S. Rakheja

Development of the rate-dependent Prandtl–Ishlinskii model for smart actuators

A generalized Prandtl–Ishlinskii model is proposed for characterizing the rate-dependent hysteresis behavior of smart actuators. A rate-dependent play operator is formulated and integrated to the Prandtl–Ishlinskii model together with a dynamic density function to predict hysteresis properties as a function of the rate of change of the input. Relaxation functions are further proposed to relax the congruency in the output of the Prandtl–Ishlinskii model. The fundamental properties of the proposed rate-dependent operator are systematically provided, which conform with important effects of the time rate of input on the hysteresis output established from the reported experimental data. Additional laboratory experiments were performed to characterize the rate-dependent hysteresis behavior of a PZT actuator under excitation in the 1–500 Hz frequency range. The measured data were used to demonstrate the validity of the proposed generalized model. The comparisons suggest that the proposed rate-dependent operator and density functions allow for prediction of the rate-dependent hysteresis under dynamically varying inputs. From the simulation results attained under varied dynamic inputs, it is shown that the proposed model can predict both major and minor hysteresis loops, and that the hysteresis increases significantly with increasing frequency.

Generalized Prandtl-Ishlinskii hysteresis model: Hysteresis modeling and its inverse for compensation in smart actuators

Smart actuators such as magneto-restrictive actuators, shape memory alloy (SMA) actuators, and piezoceramic actuators exhibit different hysteresis loops. In this paper, a generalized Prandtl-Ishlinskii model is utilized for modeling and compensation of hysteresis nonlinearities in smart actuators. In the formulated model, a generalized play operator together with a density is integrated to form the generalized Prandtl-Ishlinskii model. The capability of the formulated model to characterize hysteresis in smart actuators is demonstrated by comparing its outputs with experimental results obtained from different smart actuators. As an example, hysteresis nonlinearities of the magnetostrictive and SMA actuators are characterized by the generalized Prandtl-Ishlinskii model. Furthermore, an analytical inverse of the generalized Prandtl-Ishlinskii model is derived for compensations in different smart actuators. In other words, exact inverse of the generalized Prandtl-Ishlinskii model is achievable and it can be implemented as a feedforward compensator to migrate the effects of the hysteresis in different types of smart actuators. Such compensation is experimentally illustrated by piezoceramic actuator.

Modeling hysteretic characteristics of MR-fluid damper and model validation

Extensive laboratory measurements were performed to characterize the hysteretic force properties of a magneto-rheological damper under a wide range of magnitudes of control current and excitation conditions (frequency and stroke). A generalized model synthesis is proposed to characterize the biviscous hysteretic force characteristics using symmetric and asymmetric sigmoid functions on the basis of fundamental force generation mechanism. The global model synthesis is realized upon formulation and integration of component functions describing saturated hysteresis loop, linear rise and current-induced rise. The validity of the proposed model is demonstrated by comparing the simulation results with the measured data in terms of hysteretic force-velocity characteristics under a wide range of test conditions. The results revealed excellent correlation between the measured data and model results, irrespective of the test conditions considered. The results of the study suggest that the proposed model could be effectively applied for characterizing the damper hysteresis and for the development of optimal controller for implementation in varied applications.

Development and Relative Assessments of Models for Characterizing the Current Dependent Hysteresis Properties of Magnetorheological Fluid Dampers

Magnetorheological (MR) dampers exhibit hysteretic and nonlinear force— velocity characteristics, which are strongly dependent upon the nature of the excitation and applied current. A number of reported models for characterizing such hysteretic and nonlinear force—velocity properties are reviewed in view of their applicability for predicting the hysteretic damping force under varying applied current and excitation conditions. It is concluded that the vast majority of these models lack consideration of damping force dependence upon the control current, and the frequency and magnitude of excitation. An independent current function is proposed that could enhance the current-dependent damping force prediction ability of the selected models, when integrated with the hysteretic force function. The parameters of the resulting modified models are identified on the basis of the measured data acquired for a MR-damper under wide ranges of excitation amplitudes and frequencies, and applied currents. These include modified linear biviscous, polynomial, extended Bouc—Wen and generalized sigmoid function models. The validity of modified models and the proposed current function is examined by comparing the model results with measured data under different currents and excitation conditions. The results show that the integration of the proposed current function could significantly enhance the performance of all models in predicting the current-dependent hysteretic damping force. The relative error analyses reveal that modified Bouc—Wen and sigmoid function models can provide reasonably good characterization of nonlinear and hysteretic MR-damping force over a range of current and excitation conditions considered in the study.

