Optimization of contoured hypersonic scramjet inlets with a least-squares parabolized Navier-Stokes procedure

A new optimization procedure, in which a parabolized Navier-Stokes solver is coupled with a non-linear least-squares optimization algorithm, is applied to the design of a Mach 14, laminar two-dimensional hypersonic subscale flight inlet with an internal contraction ratio of 15:1 and a length-to-throat half-height ratio of 150:1. An automated numerical search of multiple geometric wall contours, which are defined by polynomial splines, results in an optimal geometry that yields the maximum total-pressure recovery for the compression process. Optimal inlet geometry is obtained for both inviscid and viscous flows, with the assumption that the gas is either calorically or thermally perfect. The analysis with a calorically perfect gas results in an optimized inviscid inlet design that is defined by two cubic splines and yields a mass-weighted total-pressure recovery of 0.787, which is a 23% improvement compared with the optimized shock-canceled two-ramp inlet design. Similarly, the design procedure obtains the optimized contour for a viscous calorically perfect gas to yield a mass-weighted total-pressure recovery value of 0.749. Additionally, an optimized contour for a viscous thermally perfect gas is obtained to yield a mass-weighted total-pressure recovery value of 0.768. The design methodology incorporates both complex fluid dynamic physics and optimal search techniques without an excessive compromise of computational speed; hence, this methodology is a practical technique that is applicable to optimal inlet design procedures.     

Optimal operation of thermal regenerators

The thermally most efficient operation of a thermal regenerator, a particular type of heat exchanger, is analyzed through the minimum principle for distributed parameter systems and Laplace transform techniques. It is found that for optimal operation the gas inlet temperature during the heating phase should equal its maximal allowable value, and that the optimal gas flow rate during the heating phase is constant.     

Optimal motion control for a system of two bodies on a straight line

The optimal control problem for motions of a system of two rigid bodies on an inclined straight line in a plane that are periodic in velocity is solved. The external body (frame) moves on a plane under the action of a force from the inner body in the course of its motions relative to the frame under dry friction between the frame and plane. The acceleration of the inner body relative to the outer one is the control whose absolute value is bounded. An optimal control that maximizes the average velocity of the system motion for a given period is found. It is shown that optimal relative acceleration of the inner body has three intervals of constancy on this period, and the outer body is in the state of rest on a part of the period (in the case of horizontal straight line, it is in a state of rest on half a period), and during the rest of the period, it moves in the desired direction and never performs a reversion. It is established that, for the found control law and under an additional constraint on the amplitude of oscillations of the inner body, it is possible to make the motion velocity of the system arbitrarily large under arbitrarily large accelerations of the inner body and an under arbitrarily large frequency of its oscillations simultaneously.     

Optimal rotation deceleration of a dynamically asymmetric body in a resistant medium

A minimum-time problem on deceleration of rotation of a free body is studied. The body is subject to a retarding torque of viscous friction. The body is assumed to be dynamically asymmetric. An optimal control law for deceleration of rotation of the body is synthesized, and the corresponding time and phase trajectories are determined.     

Optimal deceleration of rotation of a dynamically symmetric body with a cavity filled with viscous liquid in a resistive medium

The problem of time-optimal deceleration of rotation of a free solid body is studied. It is assumed that the body contains a spherical cavity filled with highly viscous liquid. Low decelerating moment of viscous friction forces also acts on the solid body. It is assumed that the body is dynamically symmetric. The optimal control law for deceleration of rotation of the carrier solid body in the form of synthesis, the operation time, and the phase trajectories are determined.     

Motion control of a rotor with a cavity with a viscous fluid

A formulation and solution procedure of optimal control problems for perturbed relative uniform motion of a body with a cavity filled with a viscous incompressible fluid are proposed. In this paper, the case with a cylinder is considered; however, this approach is basically true for the a cavity of an arbitrary form. The formula for the angular velocity of perturbed motion depending on an external perturbing element is devised. After that, we have a possibility to set different optimal control problems and apply the formalism elaborated in the optimal control theory. Two illustrated problems are given.     

