This article presents a new fractional-order normalized Bouc–Wen (BW) (FONBW) model to describe the asymmetric and rate-dependent hysteresis nonlinearity of piezoelectric actuators (PEAs). In view of the fact that the classical BW (CBW) model is only efficient for the symmetric and rate-independent hysteresis description, the FONBW model is devoted to characterizing the asymmetric and rate-dependent behaviors of the hysteresis in PEAs by adopting an $N$ th-order polynomial input function and two fractional operators, respectively. Different from the traditional modified BW models, the proposed FONBW model also eliminates the redundancy of parameters in the CBW model via the normalization processing. By this way, the developed FONBW model has a relatively simple mathematic expression with fewer parameters to simultaneously characterize the asymmetric and rate-dependent hysteresis behaviors of PEAs. Model parameters are identified by the self-adaptive differential evolution algorithm. To validate the effectiveness of the proposed model, a series of model verification and inverse-multiplicative-structure-based feedforward control experiments are carried out on a PEA system. Results show that the proposed model is superior to the CBW model and traditional modified BW model in modeling accuracy and hysteresis compensation.

This article proposes a new discrete-time predictive sliding mode control (DPSMC) for a parallel micropositioning piezostage to improve the motion accuracy in the presence of cross-coupling hysteresis nonlinearities and input constraints. Unlike the traditional linear discrete-time sliding mode control (DSMC), the proposed DPSMC is chattering free and has a faster convergence rate thanks to the design of a nonlinear discrete-time fast integral terminal sliding mode surface. Moreover, by combining with the receding horizon optimization, the sliding mode state is predicted to follow the expected trajectory of a predefined continuous sliding mode reaching law, which also allows the proposed controller to explicitly deal with constraints. The stability of the closed-loop system is analyzed under the model disturbances and constraints, and proves that the proposed DPSMC can offer a smaller quasi-sliding mode bandwidth than the traditional DSMC. The effectiveness of the proposed controller is validated by a series of numerical simulations and experiments. Results demonstrate the advantages of proposed DPSMC over the traditional DSMC method.

Parallel mechanisms have been employed as architectures of high-precision vibration isolation systems. However, their performances in all degrees of freedom (DOFs) are nonidentical. The conventional solution to this problem is isotropic mechanism design, which is laborious and can hardly be achieved. This article proposes a novel concept; namely, isotropic control, to solve this problem. Dynamic equations of parallel mechanisms with base excitation are established and analyzed. An isotropic control framework is then synthesized in modal space. We derive an explicit relationship between modal control force and actuation force in joint space, enabling implementation of the isotropic controller. The multi-DOF system is transformed into multiidentical single-DOF systems. Under the framework of isotropic control, parallel mechanisms obtain an identical frequency response for all modes. An identical corner frequency, active damping, and rate of low-frequency transmissibility are achieved for all modes using a combining proportional, integral, and double integral compensator as a subcontroller. A 6-UPS parallel mechanism is presented as an example to demonstrate effectiveness of the new approach.

Improving the control performance of active vibration isolation systems is crucial to provide an ultra-quiet environment for precision instruments. This paper presents a new fractional-order robust model reference adaptive controller for the piezo-actuated active vibration isolation systems with a relative-degree-one model. One advantage of the proposed controller lies in that its controller parameters are adjusted online by fractional proportional–integral-type adaptive laws, which not only speeds up the convergence of the closed-loop system, but also improves the control energy efficiency. Moreover, the proposed controller only uses the measurable input and output of the plant as feedback signals, which is convenient for controller implementation. The stability of the closed-loop system is proved based on the Lyapunov theory in detail. The optimal values of the fractional order and adaptive gains for adaptive laws are determined using the multi-objective genetic algorithm through off-line simulation. Comparative experiments on the piezo-actuated active vibration isolation systems are conducted to verify the effectiveness of the proposed controller. Results show that the proposed controller achieves satisfactory isolation performance in a wider frequency band of 20–500 Hz, and simultaneously reduces the control effort compared with the traditional MRAC methods.

This paper analyzes the lift-production system in hovering of the flapping wing robot COLIBRI of the size of a hummingbird. The paper first examines the flapping wing mechanism for which a new gear transmission is proposed to reduce the friction and facilitate the assembly. Next, a sensitivity analysis is performed on the wing size. Then, the paper discusses several options for the gearbox, various DC motors and two battery configurations (a single battery or two batteries in series) to minimize the heat generation and increase the flight time. The configuration involving two batteries has been found more effective. The flight time is predicted using Shepherd’s discharge model and it is confirmed by an experiment. The robot sustains an endurance of nearly 5 min to produce a lift force equal to the weight of the robot.