Passive Constraints Research Articles

Theoretical analysis of a non-contact spring with inclined permanent magnets for load-independent resonance frequency

In this paper a non-contact magnetic spring design is presented that uses inclined magnets to produce an adjustable relationship between load force and dynamic stiffness. With appropriate choice of parameters, the spring may either operate with a range of constant natural frequency against variable load forces, or a positive stiffness in one horizontal direction may be achieved in addition to having a positive vertical stiffness. Dynamic simulations are presented to assess the non-linear stability of a planar three degree of freedom version of the system; cross-coupling between horizontal and rotation motion is shown to compromise passive stability, in which case passive constraints or active control must be used to avoid instability. The design is scalable in that using larger magnets increases the load bearing capacity and decreases the natural frequency of the system.

An algorithm for direct identification of passive transfer matrices with positive real fractions via convex programming

AbstractThe paper presents a new algorithm for the identification of a positive real rational transfer matrix of a multi‐input–multi‐output system from frequency domain data samples. It is based on the combination of least‐squares pole identification by the Vector Fitting algorithm and residue identification based on frequency‐independent passivity constraints by convex programming. Such an approach enables the identification of a priori guaranteed passive lumped models, so avoids the passivity check and subsequent (perturbative) passivity enforcement as required by most of the other available algorithms. As a case study, the algorithm is successfully applied to the macro‐modeling of a twisted cable pair, and the results compared with a passive identification performed with an algorithm based on quadratic programming (QPpassive), highlighting the advantages of the proposed formulation. Copyright © 2010 John Wiley & Sons, Ltd.

Passive fuzzy controller design via observer feedback for stochastic Takagi-Sugeno fuzzy models with multiplicative noises

This paper investigates the fuzzy control problem of a class of nonlinear continuous-time stochastic systems with achieving the passivity performance. A model-based observer feedback fuzzy control utilizing the concept of so-called parallel distributed compensation (PDC) is employed to stabilize the class of nonlinear stochastic systems that are represented by the Takagi-Sugeno (T-S) fuzzy models. Based on the Lyapunov criteria, the Linear Matrix Inequality (LMI) technique is used to synthesize the observer feedback fuzzy controller design such that the closed-loop system satisfies stability and passivity constraints, simultaneously. Finally, a numerical example is given to demonstrate the applicability and effectiveness of the proposed design method.

Degenerate problems of optimal control. I

Considered is the practically important and theoretically challenging class of optimal control problems which can be integrated within the common notion of "degenerate problems." The general definition of such problems is given, which arises from the connection between the degeneracy and the presence of hidden passive differential constraints or discrete chains in the problem. This definition is analyzed with the focus on its relation with the classical notion of degeneracy in the variational calculus and the notion of singular and sliding modes well known in the control theory. This paper is the first one in the series of three, which are aimed at presenting a survey of the main facts and applications of the special theory of such problems, which is essentially based on finding and eliminating passive constraints. New results and generalizations are also reported.

C305 記述関数法によるセミアクティブサスペンションのスライディングモード制御(OS7非線形制御理論とその応用2)

This paper proposes a sliding mode controller of semi-active suspension systems. The switching input of the proposed sliding mode controller is designed with the describing function method in order to occur a desired limit cycle of the switching function. As a result, the proposed controller could decrease the number of switching for the passivity constraint of the controllable damper, and could suppress deterioration of the control effect due to the chattering in the high frequency range, such as increase in acceleration of the sprung mass related to the ride comfort. Finally, simulation results show the effectiveness of the proposed controller.

A Penalty Formulation for Dynamics Analysis of Redundant Mechanical Systems

Redundancy in the constraining of mechanical systems achieves more stability and larger load capacity for the system, while in actuation it provides better robustness against singularities and higher maneuverability. Few techniques have been developed with the aim to handle redundancy and singularities in dynamics analysis, and further research is still needed in this area. In this paper, we illustrate the concept of actuating and passive constraints. Then, we expand on the existing penalty techniques by incorporating the concept of actuating and passive constraints to present a penalty formulation that is capable of efficiently handling singularities and redundancy in constraining and actuation and can carry out either forward or inverse dynamics analysis of mechanical systems. As such, the proposed approach is referred to as the actuating-passive constraints penalty approach.

