Nonlinearities greatly affect the control performance of a system. A new estimation and compensation method for unknown input dead zone and backlash has been developed based on the equivalent-input-disturbance (EID) approach. Unlike other methods, it requires neither any information on the nonlinearities nor an inverse model of them. The key idea is that input nonlinearities are taken to be an input-dependent disturbance. An EID estimator is designed that produces an estimate with the same effect on the output as that of the input nonlinearities. The estimate is then used to compensate for the nonlinearities. Simulation results demonstrate the validity of the method.

Estimation of and compensation for unknown input nonlinearities using equivalent-input-disturbance approach

The magnetostrictive actuator is a widely used precision smart actuator; however, the micro-positioning and tracking performance of it is limited due to the inherent dynamic nonlinearities. In order to improve the tracking performance of actuator, a hybrid control strategy comprising a preliminary rate-independent hysteresis compensation and a further adaptive filter controller is developed. The generalized Prandtl–Ishlinskii model that has analytical inversion is used to preliminarily compensate the rate-independent hysteresis. A modified coral reef optimization algorithm is utilized to identify the model parameter and accordingly enhance the compensation accuracy. In addition, considering the input current and output displacement of magnetostrictive actuator are always positive, a one-side generalized play operator is adopted. Further, the adaptive finite impulse response controller is applied to eliminate the preliminary compensation error which is owing to the dynamic effect of nonlinearities. In order to validate the hybrid control strategy, some simulations and experiments are conducted. Compared with the feedforward inverse controller, the hybrid control strategy is of better accuracy and adaptivity. The results demonstrate that the hybrid control strategy is capable of precisely tracking step and multiple-frequency sinusoidal trajectory.

Adaptive trajectory tracking of magnetostrictive actuator based on preliminary hysteresis compensation and further adaptive filter controller

A precision positioning stage based on giant magnetostrictive actuator (PPS-GMA) shows nonlinear displacement when it is used in the field of precision positioning control. To improve the defect, the Jiles–Atherton hysteresis model and the dynamic recurrent neural network (DRNN) feed forward-fuzzy PID feedback control strategy were adopted. An accurate hysteresis nonlinearity model of PPS-GMA was established with the Jiles–Atherton model and its parameters were identified using the particle swarm optimization (PSO) algorithm. A dynamics inverse model of the PPS-GMA was established with the DRNN learning method to compensate the hysteresis nonlinearity characteristic. A fuzzy PID feedback control was used to compensate for the mapping error of DRNN. Using these control methods, the positioning accuracy of the precision positioning stage was improved. The simulation and experimental results show that the Jiles–Atherton hysteresis model can describe the hysteresis nonlinear characteristic of the precision positioning stage, the PSO algorithm has high precision for parameter identification, the DRNN feed forward-fuzzy PID feedback control strategy can effectively eliminate the nonlinear characteristics of the PPS-GMA, which has practical significance for improving the positioning accuracy of the PPS-GMA.

Hysteresis nonlinearity modeling and position control for a precision positioning stage based on a giant magnetostrictive actuator

We report an adaptive feedforward controller to address the ill-conditioned dynamic hysteresis on a custom-developed magnetostrictive vibration shaker. The vibration shaker works within low-frequency bandwidth. Magnetostrictive-induced hysteresis is a main issue that affects excitation waveform replication. Generally, the shape of dynamic hysteresis loop depends on the amplitude and frequency of input current. Many studies, e.g., Prandtl–Ishlinskii (PI)-based feedforward control approach, are conducted to address nonlinear dynamics in the hysteresis. Particularly, the dynamic hysteresis loop characterizes non-positive gradient (i.e., ill condition) when the frequency of input current is increasing. Under the ill condition, traditional PI-based feedforward control is ineffective. In this paper, we investigate this phenomenon according to a few experiments. Then, a novel static hysteresis and dynamics hybrid compensator is presented to deal with the ill-conditioned dynamic hysteresis issue. The dynamic compensator is a finite-impulse-response-based model whose coefficients are updated by the modified filtered-x normalized least mean square (MFxNLMS) algorithm. The static hysteresis compensator is constructed with the polynomial-modified PI (PMPI) model. The parameters of PMPI model are acquired by particle swarm optimization. Two simulations are conducted to show (1) the convergence of the MFxNLMS algorithm; (2) the efficacy of proposed model to describe the ill-conditioned dynamic hysteresis. Furthermore, the experimental device is constructed and a couple of experiments are implemented. The experimental results show that, with the proposed controller, the magnetostrictive vibration shaker can replicate both narrowband and wideband waveforms accurately. Moreover, it is robust to load variation.

Ill-conditioned dynamic hysteresis compensation for a low-frequency magnetostrictive vibration shaker

Energy harvesting using magnetostrictive materials is currently attracting significant attention. The additive manufacturing process can produce such materials with excellent energy-harvesting performance and various required properties, including mechanical properties—by optimizing the lattice structure of the material. This study optimized the manufacturing parameters of a laser powder bed fusion process to produce a magnetostrictive Fe52–Co48 alloy. We evaluated the energy-harvesting performance of a Fe52–Co48 alloy plate with a honeycomb structure subjected to vibrations and impacts. We compared the results with a fully dense structure and found that the honeycomb structure resulted in a lower resonant frequency. In addition, the honeycomb structure exhibited a power density 4.7 times higher than that of the fully dense structure in a vibration test and 4.9 times higher than that in an impact test. The honeycomb structure is thus an attractive structure for obtaining power efficiently. Furthermore, honeycomb structures and other designs can reduce the weight of a Fe52–Co48 alloy plate and improve its sensitivity for use as a particulate-matter sensor. 

Additive Manufacturing and Energy-Harvesting Performance of Honeycomb-Structured Magnetostrictive Fe52–Co48 Alloys

The cerebella model articulation controller is used as a feedforward controller to establish a nonlinear inverse model of giant magnetostrictive material (GMM). This controller can eliminate the effect of nonlinear hysteresis response of GMM and realize linear control. A PID feedback control is employed to improve the stability and accuracy of the system. The output of the system can map the target input of the system accurately using the compound controller. An experimental platform was built, and the availability of the compound controller was tested on it. Most of the errors of the controlled system were limited in 6 %.

Research on hysteresis compensation control of GMM

Vibration energy harvesting can solve the energy supplying problem of systems like wireless sensors networks. The Galfenol cantilever beam energy harvester is suitable for this application. According to the electromechanical conversion principle, the constitutive relation of Galfenol is built. A magnetization model is also established, based on the hysteresis model of Galfenol. Combining the magneto-mechanical coupling model, the constitutive relation of Galfenol and the electromagnetic induction law, the mathematical model of Galfenol vibration energy harvester is established. A hyperbolic curve-shaped cantilever beam is designed and its performance is compared to three types of cantilever beams: rectangle, trapezoidal, and triangle. The stress distribution, modal analysis and frequency response of these four shapes of beams are compared. The hyperbolic beam is more suitable for low frequency vibration harvesting. The strain on the beams, output voltage and power output response to these energy harvesters, under different natural vibration frequencies, are determined by simulation. Finally, the simulation results are compared to experimental electric outputs of all four types of prototype beams. The comparative study showed consistency between the experimental and the simulation results, and also that the peak-to-peak induction voltage value of the hyperbolic beam is larger than other shapes of energy harvesters, whose average value is at 269.8 mV. The maximum power output of the hyperbolic beam is 403.8 μW when connected with a 50 Ω resistance.

Mingfan Li

Papers

Research on hysteresis compensation control of GMM

Modeling and experiments on Galfenol energy harvester