Semi-active control of vehicle vibration with MR-dampers

A semi-active force tracking PI controller is formulated and analyzed for a magnetorheological (MR) fluid-based damper in conjunction with a quarter-vehicle model. Two different models of the MR-damper are integrated into the closed-loop system model, which include: a model based upon the mean force-velocity behavior; and a model synthesis comprising inherent non-smooth hysteretic force and the force limiting properties of the MR damper. The vehicle models are analyzed to study the vibration attenuation performance of the MR-damper using the semi-active force tracking PI control algorithm. The simulations results are also presented to demonstrate the influence of the damper nonlinearity, specifically the hysteresis, on the suspension performance. The results show that the proposed control strategy can yield superior vibration attenuation performance of the vehicle suspension actuated by the controllable MR-damper not only in the sprung mass resonance and the ride zones, but also in the vicinity of the wheel-hop. The results further show that the presence of damper hysteresis deteriorates the suspension performance.

Modelling rate-dependent symmetric and asymmetric hysteresis loops of smart actuators

Smart material actuators invariably exhibit hysteresis that may be either symmetric or asymmetric depending upon the actuation principle. Moreover, the shape of hysteresis loop depends on the rate of change of the input. In this study, a generalised rate-dependent Prandtl-Ishlinskii model is proposed to characterise both the symmetric and asymmetric input-output hysteresis effects of smart material-based actuators. The model is realised upon formulation and integration of a generalised rate-dependent play operator. The validity of the generalised model is demonstrated by comparing its displacement responses with the measured symmetric and asymmetric responses obtained for piezoceramic and magnetostrictive actuators under different input frequencies in the 1?200 Hz and 10?100 Hz ranges, respectively. The results suggest that the proposed rate-dependent Prandtl-Ishlinskii model can effectively characterise the symmetric as well asymmetric hysteresis properties of the smart material actuators over a wide range of input frequencies.

A Generalized Prandtl-Ishlinskii Model for Characterizing Rate Dependent Hysteresis

A generalized Prandtl-Ishlinskii model is proposed for characterizing the rate dependent hysteresis. A rate dependent play and stop operators are formulated and integrated to the Prandtl-Ishlinskii model together with a rate dependent density function to predict hysteresis properties as a function of rate of change of the input. The fundamental properties of the proposed rate dependent play and stop operators are evaluated and discussed. Experimental data obtained for a piezoceramic actuator under excitations in a wide frequency range (1-500 Hz) are analyzed to demonstrate rate dependence of the hysteretic responses. The validity of the proposed model is illustrated by comparing simulation results with the measured data over a wide frequency range. The comparisons suggest that the proposed rate dependent operator and density functions allow for accurate prediction of the rate dependent hysteresis under dynamically varying inputs.

Characterization of Rate Dependent Hysteresis of Piezoceramic Actuators

A generalized Prandtl-Ishlinskii model is proposed for characterizing the rate dependent hysteresis behavior of piezoceramic actuator. Rate dependent play operator is formulated and integrated to the Prandtl-Ishlinskii model together with dynamic density function to model hysteresis as a function of rate of change of the input. The fundamental properties of the proposed rate dependent operators are discussed. Laboratory experiments were performed to characterize the rate dependent hysteresis behavior of a piezoceramic actuator under excitation in the 0.1 to 200 Hz frequency range. The measured data were used to demonstrate validity of the proposed generalized model. The comparisons suggest that the proposed rate dependent operator and density functions allow for accurate characterization of the rate dependent hysteresis of piezoceramic actuator under dynamically varying inputs.

A discrete harmonic linearization technique for simulating non-linear mechanical systems

An efficient simulation technique referred to as DH linearization is presented. The non-linear damping mechanisms in vibration isolation systems are represented by an array of viscous damping coefficients which are functions of local values of excitation frequency, and amplitude. The non-linear system is thus represented by a number of algebraic expressions. In the DH linearization technique an iterative algorithm is used, with simulataneous solution of the algebraic expressions. Unique dynamic behaviour of the mechanical systems, specifically due to discontinuous non-linearities, is quite accurately represented. The simulation of a non-linear mechanical system is carried out by using statistical, harmonic, and DH linearization techniques. A comparison of the three technques reveals that the DH linearization technique provides non-linear system response close to the exact solution, throughout the entire frequency range. A number of examples are presented to demonstrate the effectiveness of DH linearization for harmonic as well as random inputs.

Frequency Equations for the In-Plane Vibration of Circular Annular Disks

This paper deals with the in-plane vibration of circular annular disks under combinations of different boundary conditions at the inner and outer edges. The in-plane free vibration of an elastic and isotropic disk is studied on the basis of the two-dimensional linear plane stress theory of elasticity. The exact solution of the in-plane equation of equilibrium of annular disk is attainable, in terms of Bessel functions, for uniform boundary conditions. The frequency equations for different modes can be obtained from the general solutions by applying the appropriate boundary conditions at the inner and outer edges. The presented frequency equations provide the frequency parameters for the required number of modes for a wide range of radius ratios and Poissons ratios of annular disks under clamped, free, or flexible boundary conditions. Simplified forms of frequency equations are presented for solid disks and axisymmetric modes of annular disks. Frequency parameters are computed and compared with those available in literature. The frequency equations can be used as a reference to assess the accuracy of approximate methods.