Memory-Element-Based Hysteresis: Identification and Compensation of a Piezoelectric Actuator

Hysteresis phenomena can significantly deteriorate the performance when performing servo tasks with piezo-electric actuators. The aim of this paper is to model this non-linear hysteresis effect using a memory element, in particular a MEM-element, and exploit this model to develop a feedforward controller. A one-to-one mapping is established, leading to both a systematic data-driven learning approach of a hybrid-MEM-element capturing the hysteresis phenomena and a unique inverse allowing for an intuitive design of the feedforward controller. The developed approach is experimentally validated on a piezoelectric actuator, revealing a significant performance improvement.

An underactuated multibody system has less control inputs than degrees of freedom. For trajectory tracking, often a feedforward control is necessary. Two different approaches for feedforward control design are presented. The first approach is based on a coordinate transformation into the nonlinear input–output normal-form. The second approach uses servo-constraints and results in a set of differential algebraic equations. A comparison shows that both feedforward control designs have a similar structure. The analysis of the mechanical design of underactuated multibody systems might show that they are nonminimum phase, i.e., they have unstable internal dynamics. Then the feedforward control cannot be computed by time integration and output trajectory tracking becomes a very challenging task. Therefore, based on the two presented feedforward control design approaches, it is shown that through the use of an optimization procedure underactuated multibody systems can be designed in such a way that they are minimum phase. Thus, feedforward control design using the two approaches is significantly simplified.

Piezoelectric actuator (PEA) is one of the key component in micro/nano manipulation equipment. However, the inherent hysteresis significantly limits its motion accuracy. In this paper, a Prandtl-Ishlinskii (PI) based feedforward and feedback compound control strategy is designed to eliminate the hysteretic nonlinearity of PEA, and thus linearizing the input/output relationship. An inverse hysteresis model is directly identified and validated using the open loop characteristics of the PEA. The inverse hysteresis model is used as the feedforward compensator. In order to further improve the performance of the PEA, a feedforward and feedback compound control strategy is also designed and tested. A PEA equipped with strain gauges is selected in the experimental investigation. Experimental results show that the hysteresis can be successfully compensated using only feedforward control, and better performance is achieved using the feedforward and feedback compound control.

This paper proposes a new training algorithm using a hybrid Jaya-back propagation algorithm (called H-Jaya) to optimize the neural network weights, which is applied to identify the nonlinear hysteresis Piezoelectric actuator based on the experimental input-output data. The identified H-Jaya-neural model will be used to design an advanced feed-forward (FF) controller for compensating the hysteresis nonlinearity. Furthermore as to improve the tracking performance, a feed-forward-feedback control scheme is conducted. To evaluate the effectiveness of the proposed approach, firstly, it is tested through identifying the nonlinear hysteresis of Piezoelectric (PZT) actuator and compared with other meta-heuristic techniques, including differential evolution (DE), particle swarm optimization (PSO), and Jaya. Then, the accuracy of the hysteresis model-based compensator is evaluated under various control experiments using the piezoelectric actuator. The results of experiments executed on PZT actuator configured with a PZS001 from Thorlabs prove that the proposed approach obtains an excellent performance in hysteresis modeling and compensation.

Adaptive sliding mode control with hysteresis compensation-based neuroevolution for motion tracking of piezoelectric actuator

Model-based piezoelectric hysteresis and creep compensation for highly-dynamic feedforward rest-to-rest motion control of piezoelectrically actuated flexible structures

In this paper, a new nonlinear vibration control scheme using piezoelectric actuator is proposed for a flexible plate with a free vibration and sudden perturbations. First, the effect of hysteresis nonlinearity from the piezoelectric actuator is considered by Prandtl-Ishlinskii (P-I) hysteresis model. Simultaneously, a dynamic model of the flexible plate with piezoelectric actuator is considered. Then, based on the dynamic model of the flexible plate, operator-based controllers are designed to guarantee the robust stability of the nonlinear control system. In addition, for ensuring the desired vibration control performance of the flexible plate with a free vibration and sudden perturbations, operator-based compensation method is given by the proposed design scheme. In the designed compensator, the desired compensation performances of tracking and of perturbations are obtained by increasing the number of designed n-times feedback loops. Finally, both of numerical simulation and experimental result are shown to verify the effectiveness of the proposed design scheme.

