THE SOLUTION FOR THE GENERALIZED RICCATIALGEBRAIC EQUATIONS OF LINEAR EQUALITY CONSTRAINT SYSTEM

Based on the dynamic equation, the performance functional and the system constraint equation of time-invariant discrete LQ control problem, the generalized Riccati equations of linear equality constraint system are obtained according to the minimum principle, then a deep discussion about the above equations is given, and finally numerical example is shown in this paper.

Improved Quality Prediction Model for Multistage Machining Process Based on Geometric Constraint Equation

Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.

Lie symmetry and its generation of conserved quantity of Appell equation in a dynamical system of the relative motion with Chetaev-type nonholonomic constraints

Lie symmetry and conserved quantity deduced from Lie symmetry of Appell equations in a dynamical system of relative motion with Chetaev-type nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and criterion of Lie symmetry,the condition and the expression of generalized Hojman conserved quantity deduced from Lie symmetry for the system are obtained.The condition and the expression of Hojman conserved quantity deduced from special Lie symmetry for the system under invariable time are further obtained.An example is given to illustrate the application of the results.

SMALLEST g-SUPERSOLUTION WITH CONSTRAINT

In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift coefficient in the different method from the one with Lipschitz condition.Then by considering (ξ,g) as a parameter of BSDE,and ( ξ α,g α) as a class of parameters for BSDE,where α belongs to a set A,for every α ∈A there exists a pair of solution { Y α,Z α } for the BSDE,the properties of sup α ∈A{ Y α } which is also a solution for some BSDE is studied.This result may be used to discuss optimal problems with recursive utility.

Design and Structural Analysis of Flexible Wearable Chair Using Finite Element Method

The flexible wearable chair is like a light weight mobile exoskeleton that allows people to sit any-where in any working position. The traditional chair is difficult to move to different working locations due to its large size, heavy weight (~5 - 7 kg) and rigid structure and thus, they are inappropriate for workplaces where enough space is not available. Flexible wearable chair has a gross weight of 3 kg as it utilizes light-weight aluminium alloy members. Unlike the traditional chair, it consists of kinematic pairs which enable taking halts between continuous movements at any working position and thus, it is capable of reducing the risk of the physical musculoskeletal disorder substantially among workers. The objective of this paper is to focus on the mechanical design and finite element analysis (FEA) of the mechanism using ANSYS® software. In the present work, all the parts of the mechanism are designed under static load condition. The results of the analysis indicate that flexible wearable chair satisfies equilibrium and stability criterion and is capable of reducing fatigue during working in an assembly line/factory.

STABLE PROGRAMMED MANIFOLD SOLVER FOR VIRTUAL PROTOTYPING MOTION SIMULATION

Based on constructing programmed constraint and constraint perturbation equation, a kinematics and dynamics numerical simulation model is established for virtual mechanism, in which the difference scheme guarantee precision in simulation procedure and its mtmerical solutions satisfy programmed manifold stability. A crank-piston mechanism in a car engine, a steering mechanism and a suspension mechanism are simulated in a virtual environment, then comparing the simulation results with those obtained in ADAMS under the same circumstances proved the solver valid.

Dynamics of a spacecraft with large flexible appendage constrained by multi-strut passive damper

This paper is concerned with the dynamics of a spacecraft with multi-strut passive damper for large flexible appendage.The damper platform is connected to the spacecraft by a spheric hinge,multiple damping struts and a rigid strut.The damping struts provide damping forces while the rigid strut produces a motion constraint of the multibody system.The exact nonlinear dynamical equations in reducedorder form are firstly derived by using Kane＇s equation in matrix form.Based on the assumptions of small velocity and small displacement,the nonlinear equations are reduced to a set of linear second-order differential equations in terms of independent generalized displacements with constant stiffness matrix and damping matrix related to the damping strut parameters.Numerical simulation results demonstrate the damping effectiveness of the damper for both the motion of the spacecraft and the vibration of the flexible appendage,and verify the accuracy of the linear equations against the exact nonlinear ones.

