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The feedforward inverse compensation is a typical approach to compensate for the hysteresis nonlinearity in smart materials based actuators, which often requires to develop a hysteresis model first and to compute the parameters of the inverse compensator based on the hysteresis model. Different from the above method, a direct inverse model (DIM) constructed by newly proposed clockwise relay operators is developed in this article. The direct inverse modeling approach is free from constructing the inverse compensator, and can be directly used as the inverse compensator. The parameters of DIM can be obtained via the model identification using the experimental data. In order to facilitate the numerical implementation and reduce the model complexity of DIM, a QR factorization based selection mechanism is employed to select the dominant clockwise relay operators. The reduced DIM is capable of preserving the accuracy of the full DIM. The simulation study and experiments are conducted to validate the effectiveness of the developed compensation approach.

This paper studies the dynamics and control of a flexible space structure using double-gimbal variable-speed control moment gyros (DGVSCMGs). The DGVSCMGs are mounted on the flexible structure as a...

Multiple flexible manipulators can be used to complete some repeatable missions. Each flexible manipulator can be described as an underactuated Lagrangian system based on the assumed modes method. Also, the actuator nonlinearity may deteriorate the system performance. Hence, this article aims to develop a distributed controller to solve the leader–follower consensus of multiple flexible manipulators with uncertain parameters, unknown disturbances, and actuator dead zones. The disturbances are classified as repeatable and nonrepeatable ones. The adaptive, iterative learning, and sliding-mode control techniques are used to handle uncertain parameters, repeatable, and nonrepeatable disturbances, respectively. Based on a dead-zone inverse and a finite-time observer, a distributed controller is developed to drive the flexible manipulators to track a moving leader and keep the flexible vibrations bounded simultaneously. Experimental results are presented to verify the effectiveness of the proposed controller.

This paper focuses on the robust output feedback tracking control for n-DOF (degree-of-freedom) robot manipulators with limited state measurements. An improved extended high-gain observer (EHGO) is designed to estimate the unavailable states as well as the system uncertainty and disturbance. A novel control framework combining the improved EHGO and continuous PID-sliding mode controller (PID-SMC) is proposed. The Lyapunov approach is used to prove the effectiveness of the EHGO. Moreover, the stability and convergence of the closed-loop system are confirmed through the singular perturbation theory. Numerical simulation and experimental results are presented to show the performance of the proposed control scheme.

This article presents a method for determining optimal parameters of positive position feedback controllers used for suppressing vibration of flexible structures. The method is based on solving the H∞ synthesis problem with additional constraints on the controller structure. The method allows for independent control of damping added to each mode. Moreover, optimal parameters for both simple input simple output and multiple input multiple output control formulations can be obtained. The effectiveness of the method is shown by comparing the results of both multiple input multiple output and simple input simple output positive position feedback controllers designed by the proposed method, with the simple input simple output positive position feedback controller designed by analytically derived optimal parameters. Moreover, results of controllers designed with the fixed-order transfer function control structure are also presented to emphasize the advantages offered by the positive position feedback control structure.

A distributed adaptive controller is proposed in this paper for a class of underactuated Lagrangian systems to control the actuated variables to track a dynamic leader and keep unactuated ones bounded under a directed communication graph. A finite-time observer is introduced to estimate the leader's velocity. Based on two sliding variables defined for the actuated and unactuated channels, adaptive controllers are designed for the underactuated Lagrangian systems subject to uncertain parameters and external disturbances without or with actuator faults. The convergences of the proposed controllers are proven based on the separation principle between the observer and the controller. Finally, simulations and experiments are conducted to verify the effectiveness of the proposed controllers.

This paper focuses on the distributed control of flexible payload transportation using multiple quadrotors. To design a distributed controller, the transportation system is described as a group of quadrotors subject to disturbance forces and torques from the flexible payload. A distributed finite-time observer is introduced for the quadrotors to estimate the virtual leader’s information. The disturbances acting on quadrotors due to the transverse and torsional deformation of the flexible payload are estimated based on the deformation analysis. The unmodeled disturbances are approximated using a radial basis function neural network. A distributed hierarchical controller is developed with the compensation for these disturbances.

This paper presents the development of novel fixed-time consensus controllers of simple form for the second-order multiagent systems based on input shaping under an undirected communication graph. To satisfy the requirement of multiagent systems, the input shaping technique is extended to solve the control of an oscillation system with nonzero initial position first. Then, three cases are considered under the connected undirected graph. Theoretical analyses are presented to solve the exact convergence time based on the responses of the closed-loop multiagent systems. Finally, numerical simulations and experiments are conducted to verify the effectiveness of the proposed controllers.

