Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist

Controllability of kinematic control systems on stratified configuration spaces

This paper considers nonlinear kinematic controllability of a class of systems called stratified. Roughly speaking, such stratified systems have a configuration space which can be decomposed into submanifolds upon which the system has different sets of equations of motion. For such systems, considering controllability is difficult because of the discontinuous form of the equations of motion. The main result in this paper is a controllability test, analogous to Chow's theorem, is based upon a construction involving distributions, and the extension thereof to robotic gaits

Motion control - A SMC approach

Motion control involves many diversified control problems of complex nonlinear systems. In this paper we will be addressing the SMC approach for multi-body mechanical systems control. The main feature of the SMC is constraint of the system motion into manifold in system state space. It will be shown that usage of the SMC methods is a natural way of addressing problems in motion control including constrained systems, redundant systems and functionally related systems to name some. The consistent application of the SMC methods leads to natural decomposition of system motion for redundant tasks and allows simple, straight forward dynamical decoupling of the multiple tasks

Identification and analysis of factors affecting thermal shock resistance of ceramic materials in solar receivers

An analysis was conducted of the possible modes of thermal stress failure of brittle ceramics for potential use in point-focussing solar receivers. The pertinent materials properties which control thermal stress resistance were identified for conditions of steady-state and transient heat flow, convective and radiative heat transfer, thermal buckling and thermal fatigue as well as catastrophic crack propagation. Selection rules for materials with optimum thermal stress resistance for a particular thermal environment were identified. Recommendations for materials for particular components were made. The general requirements for a thermal shock testing program quantitatively meaningful for point-focussing solar receivers were outlined. Recommendations for follow-on theoretical analyses were made

Identifying parameters of a broaching design using non-linear optimisation

Broaching is one of the most recognised machining processes that can yield high productivity and high quality when applied properly. One big disadvantage of broaching is that all process parameters, except cutting speed, are built into the broaching tools. Therefore, it is not possible to modify the cutting conditions during the process once the tool is manufactured. Optimal design of broaching tools has a significant impact to increase the productivity and to obtain high quality products. In this paper, an optimisation model for broaching design is presented. The model results in a non-linear non-convex optimisation problem. Analysis of the model structure indicates that the model can be decomposed into smaller problems. The model is applied to a turbine disc broaching problem which is considered as one of the most complex broaching operations