Passive-Set-Position-Modulation Framework for Interactive Robotic Systems

In this paper, we propose a novel framework, passive set-position modulation (PSPM), which enables us to connect a (continuous-time) robot's position to a sequence of slowly updating/sparse (discrete-time) set-position signal via the simple (yet frequently used in practice) spring coupling with damping injection, while enforcing passivity of the closed-loop robotic system. The PSPM modulates the original set-position signal in such a way that the modulated signal is as close to the original signal as possible (i.e., maximum information recovery for better performance), yet only to the extent permissible by the available energy in the system (i.e., passivity constraints). We present its algorithm and theoretically show its passivity and performance. We also show how this PSPM can be applied for two applications, with some experimental results: Internet teleoperation with varying delay and packet loss; and haptics with slow and variable-rate data update.

Constrained optimization of structures with displacement constraints under various loading conditions

Optimization problems often involve constraints and restrictions which must be considered in order to obtain an optimum result and the resultant solution should not deviate from any of the imposed constraints. These constraints and restrictions are imposed either on the design variables or on the algebraic relations between them. Constraints of allowable stress, minimum size and buckling of members in the absence of allowable displacement constraint are the most important factors in optimization of the cross-sectional area of structural elements. When the allowable displacement constraint is included in the problem as a determinant parameter, since the specifications of most of elements affect the displacement rate, the way of imposing and considering this constraint requires special care. In this research the way of simultaneous imposition of multi displacement constraints for optimum design of truss structures in several load cases is described. In this method various constraints for different load cases are divided into active and passive constraints. The mathematical formulation is based on the classical method of Lagrange Multipliers. Overall, this simple method can be employed along with other constraints such as buckling, allowable stress and minimum size of members for imposing the displacement constraint in various load cases.

A Comparative Study of Passivity Enforcement Schemes for Linear Lumped Macromodels

This paper presents a comparative study of several passivity enforcement schemes for linear lumped macromodels. We consider three main classes of algorithms. First class is represented by those methods based on a direct enforcement of positive/bounded real lemma constraints via convex optimization. Second class includes those algorithms that enforce the passivity constraints at discrete frequency samples. These schemes are here formulated as second-order cone programs in order to optimize performance. Finally, we consider algorithms based on Hamiltonian eigenvalue perturbation. These three classes are applied to a significant set of benchmark examples, essentially various kinds of high-speed interconnects and packages, with the aim of comparing their performance in terms of accuracy, efficiency, applicability, and robustness. These examples are specifically selected in order to be critical for one or more algorithms, in terms of excessive accuracy degradation, computational complexity, or even lack of convergence. One important result is that carefully designed weighting schemes may dramatically improve performance for all considered algorithm classes.

Dynamic response of objects with shock-absorbers to seismic loads

The paper outlines a mathematical model describing the vibrations of buildings and engineering structures with general-type passive shock-absorbers, rigid bodies, and ideal constraints. Two modifications of systems with passive shock absorbers are considered assuming constancy of their structure. These systems are studied numerically; the dynamic processes excited in them are compared

Realisable rational function approximations for the equivalent circuit modelling of broadband antennas

The vector fitting (VF) algorithm is applied to the equivalent circuit modelling of an antenna over a broad frequency band. To ensure that the resulting circuit model is realisable, the passivity constraint must be imposed during the modelling process. Three methods are investigated to ensure the passivity, each based on VF: (i) the use of quadratic programming proposed earlier by Gustavsen and Semlyen, (ii) a technique based on constraining a second-order rational function and (iii) a search method using a particle swarm optimisation with constraints. These techniques are evaluated through three sample antennas: a commercial broadband horn, an ultra-wideband planar monopole with a notch-band and an active integrated microstrip antenna. The results are compared in terms of the modelling error against the model order and the computation time required.