Three piezoelectric actuators (PEAs) are assembled in a Fabry–Perot spectrometer (FPS) to adjust the spacing between two optical plates. The measurement of the FPS requires that the actuated optical plates move in parallel with nanometer resolution. To meet this requirement, the motion of the three PEAs should be controlled synchronously. Thus, the challenging tasks in control of the Fabry–Perot (F–P) system lie in two aspects: control of each PEA precisely at the nanometer level and control of the three PEAs to achieve a synchronized motion. To this end, a novel dynamic model is first proposed to describe the inherent hysteresis effect and the system dynamical behaviors in the F–P system. Based on the proposed model, an inversion-based synchronized model predictive control (SMPC) design is developed. The experimental results validate the proposed control scheme.

The classical Preisach model, which is built by the superposition of a great number of relay operators, is one of the most popular models to represent the hysteretic behaviors in various applications, such as the smart materials-based actuators. However, the construction of the inverse compensator for the classical Preisach model is very challenging for some reasons, first, the analytical inverse of the classical Preisach model is not available, and, second, due to a huge amount of the relay operators the implementation of the inverse compensator is troublesome and causes heavy computational burden. To overcome these drawbacks, a simplified discrete Preisach model is developed in this paper. The simplified model has an explicit expression with respect to the input of the model, thus it is simple to construct its inverse compensator using the inverse multiplicative structure approach. To reduce the computational effort in implementing the inverse compensator, the model-order reduction method is employed to reduce the complexity of the inverse compensator. Experimental tests are carried out to validate the effectiveness of the proposed approach.

This paper studies the vibration control of gyroelastic spacecraft. The dynamics of gyroelastic spacecraft considering the angular momentum devices are derived using Kane's method. A novel control strategy combining input shaping (IS) and variable-speed control moment gyros (VSCMGs) is proposed to suppress the flexible vibration of gyroelastic spacecraft. Input shaping technique is used to suppress the flexible vibration due to attitude motion. An adaptive controller is designed to further reduce the residual vibration using VSCMGs. Considering that the modal variable cannot be measured in practice, a novel modal observer is designed to estimate the modal variables for vibration control. Simulations are conducted to verify the effectiveness of the proposed control strategy.

This paper studies the distributed adaptive control of a team of underactuated flexible spacecraft under a leader–follower architecture with the measurements of the rigid bodies only. By treating the flexible spacecraft as an underactuated Lagrange system, an adaptive control strategy is proposed with the feedback of the generalized coordinates, velocities, and accelerations of the rigid bodies. Then, an extended state observer is introduced to design a distributed adaptive controller without the measurement of the generalized accelerations.

This paper presents distributed adaptive fault-tolerant control for the attitude tracking of multiple flexible spacecraft on $$\textit{SO}(3)$$ without modal variable measurement. Assume that the communication graph among the followers is undirected and connected and there exists at least one follower linked to the leader. To deal with the distributed tracking on $$\textit{SO}(3)$$, a finite-time observer is designed to estimate the leader’s information for the followers. A distributed adaptive fault-tolerant controller is proposed to achieve the attitude tracking based on the estimation of the unmeasurable modal variables. The separation principle between the finite-time observer and the proposed controller is adopted to prove the controller convergence. Since the controllers are developed on $$\textit{SO}(3)$$ directly, the singularity and ambiguity associated with other attitude representations can be avoided. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed control protocols.

This paper considers a transportation system consisting of a quadrotor with a cable-suspended payload. The main focus of this paper is to investigate the effect of polynomial trajectories on the vibration of the cable-suspended payload and to show which polynomial trajectory results in less vibration. A mathematical analysis and a parametric study were carried out to investigate the effect of the degree of the polynomial trajectory on its kinematic behavior. A conjecture relates the degree of the polynomial trajectory and its kinematic behavior to the corresponding payload vibration was introduced. The base excitation model of vibratory systems was proposed as the model of the transportation system of interest. The vibration analysis of both the transportation system and the polynomial trajectories was conducted analytically to show which polynomial trajectory has the least payload vibration. A second stage of payload vibration reduction was provided by introducing a method to reduce the transmitted vibration from the quadrotor to the payload for any quadrotor trajectory. A roadmap to design the transportation task that can reduce the payload vibration was proposed. Both the simulation and the experimental results were presented, discussed and analyzed to verify the findings of this paper.

