Linear Optimization Approach Research Articles

Sensitivity of the deconvolution of ocean transients to environmental mismatch.

The single-channel deconvolution of acoustic transients for source classification purposes can be sensitive to small errors in the computed ocean Green’s functions. These errors arise due to incomplete environmental and source location information. The sensitivity was studied by perturbing the Green’s functions in such a way as to produce improved source estimates from field measurements. A systematic technique to do this was developed using a weighted, linear optimization approach. It was discovered that small changes in the computed Green’s functions could improve the source estimate significantly. It was also determined that the match between the simulations and the measured data is closely connected to the match between the source estimates and the measured source waveform, hence the sensitivity is not just due to deconvolution. This relationship was quantified by using the correlation coefficient. This study is part of an effort to determine the applicability of deterministic deconvolution to the problem of transient classification. [Work supported by ONR under NRL program management.]

A sequential linear optimization approach for controller design

A linear optimization approach with a simple, real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first-order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam, finite element model for the optimal sizing and placement of active/passive structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to the initial conditions of the linear optimization approach is also demonstrated.

Multivariable Direct Adaptive Control of Thermal Mixing Processes

Multivariable direct adaptive control is tested on a nonlinear thermal mixing process and is compared with state space based nonadaptive controllers. The linear quadratic optimal control approach is used to design two nonadaptive controllers: one without integral action (ordinary LQ) and the other with integral action (LQI). The operating point is changed over a wide region in the experiment. The adaptive controller is verified to perform most consistently under the tested conditions.

Controller Design for Kinetic Control Systems

The current need to improve the performance of robot drive systems focusses attention upon controller design for kinetic control systems which are characterised by high compliance.The paper describes a linear optimal control approach which is supported by experiments on a laboratory rig.Optimal state feedback elements are derived on the basis of a non-dimensionalised, reduced model. With the feedback elements expressed as an algebraic function of one of its members, a novel form of root locus offers a design methodology which combines the elegance of optimal control with the practical convenience of the classical approach.

Pitch control system for large-scale wind turbines

The purpose of this analysis is to study the design of a pitching blade segment control system for the NASA-DOE MOD 0 wind turbine to alleviate some of the problems associated with shear, tower shadow, and gravity phenomena, such as shortened lifetime and noise generation. The classical linear quadratic Gaussian optimal regulator approach is used in the control formulation. A quasisteady aerodynamic analysis incorporating wind shear and tower shadow is utilized. An equivalent hinge model describes the turbine structural dynamics. The study shows that the proposed control system can provide significant vibration and noise reduction as well as a cleaner power signal, better gust response, and increased annual energy output.

A Successive Linear Optimization Approach to the Dynamic Traffic Assignment Problem

A dynamic model for the optimal control of traffic flow over a network is considered. The model, which treats congestion explicitly in the flow equations, gives rise to nonlinear, nonconvex mathematical programming problems. It has been shown for a piecewise linear version of this model that a global optimum is contained in the set of optimal solutions of a certain linear program. This paper presents a sufficient condition for optimality which implies that a global optimum can be obtained by successively optimizing at most N + 1 objective functions for the linear program, where N is the number of time periods in the planning horizon. Computational results are reported to indicate the efficiency of this approach.

Digital Controllers for VTOL Aircraft

Using linear-optimal estimation and control techniques, digitaladaptive daptive control laws have been designed for a tandem-rocopteror heliopter which is equipped for fully automatic flight in terminal area operations. Two distinct discrete-time control laws are designed to interface with velocity-command and attitude-command guidance logic, and each incorporates proportional-integral compensation for nonzero-set-point regulation, as well as reduced-order Kalman filters for sensor blending and noise rejection. Adaptation to flight condition is achieved with a novel gain-scheduling method based on correlation and regression analysis. The linear-optimal design approach is found to be a valuable tool in the development of practical multivariable control laws for vehicles which evidence significant coupling and insufficient natural stability.

On Solving Nonlinear Equations with a One-Parameter Operator Imbedding

One parameter operator imbedding to modify Newton method for solution of nonlinear equations