Modeling and Compensation of Rate-Dependent Asymmetric Hysteresis Nonlinearities of Magnetostrictive Actuators (2013)

Smart material actuators are increasingly being explored for various micropositioning applications. Magnetostrictive actuators, in particular, are considered attractive for micro/nano positioning and high speed precision machining due to their high energy density, resolution and force capacity. The magnetostrictive actuators, similar to other smart material actuators, however, exhibit considerable hysteresis and output saturation nonlinearities that tend to become far more significant under high rates of input. Such nonlinearities cause response oscillations and errors in the positioning tasks. Reliable compensation of such nonlinearities is thus highly desirable to enhance micro/nano positioning performance of the actuator over a wide range of operating conditions.\nThis dissertation research is concerned with characterization of output-input nonlinearities of a magnetostrictive actuator and control of hysteresis nonlinearities under a wide range of inputs. A comprehensive experimental study was performed to characterize output-input characteristics of a magnetostrictive actuator under a wide range of excitation conditions include amplitude, frequency, and bias of the input and the mechanical loading of the actuator. The measured data were analyzed to characterize output-input properties and to formulate a hysteresis model, to describe the hysteresis properties of these actuators. A Prandtl-Ishlinskii model was considered due to its continuous nature and thereby the invertability to seek hysteresis compensation. A rate-dependent threshold function was proposed to describe hysteresis properties of the actuator over a wide range of input frequencies. The inverse of the proposed rate-dependent hysteresis model was subsequently formulated for compensation of rate-dependent symmetric hysteresis nonlinearities. The effectiveness of the inverse model was investigated through simulations and hardware-in-the-loop test methods considering a 100 μm magnetostrictive actuator acquired from Etrema Inc. The results clearly illustrated effective compensation of symmetric hysteresis nonlinearities under low magnitude excitation currents over the entire frequency range. The method, however, revealed substantial errors under medium to high amplitude excitation, which was attributed to output saturation and asymmetry. The concept of a stop-operator based Prandtl-Ishlinskii model was proposed to achieve compensation of hysteresis nonlinearities described by the play-operator based hysteresis model on the basis of the initial loading curve, it was shown that the complementary properties of stop operators can be effectively applied for compensation of actuator hysteresis described by the Prandtl-Ishlinskii model.\nThe inverse rate-dependent Prandtl-Ishlinskii model and the stop-operator based Prandtl-Ishlinskii model, however, are applicable only for compensation rate-dependent symmetric hysteresis and rate-independent hysteresis nonlinearities, respectively. The proposed rate-Prandtl-Ishlinskii model was refined to describe the rate-dependent asymmetric hysteresis nonlinearities together with output saturation by integrating a memoryless function to the rate-dependent Prandtl-Ishlinskii model. The resulting integrated model could accurately describe the asymmetric hysteresis nonlinearities and output saturation of the magnetostrictive actuator. The inverse of the integrated model was obtained by integrating the inverse of the rate-dependent Prandtl-Ishlinskii model with that of the memoryless function. The effectiveness of the integrated inverse model in compensating for hysteresis nonlinearities was investigated through simulations and experimentally using hardware-in-the-loop test method. The results suggested that the proposed integrated model and its inverse could effectively characterize and compensate for rate-dependent asymmetric hysteresis nonlinearities of magnetostrictive actuator. Both the experimental and simulation results showed that the peak hysteresis observed under high magnitude excitation could be reduced from 49.1 % to 3.7 % in the 1-250 Hz range when the integrated model inverse is applied.