The Preisach model, which is constructed by the superposition of relay operators, is one of the most popular hysteresis models to describe the hysteresis nonlinearities in smart-materials-based actuators. The application of the Preisach model suffers from the tradeoff between the model accuracy and the number of the relay operators. With a large number of relay operators, the Preisach model can predict the hysteretic effect very precisely; however, a large number of relay operators may lead to a heavy computation burden. To deal with this tradeoff, in this paper, a model order reduction method, namely discrete empirical interpolation method, is applied to reduce the number of the relay operators and meanwhile to preserve the model accuracy of the original Preisach model. Simulations under different conditions (different input signals and different density functions) and experimental tests on a magnetostrictive-actuated platform are conducted to validate the effectiveness of the proposed reduced Preisach model.

This paper is concerned with a leader-follower consensus problem for networked Lipschitz nonlinear multi-agent systems. An event-triggered consensus controller is developed with the consideration of discontinuous state feedback. To further enhance the robustness of the proposed controller, modeling uncertainty and switching topology are also considered in the stability analysis. Meanwhile, a time-delay equivalent approach is adopted to deal with the discrete-time control problem. Particularly, a sufficient condition for the stochastic stabilization of the networked multi-agent systems is proposed based on the Lyapunov functional method. Furthermore, an optimization algorithm is developed to derive the parameters of the controller. Finally, numerical simulation is conducted to demonstrate the effectiveness of the proposed control algorithm.

An imaging Fabry–Perot spectrometer (FPS) utilizes multiple piezoelectric actuators (PEAs) to tune the gap spacing between two optical lenses at nanometer level in order to scan the desired optical band. Due to the nonlinear hysteresis in PEAs and the mechanical coupling, the output responses of the PEAs are quite different, which cause unparallel movement of the FPS positioning stage. For precise positioning control, a model for describing the coupled hysteresis effect is proposed in this paper and a decoupling hysteresis feedforward compensator is constructed based on this model. Experimental results show that the proposed model predicts the coupled hysteresis effect very well and the compensator mitigates the coupled hysteresis efficiently.

In this paper, output feedback integral control of piezoelectric actuators is considered with respect to the hysteresis effect. The linear dynamics of the piezoelectric actuator is modeled as a linear state space system with an input nonlinearity that considers the hysteresis effect. A proof of the Lyapunov stability of the system with integral control is presented, and a method for deriving the upper bound for the regulating gain is shown. A simple example is used to illustrate the approach, and then the approach is applied for tracking a step signal with an experimental single-axis piezoelectric actuator to verify that the system is stable.

This paper proposes a control method with input shapers to complete the cooperative transportation of a slender payload using two quadrotors under a leader-follower framework. Based on the assumption of the small swing of payload, a Lagrangian system with five degrees of freedom is built to describe the transportation system in OYZ plane. The follower is driven by a PID controller to track the pose of the leader. Three input shapers are introduced to reduce the residual oscillations of the follower and the payload. Finally, experimental results are presented to verify the proposed controller for the cooperative transportation mission.

The distributed attitude tracking of multiple flexible spacecraft is addressed on SO(3) under directed graph. Since only some followers know the desired attitude, a sliding model observer is introduced for each spacecraft to estimate the moving leader’s information. A distributed adaptive controller is designed to drive the networked flexible spacecraft to track the leader and keep the flexible vibration bounded. Separation principle is adopted to prove the stability of the resulting closed-loop system. Finally, numerical simulations are conducted to verify the effectiveness of the proposed controller.

Reaction wheels are one of the main actuators for spacecraft attitude control. However, they generate undesired micro-vibrations that affect the attitude control performance. Some space missions that have high-resolution instruments such as telescopes and cameras require high-accuracy attitude control. In such missions, these micro-vibrations cause stability problems, which negatively affect the performance of these instruments. This paper introduces a nonlinear dynamics model for these micro-vibrations in five degrees of freedom. The main advantage of the proposed model is that it analytically considers various disturbance sources. This allows the reaction wheel designers to predict the micro-vibration behavior of the reaction wheel even before the manufacturing of the reaction wheel, i.e., in the design stage. The model considers static and dynamic imbalances of the wheel and the bearing disturbances that come from the waviness in all bearing parts (inner/outer races and balls). Experiments are conducted to validate the effectiveness of the nonlinear model.