Optimal deceleration of rotations of an asymmetric body with a cavity filled with viscous fluid in a resistive medium

A minimum-time problem on deceleration of rotations of a free rigid body is studied. It is assumed that the body contains a spherical cavity filled with highly viscous fluid. The body is subjected to a retarding torque of viscous friction. It is assumed that the body is dynamically asymmetric. An optimal control law for the deceleration of rotations of the body is synthesized, and the corresponding time and phase trajectories are determined.     

Optimal rotation deceleration of a dynamically symmetric body with movable mass in a resistant medium

A minimum-time problem on deceleration of rotation of a free rigid body is studied. The body is assumed to contain a viscous-elastic element, which is modeled as a movable point mass attached to the body via a damper. In addition, the body is subjected to a retarding torque generated by linear medium resistance forces. In an undeformed state, the body is assumed to be dynamically symmetric, with the mass being located on the symmetry axis. An optimal control law for deceleration of rotation of the body is synthesized, and the corresponding time and phase trajectories are determined.     

A control for a rotor with a cavity containing an ideal liquid, II

For a motion perturbed with respect to uniform rotation of a body with a cavity containing an ideal liquid, two problems of optimal control with terminal functionals are considered. The model with discontinuous optimal control is studied. Numerical solutions for the problem with constraints on control of the type of inequalities are obtained.     

Brachistochrone for a rigid body sliding down a curve

Extremality conditions in the brachistochrone problem for a perfectly rigid body sliding without friction down an unknown (to be determined) curve in a vertical plane are found. In this case, the body has to track the tangent to the trajectory. According to the principle of constraint release, the reaction of the support creates a torque used as control. For dimensionless Appell’s equations with a single similarity coefficient, the standard problem of the fastest descent from a given initial point to a given terminal point assuming that the initial velocity is zero is formulated. The Okhotsimskii-Pontryagin method is used to analyze the differential of the objective function. Necessary optimality conditions are found, and a formula for the optimal control that does not involve adjoint variables is derived from them. Properties of the optimal trajectories are investigated analytically both in the general case and for the limiting (zero and infinite) values of the similarity coefficient. It is found that cycloid-shaped brachistochrones occur as the similarity coefficient tends to infinity. For some values of the similarity coefficient, numerical results are presented that demonstrate the shape of the corresponding brachistochrones and the optimal time of motion. The results are compared with those obtained by solving the classical brachistochrone problem.     

Optimal Control of the Dynamic Viscoelastic Stress-Strain State of a Composite Body

New optimal control problems for the dynamic viscoelastic stress-strain state of a composite body with quadratic cost functionals are considered. Existence theorems for unique optimal controls are proved for all the cases considered. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 73–92, September–October 2005.     

Optimal control of dual-mass system motion in a medium with a piecewise linear resistance

Linear motion of a mechanical system consisting of two bodies??a container and an inner body??is considered. The container is located in an external medium with resistance, and the inner body moves inside the container without the interaction with the external medium. Under certain conditions, the periodic motion of the inner body causes the system as a whole to move. The external medium acts on the container with a force that is proportional to its velocity with a resistance coefficient depending on the motion direction. Only the motions of the inner body with continuous relative velocity are studied. The optimal periodic motion of the inner body corresponding to the greatest period-averaged velocity of the system as a whole is constructed and analyzed.     

Optimal Control of Rigid Body’s Rotation Movement with a Combined Quality Criterion

Journal of Computer and Systems Sciences International - The results of a numerical and analytical solution of the optimal control problem for a rigid body rotation with a combined criterion of the...     

Temperature control of the inertial-grade floated rate-integrating gyroscope

The performance of the inertial-grade floated rate-integrating gyroscope is critically dependent on the instrument surface temperature distribution. During operation, the instrument is degraded by distributed surface heat-flux disturbances, and it is desired to control the surface temperature distribution in a closed-loop feedback configuration such that the instrument degradation is minimized. This is achieved via optimal control theory, where a distributed feedback controller is determined such that the square of thermally induced drift rate is minimized. The structure of the resulting controller is examined, and various configurations for implementation are suggested.     

