The Prandtl-Ishlinskii (PI) model is widely utilized in hysteresis modeling and compensation of piezoelectric actuators. For systems with rate-independent hysteresis, the inverse PI model is analytically feasible and it can be adopted as a feedforward compensator for the hysteretic nonlinearity of piezoelectric actuators. However, for the rate-dependent PI model, the applicable valid inversion methodology is not yet available. Although simply replacing all the rate-independent terms in the conventional inversion law with the rate-dependent terms can achieve acceptable results at very slow trajectories. However, a large theoretical modeling error is inevitable at fast trajectories, which is investigated through simulations. This paper proposes a new direct approach to derive the inverse PI model directly from experimental data. As no inversion calculation is involved, the proposed direct approach is efficient and the theoretical modeling error can be avoided. In order to validate the accuracy of the direct approach, a number of experiments have been implemented on a piezo-driven compliant mechanism by utilizing the inverse PI model as a feedforward controller. The tracking performance of the mechanism is significantly improved by the direct approach.

Pneumatic artificial muscle (PAM) systems are a kind of tube-like actuators, which can act roughly like human muscles by performing contractile or extensional motions actuated by pressurized air. At present, it is still an open and challenging issue to tackle positioning and tracking control problems of PAM systems, due to inherent characteristics, e.g., unidirectional inputs, high nonlinearities, hysteresis, time-varying characteristics, etc. In this paper, a new adaptive control method is proposed for PAM systems, which achieves satisfactory tracking performance. To this end, an update law is designed to estimate unknown system parameters online. Also, some control input transforming operations are applied to address unidirectional constraints (i.e., control inputs of PAM systems should always be positive). As far as we know, compared with most of the existing control methods, this paper gives the first continuous control solution for PAM systems that can simultaneously compensate parametric uncertainties, reject external disturbances, and meet unidirectional constraints. Without linearizing the nonlinear dynamics, the closed-loop system is theoretically proven to be asymptotically stable at the equilibrium point with the stability analysis. In addition, a series of hardware experiments are implemented on a self-built hardware platform, indicating that the proposed method achieves satisfactory tracking control and exhibits robustness against parametric uncertainties and disturbances.

This paper presents the mechanical design, computational optimization, and experimentation of a decoupled 2-DOF monolithic mechanism. In the mechanical design, statically indeterminate leaf parallelograms provide the decoupling effect, and the displacement of the piezoelectric actuator (PEA) is amplified with a statically indeterminate lever mechanism. In a piezo-driven mechanism, the contact interface between the PEA and the mechanism is a major cause of the discrepancies between the estimated and measured characteristics. However, no explicit and reliable model is available to estimate the contact stiffness. In this paper, a computational optimization based on the response surface methodology is performed and the influence of the contact interface is taken into consideration by adding adequate safety margin to the design objectives. Ultimately, a prototype is manufactured and experimentally investigated for its characteristics and performances. Experimental results show that the developed mechanism has a workspace range in excess of 82 μm × 82 μm with a first natural frequency of 423 Hz (with a 53.4-g load mass). The cross-axis coupling ratio is experimentally measured to be below 1%, indicating excellent decoupling performances.

This paper proposes the design of a novel 3-DOF monolithic manipulator. This manipulator is capable of performing planar manipulations with three kinematically coupled DOFs, i.e., the translations in the X and Y axes and the rotation about the Z axis. An improved Scott-Russell (ISR) mechanism is utilized to magnify the displacement of the piezoelectric actuator (PEA). Unlike the SR mechanism, a set of leaf parallelograms is incorporated into the drive point of the ISR mechanism as a prismatic joint. As a result, the linearity of motion and stability are improved. With circular flexure hinges being treated as revolute joints, the forward kinematics and inverse kinematics of the 3-DOF manipulator are analytically derived. Computational analyses are performed to validate the established kinematics models. Due to the unwanted compliance of the flexure hinges, the actual displacement amplification ratio of the ISR mechanism is smaller than its theoretical value. This is the main cause of the discrepancies between the analytical and computational results. The reachable workspace and the static/dynamic characteristics of the 3-DOF manipulator are also analyzed.