroelastic code called CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) was developed for application to realistic aircraft configurations. It permits the calculation of steady and unsteady flows about complete aircraft configurations for aeroelastic analysis of the flutter critical transonic speed range. The CAP-TSD code uses a time accurate approximate factorization algorithm for solution of the unsteady transonic small disturbance potential equation. An overview is given of the CAP-TSD code development effort along with recent algorithm modifications which are listed and discussed. Calculations are presented for several configurations including the General Dynamics 1/9th scale F-16C aircraft model to evaluate the algorithm and hence the reliability of the CAP-TSD code in general. Calculations are also presented for a flutter analysis of a 45 deg sweptback wing which agree well with the experimental data. Descriptions are presented of the CAP-TSD code and algorithm details along with results and comparisons which demonstrate the stability, accuracy, efficiency, and utility of CAP-TSD

CAP-TSD: A program for unsteady transonic analysis of realistic aircraft configurations

The development of a new transonic code to predict unsteady flows about realistic aircraft configurations are described. An approximate factorization algorithm for solution of the unsteady transonic small disturbance equation is first described. Because of the superior stability characteristics of the AF algorithm, a new transonic aeroelasticity code was developed which is described in some detail. The new code was very easy to modify to include the additional aircraft components, so in a very short period of time the code was developed to treat complete aircraft configurations. Finally, applications are presented which demonstrate many of the geometry capabilities of the new code

Improving CAP-TSD steady pressure solutions through airfoil slope modification

A modification of airfoil section geometry is examined for improvement of the leading edge pressures predicted by the Computational Aeroelasticity Program - Transonic Small Disturbance (CAP-TSD). Results are compared with Eppler solutions to assess improvement. Preliminary results indicate that a fading function modification of section slopes is capable of significant improvements in the pressures near the leading edge computed by CAP-TSD. Application of this modification to airfoil geometry before use in CAP-TSD is shown to reduce the nonphysical pressure peak predicted by the transonic small disturbance solver. A second advantage of the slope modification is the substantial reduction in sensitivity of CAP-TSD steady pressure solutions to the computational mesh

Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics

An unsteady, 3D, implicit upwind Euler/Navier-Stokes algorithm is here used to compute the flutter characteristics of Wing 445.6, the AGARD standard aeroelastic configuration for dynamic response, with a view to the discrepancy between Euler characteristics and experimental data. Attention is given to effects of fluid viscosity, structural damping, and number of structural model nodes. The flutter characteristics of the wing are determined using these unsteady generalized aerodynamic forces in a traditional V-g analysis. The V-g analysis indicates that fluid viscosity has a significant effect on the supersonic flutter boundary for this wing