OPTIMIZATION OF ELECTRO-CHEMICAL MACHINING PROCESS PARAMETERS USING GENETIC ALGORITHMS

ECM and ECM-based processes (derived and hybrid processes) are one of the most widely used advanced machining processes (AMPs) to make complicated shapes of varying sizes in the products made of electrically conducting but difficult-to-machine materials such as superalloys, Ti-alloys, alloy steel, tool steel, stainless steel, etc. These materials are extensively used in aerospace, automobile, space, nuclear, defense, cutting tools, dies and mold making applications. ECM offers some unique advantages over other conventional and advanced machining processes but its use incurs relatively higher initial investment cost, operating cost, tooling cost, and maintenance cost. Use of optimum ECM process parameters can significantly reduce the ECM operating, tooling, and maintenance cost and will produce components of higher accuracy which is very important in some critical areas such as aerospace, space, defense, nuclear applications. Therefore, choice of optimum process parameters is essential to ensure the most cost-effective, efficient, and economic utilization of ECM process potentials. This paper describes optimization of three most important ECM process parameters namely tool feed rate, electrolyte flow velocity, and applied voltage with an objective to minimize geometrical inaccuracy subjected to temperature, choking, and passivity constraints using real-coded genetic algorithms. Comparison of the obtained optimization results with the results of past work in this direction shows an improvement in terms of geometrical accuracy.

Hybrid model predictive control application towards optimal semi-active suspension

The optimal control problem of a quarter-car semi-active suspension has been studied in the past. Considering that a quarter-car semi-active suspension can either be modelled as a linear system with state dependent constraint on control (of actuator force) input, or a bi-linear system with a control (of variable damping coefficient) saturation, the seemingly simple problem poses several interesting questions and challenges. Does the saturated version of the optimal control law derived from the corresponding un-constrained system, i.e. “clipped-optimal”, remain optimal for the constrained case as suggested in some previous publications? Or should the optimal deviate from the “clipped-optimal” as suggested in other publications? If the optimal control law of the constrained system does deviate from its unconstrained counter-part, how different are they? What is the structure of the optimal control law? Does it retain the linear state feedback form (as the unconstrained case)? In this paper, we attempt to answer some of the above questions by utilizing the recent development in model predictive control (MPC) of hybrid dynamical systems. The constrained quarter-car semi-active suspension is modelled as a switching affine system, where the switching is determined by the activation of passivity constraints, force saturation, and maximum power dissipation limits. Theoretically, over an infinite prediction horizon the MPC controller corresponds to the exact optimal controller. The performance of different finite-horizon hybrid MPC controllers is tested in simulation using mixed-integer quadratic programming. Then, for short-horizon MPC controllers, we derive the explicit optimal control law and show that the optimal control is piecewise affine in state. In the process, we show that for horizon equal to one the explicit MPC control law corresponds to clipped LQR as expected. We also compare the derived optimal control law to various semi-active control laws in the literature including the well-known “clipped-optimal”. We evaluate their corresponding performances for both a deterministic shock input case and a stochastic random disturbances case through simulations.

On the Generation of Large Passive Macromodels for Complex Interconnect Structures

This paper addresses some issues related to the passivity of interconnect macromodels computed from measured or simulated port responses. The generation of such macromodels is usually performed via suitable least squares fitting algorithms. When the number of ports and the dynamic order of the macromodel is large, the inclusion of passivity constraints in the fitting process is cumbersome and results in excessive computational and storage requirements. Therefore, we consider in this work a post-processing approach for passivity enforcement, aimed at the detection and compensation of passivity violations without compromising the model accuracy. Two complementary issues are addressed. First, we consider the enforcement of asymptotic passivity at high frequencies based on the perturbation of the direct coupling term in the transfer matrix. We show how potential problems may arise when off-band poles are present in the model. Second, the enforcement of uniform passivity throughout the entire frequency axis is performed via an iterative perturbation scheme on the purely imaginary eigenvalues of associated Hamiltonian matrices. A special formulation of this spectral perturbation using possibly large but sparse matrices allows the passivity compensation to be performed at a cost which scales only linearly with the order of the system. This formulation involves a restarted Arnoldi iteration combined with a complex frequency hopping algorithm for the selective computation of the imaginary eigenvalues to be perturbed. Some examples of interconnect models are used to illustrate the performance of the proposed techniques.

Generalized Cable Equation Model for Myelinated Nerve Fiber

Herein, the well-known cable equation for nonmyelinated axon model is extended analytically for myelinated axon formulation. The myelinated membrane conductivity is represented via the Fourier series expansion. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficients, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the entire periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent nonmyelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the myelinated axon model. Hill's equation is explicitly integrated for the specific choice of piecewise constant membrane conductivity profile, thereby resulting in an explicit closed form expression for the transmembrane potential in terms of trigonometric functions. The Floquet's modes are recognized as the nerve fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model, provided that the periodic membrane point-wise passivity constraint is properly modified. Indeed, the modified condition, enforcing the periodic membrane passivity constraint on the average conductivity only leads, for the first time, to the inclusion of the nerve fiber activation modes in our novel model. The validity of the generalized transmission-line and cable equation models for a myelinated nerve fiber, is verified herein through a rigorous Green's function formulation and numerical simulations for transmembrane potential induced in three-dimensional myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.