Distributed adaptive controllers are developed for attitude tracking and synchronization on S O ( 3 ) of multiple flexible spacecraft under a directed graph. Since not all spacecraft can receive the virtual leader's information, a finite-time observer is designed for each follower spacecraft to estimate the moving virtual leader's information. An adaptive controller is then proposed to realize the distributed attitude tracking synchronously and achieve the bounded flexible vibration. A rigorous theoretical proof is presented based on the separation principle. Furthermore, an adaptive controller with a modal variable observer is designed for the case without the measurements of the modal variables. Finally, numerical and experimental verifications are presented.

This paper studies the trajectory tracking control of space manipulator in the presence of actuator uncertainties, such as actuator fault, actuator saturation and the bias control torque. In addition, parametric uncertainty and external disturbances are also taken into consideration. A novel continuous adaptive integral sliding mode controller, which is chattering free and singularity free compared to the traditional terminal sliding mode control, is proposed to achieve the finite-time trajectory tracking control for space manipulator with uncertainties. Lyapunov theory is employed to prove the stability of the closed-loop system. The main advantage of the proposed controller is that it is easy to be implemented with continuous chattering-free control command. Numerical simulations are used to verify the effectiveness of the proposed controller.

A distributed controller is presented for nonlinear multi-agent systems in this paper. The nonlinear dynamics of each agent are characterised by the Lipschitz condition. With the appearance of system uncertainty and external disturbance, a sampled-data feedback control protocol is carried out along the Lyapunov functional approach. Meanwhile, a state observer is incorporated to reinforce the capability of the proposed control strategy. It is demonstrated that the synchronisation of the networked nonlinear agents are essentially achieved with locally shared information. Remarkably, the system uncertainty and external disturbance are considered in the controller design and the influence caused by -bounded disturbance is minimised effectively. Furthermore, the control gain and observer gain derivation are equivalently transformed to a convex optimisation problem, which is solved by an iterative algorithm developed based on the sufficient conditions of system stability. The effectiveness of the proposed controller is verified by simulations.

This paper studies the development of a novel quadrotor aerial transportation system, which carries payload with four cables. The possible stable configurations are discussed to show the advantages of the four-cable system. The bounds of the disturbance forces and torques acting on the quadrotor from the payload are estimated based on the dynamics analysis. Then a hierarchical adaptive controller is designed on the Lie group S O ( 3 ) for the transportation of the payload by the quadrotor. Finally, experimental results are presented to show the effectiveness of the proposed transportation system and the controller.

Gyroelastic body refers to a flexible structure with a cluster of angular momentum devices. The torques exerted by the angular momentum devices can be used for active vibration suppression. This paper addresses the vibration suppression of gyroelastic body in the presence of uncertainties and external disturbances. Considering that the modal variables of the gyroelastic body cannot be measured directly. Therefore, a neural network (NN) based adaptive modal observer is designed to estimate the modal information of the gyroelastic body. Based on the modal observer, a NN-based adaptive sliding mode output feedback controller (NNASMOFC) is designed. The stabilities of the NN-based modal observer and the NNASMOFC are proved using Lyapunov theory. The possible spillover problem is considered by optimal actuator placement. Simulation results demonstrate the effectiveness of the proposed controller and observer.

This paper presents novel fixed-time control for second-order multi-agent systems based on input shaping technique under undirected and directed graphs. To satisfy the requirement of multi-agent systems, the input shaping technique is extended to solve the control of an oscillation system with non-zero initial position firstly. The distributed fixed-time controllers are proposed based on the shaped command to achieve rest-to-rest maneuver of multi-agent systems under connected undirected graph where there is at least one node linked to the leader. For the directed graph with a globally reachable leader and no circle, distributed fixed-time controllers are designed by placing input shapers in all communication edges in the graph. Finally, experimental results are presented to verify the effectiveness of the proposed controllers.

This paper studies the distributed adaptive control of a team of underactuated flexible spacecraft under leader-follower architecture with the feedback of rigid bodies. For each flexible spacecraft, it is assumed that only the rigid body is actuated and measured directly. First, a distributed adaptive control strategy is proposed with the feedback of the generalized coordinates, the generalized velocities and the generalized accelerations of the rigid bodies. Second, a distributed adaptive controller is presented based on the states and the estimation of the generalized accelerations of the rigid bodies in the team. Finally, one numerical simulation is conducted to verify the effectiveness of the proposed control law.