TIME PRECISE INTEGRATION METHOD FOR CONSTRAINED NONLINEAR CONTROL SYSTEM

For the constrained nonlinear optimal control problem, by taking the first term of Taylor series, the dynamic equation is linearized. Thus by, introducing into the dual variable (Lagrange multiplier vector), the dynamic equation can be transformed into Hamilton system from Lagrange system on the basis of the original variable. Under the whole state, the problem discussed can be described from a new view, and the equation can be precisely solved by, the time precise integration method established in linear dynamic system. A numerical example shows the effectiveness of the method.

The Integration Methods of Vacco Dynamics Equation of Nonlinear Nonholonomic

This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods the single-componentmethods and the field method are used to integrate the dynamics equations of the corresponding holonomic system respectively.And considering the restriction of nonholonomic construint to the initial conditions the solutions of Vacco dynamics cquations of nonlinear nonholonomic system are obtained.

Solving Topological and Geometrical Constraints in Bridge Feature Model

The capacity that computer can solve more complex design problem was gradually increased. Bridge designs need a breakthrough in the current development limitations, and then become more intelligent and integrated. This paper proposes a new parametric and feature-based computer aided design (CAD) models which can represent families of bridge objects, includes knowledge representation, three-dimensional geometric topology relationships. The realization of a family member is found by solving first the geometric constraints, and then the topological constraints. From the geometric solution, constraint equations are constructed. Topology solution is developed by feature dependencies graph between bridge objects. Finally, feature parameters are proposed to drive bridge design with feature parameters. Results from our implementation show that the method can help to facilitate bridge design.

Influence of shock attenuation on tailored operation in free piston shock tunnels

The free piston shock tunnel is a type of shock tunnel with high performance. For this type of tunnel, the influence mechanism of shock wave attenuation on tailored operation is explored by numerical simulation and theoretical analysis. By introducing the normalized velocity, the simple constraint equation for shock wave under the tailored operation is deduced. Moreover, the real gas effect is also taken into account in this equation. Based on the equation, the tailored operation of shock tunnels can be predicted with very few calculations. The present study shows that the change rate of the thermodynamic state of the gas behind the shock wave is inconsistent with the attenuation rate of the shock wave, which is the fundamental reason why the wind tunnel achieves tailored operation at a lower Mach number of shock waves. This lower Mach number of shock waves differs from the corresponding ideal value by a factor, which is about the square root of shock attenuation rate.

A Symmetric Inertial Alternating Direction Method of Multipliers for Elliptic Equation Constrained Optimization Problem

A new algorithm,called symmetric inertial alternating direction method of multipliers(SIADMM),is designed for separable convex optimization problems with linear constraints in this paper.The convergence rate of the SIADMM is proved to be O(1/√k).Two kinds of elliptic equation constrained optimization problems,the un-constrained cases as well as the box-constrained cases of the distributed control and the Robin boundary control,are analyzed theoretically and solved numerically.First,the existence and uniqueness of the solutions to these problems are proved.Second,these continuous optimization problems are transformed into discrete optimization problems by thefinite element method,and then the discrete optimization problems are solved by the proposed SIADMM.Numerical experiments with different problems are investigated to demonstrate the efficiency of the SIADMM.And the numerical per-formance of the SIADMM is better than the performance of the ADMM.Moreover,the numerical results show that the convergence rate of the SIADMM tends to be faster than O(1/√k)in calculation process.

Trajectory-tracking controller for vehicles on inclined road based onUdwadia–Kalaba equation

Vehicle lateral control is an important subtask of vehicle autonomous driving.There are many external disturbances that will affect the lateral control accuracy of the vehicle,and the inclination of the road is one of the most important ones.The inclined road will lead to additional lateral forces on the vehicle and will also change the magnitude of support force on the vehicle.The change of lateral force and support force will ultimately affect the trajectory tracking performance of the vehicle.Most of the current trajectory tracking methods only consider the trajectory tracking problem on the plane.If the influence of the road surface is considered in the design of the vehicle's trajectory tracking controller,the dynamic response and the tracking accuracy of the vehicle can be improved.This paper proposes a method based on Udwadia–Kalaba equation to calculate the normal and lateral force on a vehicle tracking a desired trajectory on an inclined road.Further,a trajectory tracking controller that considers the road inclination is designed.Finally,the simulation of trajectory tracking performance with an inclination angle is carried out to verify the effectiveness of the proposed controller.