A Convex Programming Approach for Generating Guaranteed Passive Approximations to Tabulated Frequency-Data

In this paper, we present a methodology for generating guaranteed passive time-domain models of subsystems described by tabulated frequency-domain data obtained through measurement or through physical simulation. Such descriptions are commonly used to represent on- and off-chip interconnect effects, package parasitics, and passive devices common in high-frequency integrated circuit applications. The approach, which incorporates passivity constraints via convex optimization algorithms, is guaranteed to produce a passive-system model that is optimal in the sense of having minimum error in the frequency band of interest over all models with a prescribed set of system poles. We demonstrate that this algorithm is computationally practical for generating accurate high-order models of data sets representing realistic, complicated multiinput, multioutput systems.

415 セミアクティブサスペンションの受動性を考慮したスライディングモード制御

This paper presents a sliding mode controller for semi-active suspension systems. The structure of the proposed controller is basically designed by applying the integral sliding mode control theory, which consists of two control laws. One of them is a state feedback law to realize an ideal closed-loop dynamics such as a sky-hook suspension without disturbances. Another one is a discontinuous control law to induce a sliding mode for rejecting the disturbances. It is shown that not only the discontinuous control mentioned above but also the passivity constraint induces a high frequency vibration known as chattering. That is, the passivity constraint brings about a discontinuous control signal naturally. Then, in order to reduce the chattering, it is attempted to smooth the passivity constraint by using a continuous function as is done in a relay control. Numerical simulation results illustrate the effectiveness of the proposed control strategy.

A Behavioural Approach to Positive Real Interpolation

We study interpolation by positive real functions from a behavioural point of view. In particular, by considering the notion of mirror image data, the interpolation problem with passivity constraint is transformed into an unconstrained behavioural modeling one. The main conclusion is that the generating system for this problem has to be unitary with respect to an indefinite matrix. In addition we investigate the multiple-point positive real interpolation problem. This leads to a solution of the positive real realization problem where the data are Markov parameters.

Muscle force and its role in joint dynamic stability.

The study of loading in the muscle is essential to better understanding the adaptation and plasticity of the muscle under pathologic or surgically-altered conditions. Muscle recruitment and muscle force are determined by the muscle's mechanical function as a joint mover and a joint stabilizer. The coordination of muscle contraction affects joint stability. However, the conditions of the joint passive constraints influence the muscle recruitment. Furthermore, muscle force is regulated based on muscle size, such as the physiologic cross-sectional area, and its physiology, namely, the length-tension and the tension-velocity relationship. Alterations of these physiologic relationships also will influence the overall mechanical function of the muscle.

A Syndrome of Joint Laxity and Impaired Tendon Integrity in Lumican- and Fibromodulin-deficient Mice

Lumican and fibromodulin regulate the assembly of collagens into higher order fibrils in connective tissues. Here, we show that mice deficient in both of these proteoglycans manifest several clinical features of Ehlers-Danlos syndrome. The Lum(-/-)Fmod(-/-) mice are smaller than their wild type littermates and display gait abnormality, joint laxity, and age-dependent osteoarthritis. Misaligned knee patella, severe knee dysmorphogenesis, and extreme tendon weakness are the likely causes for joint laxity in the double-nulls. Fibromodulin deficiency alone leads to significant reduction in tendon stiffness in the Lum(+/+)Fmod(-/-) mice, with further loss in stiffness in a Lum gene dose-dependent way. At the protein level, we show marked increase of lumican in Fmod(-/-) tendons, which may partially rescue the tendon phenotype in this genotype. These results establish fibromodulin as a key regulator and lumican as a modulator of tendon strength. A disproportionate increase in small diameter immature collagen fibrils and a lack of progression to mature, large diameter fibrils in the Fmod(-/-) background may constitute the underlying cause of tendon weakness and suggest that fibromodulin aids fibril maturation. This study demonstrates that the collagen fibril-modifying proteoglycans, lumican and fibromodulin, are candidate genes and key players in the pathogenesis of certain types of Ehlers-Danlos syndrome and other connective tissue disorders.