This paper investigates a reliability-based trajectory optimization method for the design of soft landing trajectory on an irregular shape asteroid with highly uncertain gravitational field. First, the gravitational field of the irregular asteroid is described by the finite particle model. Second, to avoid the singularity and reduce the sensitivity, the original finite particle model is modified to an “N-body/two-body” switching dynamic model. The trajectory optimization problem in the switching dynamic model is summarized as an optimal control problem and is then transformed into a two-point boundary value problem by Pontryagin’s maximum principle. By solving the two-point boundary value problem with a homotopic continuation procedure, the nominal optimal trajectory is obtained. Third, the uncertainty caused by the nonuniform mass distribution of the asteroid is considered. With high uncertainty, the deterministic optimal control problem becomes a parameter optimization problem with reliability constrain...

A distributed leader–follower formation tracking controller is presented in this paper. The dynamics of each agent are modeled by Euler–Lagrange equations, and all agents are guaranteed to track a desired time-varying trajectory in the workspace. The system uncertainties and external disturbances, which are equivalently described by a bounded additive noise, are considered in the controller design, and the proposed controller is robust to noise. Fault diagnosis of the nonlinear multi-agent system is also discussed with the help of differential geometry tools and an active fault recovery strategy is incorporated into the proposed control scheme. The effectiveness of the proposed controller is verified through simulations.

In this study, a consensus algorithm for multiple non-linear Euler–Lagrange systems is presented. This controller guarantees that all agents can reach a common state in the workspace. External disturbances acting on the system are included in the closed-loop stability analysis, and the input-to-state properties of the proposed controller are investigated based on the concept of input-to-state consensus. Moreover, the influence of structural uncertainty is further discussed on the basis of passivity theory. The robustness of the proposed consensus algorithm is then demonstrated in the presence of both external disturbances and structural uncertainty. Experiments are conducted to validate the effectiveness of the proposed consensus algorithm.

In this paper, combined with the direct approach, particle swarm optimization (PSO) is applied to low-thrust trajectory optimization problems. A double-loop trajectory optimization algorithm is developed. The outer loop of this algorithm is a modified PSO optimizer, which can deal with constrained optimization problems and avoid premature convergence. The function of the outer loop is generating a series of time histories of control, called particles, and driving the particles toward the optimal solution. The direct approach (fourth-order Runge–Kutta shooting/parallel shooting method) is adopted as the inner loop algorithm, whose main task is to correct the particles provided by the outer loop and ensure that all the constraints are satisfied. This algorithm has the global search feature of the PSO and the relative large radius of convergence of the direct approach. Its efficiency is substantiated by solving a fixed-time fuel-optimal transfer problem from an asteroid to the Earth. Furthermore, this algorithm can be considered to be a universal low-thrust optimizer, and it can easily be used to solve more complex trajectory optimization problems such as multi-swingby problem and multidisciplinary design optimization (MDO) problems.

This paper presents a vibration control strategy for a flexible manipulator with a collocated piezoelectric sensor/actuator pair. A hybrid vibration controller is proposed by combining the input shaping technique with auto disturbance rejection controller. The parameters of the closed-loop system can be adjusted to the known values by disturbance compensation and linear feedback using the auto disturbance rejection controller. This way, input shaper can be designed without accurate parameters of the flexible manipulator. Both simulation and experiments are conducted to validate the proposed control algorithm. The results verified the effectiveness of the proposed controller in vibration suppression of flexible manipulator.

In this paper, three piezoelectric actuators (PEAs) in parallel installation are utilized in the Fabry-Perot spectrometer for adjusting the optical lens at the nanometer level. Due to the mechanical coupling and uneven preloads to the actuators, the responses of each PEA is rather different, which causes unparallel movement of the positioning stage in the Fabry-Perot spectrometer leading to poor measurement results. Therefore, the controller is highly demanded to enable the synchronized motion of the three PEAs. To this end, the linear-quadratic-Gaussian (LQG) controller combining a synchronization control strategy is developed. The effectiveness of the proposed controller is validated via the experimental tests.

This paper presents an experimental study on wrinkle reduction in a rectangular membrane structure with elliptical boundary cuts. The structure is subjected to two different heat loads: 145 °C and 205 °C. Wrinkling induced by the thermal expansion of the membrane is measured using a photogrammetry system and the root mean square of the membrane's surface above a plane of best fit. A fuzzy logic controller is developed to track a desired flatness level when the membrane is subject to either application or removal of a thermal load. Experimental verification is conducted using a membrane structure test facility and the results show that wrinkles have been reduced significantly and quickly using the proposed fuzzy logic controller.