Synthesis of a high-speed tracked vehicle suspension system--Part I: Problem statement, suspension structure, and decomposition

This two-part paper is concerned with the problem of synthesizing a high-speed vehicle suspension system. Using a new decomposition technique, it is shown that there exists an optimal structure which a high-speed suspension must have in order to fulfill the requirements of vehicle body vibration isolation within given displacement constraints, external force cancellation, vehicle body tilting and guideway tracking while maintaining primary gaps or contact forces within given limits, and assuring maintenance of nominal mass and inertia parameters of the vehicle body. The suspension structure derived in this part is such that the incompatibility of vibration isolation and guideway tracking under the influence of external forces which is present for all suspensions synthesized heretofore-whether optimal control approaches have been used or not-has been removed. The new suspension structure features three independent parts: the nonlinear and time-varying preload-and-mass control operating on external forces and vehicle body accelerations, the linear time-invariant tracking control operating on the means of certain vehicle states, and the linear time-invariant vibrating control which operates on the difference between the actual vehicle state vector and its mean.     

理想物系内部热耦合精馏塔操作费用的估计与优化

给出了理想物系内部热耦合精馏塔操作费用和费用节省的估计方法.首次建立了过程操作费用的优化数学模型,并以苯-甲苯物系作为实例进行了操作费用节省的优化研究.研究结果揭示出理想物系内部热耦合精馏塔巨大的操作费用节省潜力,同时得到了最大操作费用节省目标下的过程最优操作条件.     

Investigation of a method for the three-dimensional rigid body dynamics inverse problem

The three-dimensional rigid body dynamics inverse problem is cast as a discrete optimal control problem and solved using dynamic programming. The optimal control problem uses a forward dynamic model to provide estimates of unknown forces while matching noisy measurement histories. An L curve analysis is used to objectively select the amount of smoothing by trading off the magnitude of the estimated unknown forces with the fit to the noisy measurements. The forward dynamic model is derived using finite-element methodology and accounts for the inertia and mass properties of rigid bodies with the use of natural coordinates. The advantages of this forward model are that the large displacements’ nonlinearities can be routinely represented in the inverse problem and that it also allows the use of an exact energy conserving method to numerically integrate the equations of motion. A numerical example of a large displacement three body model is included to demonstrate the performance of the methodology.     

Analytical solution of the of optimal slew problem of a spherically symmetric spacecraft in the class of conical motions

The of energy optimal slew problem for of a spacecraft considered as a solid body with a spherical mass distribution is studied in a quaternion formulation without restrictions on the control function. For this problem, a new analytical solution in the class of conical motions is obtained. Numerical examples are discussed.     

Fast, curvature-based prediction of rolling forces for porous media based on a series of detailed simulations

Using thermal spraying various surface coatings consisting of different material compositions can be manufactured. Besides different solid phases the resulting coating microstructure often contains a non-negligible amount of pores. In this context a roller burnishing process with a hydrostatic ball-point-tool is examined to compact the thermally sprayed coating, thereby reducing porosity. The rolling process is performed by a robot on free-formed workpieces. A simulation concept for the prediction of forces in a robot-guided roller burnishing process based on a series of detailed ABAQUS simulations is presented. It is shown that, based on these test configurations, the process forces can be calculated much faster and with sufficient precision. Thereby an optimal rolling path, which requires the least amount of normal force to be applied, can be determined efficiently leading to the decision whether a specific robot is equipped to handle the path. Furthermore, the described approach may be used as a pattern to apply similar methods to other engineering problems where accurate simulative solutions exist, but cannot be applied to problems of realistic size due to their expenditure of time.     

A control for a rotor with a cavity containing an ideal liquid. I

The Cauchy problem in the linear statement is considered for the motion of a body with a cavity containing an ideal liquid. The motion is perturbed relative to uniform rotation. Note that there are no constraints imposed on the cavity shape and the nature of the perturbed motion. The problem of the joint solution of hydrodynamical and mechanical equations is reduced to solving a certain eigenvalue problem depending only on the cavity geometry and to the subsequent integration of a system of differential equations. Based on the equations obtained, the stability of steady-state rotation of a body with liquid is investigated. For the system considered, the problem of optimal control with a terminal functional is posed. Analytical solutions are presented for the case when there are no constraints on the control.