Piezo-actuated stages are widely applied in the field of high-precision positioning. However, piezo-actuated stages produce hysteresis between the input voltage and the output displacement that negatively influences the positioning accuracy. In this paper, the Bouc–Wen model is established and identified using the bat-inspired optimization algorithm. Subsequently, based on the established hysteresis model, we propose a sliding mode control method with a new reaching law to suppress the hysteresis nonlinearity and achieve high-precision tracking control for the piezo-actuated stages. In addition, the proposed control method contains the perturbation estimation part, which can estimate online the modeling uncertainty and the unknown external disturbances. The stability of the proposed control method is demonstrated through the Lyapunov theory. Finally, to validate the effectiveness of the proposed control method, experiments are conducted on the piezo-actuated stages. Experimental results demonstrate that the proposed control method is superior to the feed-forward control and the conventional sliding mode control method.

Sliding Mode Tracking Control With Perturbation Estimation for Hysteresis Nonlinearity of Piezo-Actuated Stages

Identification and composite control of Hammerstein system with unknown order linear dynamics and a static hysteresis non-linearity modelled by Preisach operator is investigated. The order of linear dynamics is firstly determined by Hankel matrix approach and then a blind identification is implemented to identify the linear dynamics based on the over-sampling output measurements only. Then a novel deterministic approach is proposed to identify the Preisach model for hysteresis non-linearity, which is devoted to identify a triangle matrix. This novel approach needs less dimensions to obtain Preisach density function than other existing methods. Finally, a composite control consisting of discrete inverse model-based controller (DIMBC) and discrete adaptive sliding mode controller (DASMC) is developed to achieve tracking control. The composite control can reduce the reaching time of DASMC and improve the robustness of DIMBC. Experiments based on a turntable servo system demonstrate the effectiveness of the proposed identification and control methods.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2015.0116

Identification and control for Hammerstein systems with hysteresis non-linearity

Twisted string actuators (TSAs) have exhibited great promise in robotic applications by generating high translational force with low input torque. To further facilitate their robotic applications, it is strongly desirable but challenging to enhance their consistent strain generation while maintaining compliance. Existing studies predominantly considered overtwisting and coiling after the regular twisting stage to be undesirable-nonuniform and unpredictable knots, entanglements, and coils formed to create an unstable and failure-prone structure. Overtwisting would work well for TSAs when uniform coils can be consistently formed. In this study, we realize uniform and consistent coil formation in overtwisted TSAs, which greatly increases their strain. Furthermore, we investigate methods for enabling uniform coil formation upon overtwisting the strings in a TSA and present a procedure to systematically "train" the strings. To the authors' best knowledge, this is the first study to experimentally investigate overtwisting for TSAs with different stiffnesses and realize consistent uniform coil formation. Ultrahigh molecular-weight polyethylene strings form the stiff TSAs, whereas compliant TSAs are realized with stretchable and conductive supercoiled polymer strings. The strain, force, velocity, and torque of each overtwisted TSA were studied. Overtwisting and coiling resulted in ∼70% strain in stiff TSAs and ∼60% strain in compliant TSAs. This is more than twice the strain achieved through regular twisting. Finally, the overtwisted TSA was successfully demonstrated in a robotic bicep.

Overtwisting and Coiling Highly Enhances Strain Generation of Twisted String Actuators

Smart material based actuators, such as piezoelectric, magnetostrictive, and shape memory alloy actuators, are known to exhibit hysteresis effects. When the smart actuators are preceded with plants, such non-smooth nonlinearities usually lead to poor tracking performance, undesired oscillation, or even potential instability in the control systems. The development of control strategies to control the plants preceded with hysteresis actuators has become to an important research topic and imposed a great challenge in the control society. In order to mitigate the hysteresis effects, the most popular approach is to construct the inverse to compensate such effects. In such a case, the mathematical descriptions are generally required. In the literature, several mathematical hysteresis models have been proposed. The most popular hysteresis models perhaps are Preisach model, Prandtl-Ishlinskii model, and Bouc-Wen model. Among the above mentioned models, the Prandtl-Ishlinskii model has an unique property, i.e., the inverse Prandtl-Ishlinskii model can be analytically obtained, which can be used as a feedforward compensator to mitigate the hysteresis effect in the control systems. However, the shortcoming of the Prandtl-Ishlinskii model is also obvious because it can only describe a certain class of hysteresis shapes. Comparing to the Prandtl-Ishlinskii model, a generalized Prandtl-Ishlinskii model has been reported in the literature to describe a more general class of hysteresis shapes in the smart actuators. However, the inverse for the generalized Prandtl-Ishlinskii model has only been given without the strict proof due to the difficulty of the initial loading curve construction though the analytic inverse of the Prandtl-Ishlinskii model is well documented in the literature. Therefore, as a further development, the generalized Prandtl-Ishlinskii model is re-defined and a modified generalized Prandtl-Ishlinskii model is proposed in this dissertation which can still describe similar general class of hysteresis shapes. The benefit is that the concept of initial loading curve can be utilized and a strict analytical inverse model can be derived for the purpose of compensation. The effectiveness of the obtained inverse modified generalized Prandtl-Ishlinskii model has been validated in the both simulations and in experiments on a piezoelectric micropositioning stage. It is also affirmed that the proposed modified generalized Prandtl-Ishlinskii model fulfills two crucial properties for the operator based hysteresis models, the wiping out property and the congruency property.

Usually the hysteresis nonlinearities in smart actuators are unknown, the direct open-loop feedforward inverse compensation will introduce notably inverse compensation error with an estimated inverse construction. A closed-loop adaptive controller is therefore required. The challenge in fusing the inverse compensation and the robust adaptive control is that the strict stability proof of the closed loop control system is difficult to obtain due to the fact that an error expression of the inverse compensation has not been established when the hysteresis is unknown. In this dissertation research, by developing the error expression of the inverse compensation for modified generalized Prandtl-Ishlinskii model, two types of inverse based robust adaptive controllers are designed for a class of uncertain systems preceded by a smart material based actuator with hysteresis nonlinearities. When the system states are available, an inverse based adaptive variable structure control approach is designed. The strict stability proof is established thereafter. Comparing with other works in the literature, the benefit for such a design is that the proposed inverse based scheme can achieve the tracking without necessarily adapting the uncertain parameters (the number could be large) in the hysteresis model, which leads to the computational efficiency. Furthermore, an inverse based adaptive output-feedback control scheme is developed when the exactly knowledge of most of the states is unavailable and the only accessible state is the output of the system. An observer is therefore constructed to estimate the unavailable states from the measurements of a single output. By taking consideration of the analytical expression of the inverse compensation error, the global stability of the close-loop control system as well as the required tracking accuracy are achieved. The effectiveness of the proposed output-feedback controller is validated in both simulations and experiments.

Motion Control of Smart Material Based Actuators: Modeling, Controller Design and Experimental Evaluation

In this paper, a Hammerstein model with Preisach operator is proposed to model the rate-dependent hysteresis nonlinearity of a Giant Magnetostrictive Actuator (GMA). The Preisach operator is used to represent the nonlinear block of this model. The model's validity is verified by experimental data. Based on this model, a PID feedback controller combined with an inverse compensation in the feed-forward loop is proposed for tracking control. Experimental results show that the control method is effective.

http://ieeexplore.ieee.org/iel5/6264153/6282333/06282866.pdf

Yongxin Guo

Papers

Rate-dependent modeling and control of GMA based on Hammerstein model with Preisach operator