DOI: 10.2514/1.52287 This paper presents a vibration control strategy for a flexible manipulator with a collocated piezoelectric sensor/ actuator pair. Dynamic modeling of the flexible manipulator is first shown, and then a control law is developed. The proposed vibration controller combines the input shaping technique with multimode adaptive positive position feedback. An adaptive parameter estimator based on the recursive least-square method is developed to update the system’s natural frequencies, which are used by the adaptive positive position feedback. A proportional-derivative controller is combined with the proposed vibration controller to suppress vibration while slewing the manipulator. Simulation results are presented to illustrate the efficacy of the proposed controller.

PurposeThe purpose of this paper is to develop a tri‐axis spacecraft simulator to simulate the three‐axis attitude motion of a satellite and for ground‐based hardware‐in‐the‐loop simulation.Design/methodology/approachThe structure of tri‐axis satellite attitude simulator is designed first. Full dynamic model is then derived. Based on the dynamic model, a simple proportional‐integral‐derivative controller is developed and applied to control the motion of simulator.FindingsThe effectiveness of the proposed simulator configuration has been verified through numerical simulations. The tri‐axis simulator can follow the satellite attitude motion precisely.Originality/valueThis paper is valuable for researchers working on the development of tri‐axis spacecraft attitude simulator. This work is original. The simulator configuration has been applied to a satellite mission that was launched successfully in 2006.

This article presents an adaptive synchronization control strategy for six-degree of freedom spacecraft formation flying based on the cross-coupling concept. The proposed strategy allows the spacecraft track the desired attitude and position trajectories, while simultaneously guarantees the synchronized motion among all spacecraft in formation. The generic synchronization error concept enables the design of a suitable synchronization strategy to obtain a desired synchronization performance. Simulation results of multiple spacecraft formation flying are conducted to verify the effectiveness of the proposed controller.

This paper presents a non-linear filter-based adaptive output control for spacecraft formation flying missions. The study is motivated by the fact that only accurate position measurements are available for some systems, and velocities have to be estimated from those measurements. The proposed adaptive output controller guarantees asymptotic stability of the position and velocity tracking motion, even in the presence of uncertainties and external perturbations. The effectiveness of the proposed controller is verified by numerical simulations.

An adaptive learning synchronisation control strategy for six-degree-of-freedom spacecraft formation flying based on the cross-coupling concept is presented. The proposed strategy allows the spacecraft track the desired attitude and position trajectories in a synchronised fashion, in the presence of periodic disturbances and uncertainties in constant parameters. Illustrative simulations of spacecraft formation flying are conducted to verify the effectiveness of the proposed approach.

Observability and motion planning based on optimal information gathering of mobile robot navigation system is considered in this paper. In order to obtain the minimum standard of observable for the bearing-only mobile robot navigation system, the observability is analyzed in this paper. It is known that the observability analysis can only be used to illustrate the observable condition of mobile robot localization system. However it cannot be used to illustrate which observation is the best for observability. As a result, entropy based optimal information gathering method is introduced in this paper and is used to evaluate the effectiveness and difference of the different observations. Simulation results are presented to verify the effectiveness of the proposed optimal information gathering method.

In this paper, a model characterizing hysteresis, creep, and dynamic effects is proposed for simulation and control system design of piezoactuator-based nano-positioning system. Fractional-order integrator is employed to characterize the creep behavior at low frequencies. Maxwell resistive capacitor (MRC) model is used to capture the rate-independent hysteresis lying in the electric domain between the applied voltage and the surface charge. The remaining high-frequency dynamics, including the dynamics of the mechanical structure, the voltage amplifier, and the capacitive sensor, are described by a high-order linear system. The proposed model is verified experimentally.

In this paper, an integral plus double integral synchronization controller is developed for multiple piezoelectric actuators through a state feedback approach. Dynamic modeling of the piezoelectric nanopositioner is conducted through both linear and nonlinear phenomenological models. The linear and nonlinear models are then used along with the experimental system to perform hardware in the loop (HITL) simulations of the synchronization controller for a parallel three-axis nanopositioning system. This would allow the piezoelectrics to form the basis of an ultra-precise 2-D Fabry-Perot interferometer as the gap spacing of the device could be controlled at the nanometer level.

This paper presents the hysteresis modeling of shape memory alloy actuators (SMA) using Maxwell resistive capacitor (MRC or Maxwell model). The SMA actuators exhibit nonlinearity between electrical input and output displacement. Its hysteretic behavior can cause inaccuracy in tracking if it is not modeled properly. Modified Maxwell model is adopted to compensate for the asymmetric hysteresis loop obtained from the experimental system. Control system design containing inverse Maxwell model is developed and experiments are conducted to verify the effectiveness of the dynamic model and controller.