This paper illustrates the synthesis of nonlinear feedforward controllers for chemical reactors. In most of the theoretical development and application of feedforward control only linear systems have been considered. There are, however, no inherent linear limitations in feedforward control. Since chemical reactors are usually nonlinear, the effectiveness of control should be improved by including nonlinearities in the design of feedforward controllers. This is particularly true for batch reactors because of the large changes in variables during a batch cycle. Continuous stirred‐tank reactors are studied with single and consecutive reactions of first and higher order. Effectiveness of linear and nonlinear feedforward controllers is compared for disturbances of various magnitude and direction. Feedforward control of batch and tubular reactors is also discussed.

Feedforward control is widely applied on active vibration isolation system to attenuate vibration caused by base disturbance. Design of feedforward controller is conventionally based on plant model. Nevertheless, accurate plant model is normally not easy to be obtained. A data-driven feedforward control method is proposed in this paper to tackle this issue. In this method, no accurate plant model is needed and the problem of designing feedforward controller is formulated as a parameter optimization problem. By adopting FIR filter as feedforward controller structure, the parameter optimization problem is proved to be a convex optimization problem. A parameter iteration scheme based on Gauss-Newton algorithm is proposed to solve this parameter optimization problem. Gradient acquisition is achieved by Toeplitz matrix method. Employing certain step size, the optimal solution can be obtained with only one iteration. The proposed data-driven feedforward control method is validated by simulation and experiments. Experiments are conducted on a pneumatic spring active vibration isolation system.

Feedforward control can be considered as the most well-known control approach to deal with measurable disturbances. It started to be used almost 100 years ago, and since then it is being used in most industrial processes. It is a very simple technique that has been used typically as a complement to PID control, although it can be combined with any feedback controller. The feedforward control design has traditionally been performed assuming perfect cancellation of the disturbance signal, and when this solution was not possible because of non-realisable problems, static design solutions were usually implemented. In the last decade, this issue has been researched and analysed, and new designs for feedforward control have appeared to face these problems. As a result, a set of new simple tuning rules have been obtained providing considerable improvements in the control system performance. This paper presents a summary of these contributions and a short history of feedforward control.

In this paper, the feedforward controller design problem for high-precision electromechanical servo systems that execute finite time tasks is addressed. The presented procedure combines the selection of the fixed structure of the feedforward controller and the optimization of the controller parameters by iterative trials. A linear parametrization of the feedforward controller in a two-degree-of-freedom control architecture is chosen, which results in a feedforward controller that is applicable to a class of motion profiles as well as in a convex optimization problem, with the objective function being a quadratic function of the tracking error. Optimization by iterative trials avoids the need for detailed knowledge of the plant, achieves the controller parameter values that are optimal with respect to the actual plant, and allows for the adaptation to possible variations that occur in the plant dynamics. Experimental results on a high-precision wafer stage and a desktop printer illustrate the procedure.

On Optimal Feedforward and ILC: The Role of Feedback for Optimal Performance and Inferential Control

A novel active method for multi-mode vibration control of an all-clamped stiffened plate (ACSP) is proposed in this paper, using the extended-state-observer (ESO) approach based on non-collocated acceleration sensors and piezoelectric actuators. Considering the estimated capacity of ESO for system state variables, output superposition and control coupling of other modes, external excitation, and model uncertainties simultaneously, a composite control method, i.e., the ESO based vibration control scheme, is employed to ensure the lumped disturbances and uncertainty rejection of the closed-loop system. The phenomenon of phase hysteresis and time delay, caused by non-collocated sensor/actuator pairs, degrades the performance of the control system, even inducing instability. To solve this problem, a simple proportional differential (PD) controller and acceleration feed-forward with an output predictor design produce the control law for each vibration mode. The modal frequencies, phase hysteresis loops and phase lag values due to non-collocated placement of the acceleration sensor and piezoelectric patch actuator are experimentally obtained, and the phase lag is compensated by using the Smith Predictor technology. In order to improve the vibration control performance, the chaos optimization method based on logistic mapping is employed to auto-tune the parameters of the feedback channel. The experimental control system for the ACSP is tested using the dSPACE real-time simulation platform. Experimental results demonstrate that the proposed composite active control algorithm is an effective approach for suppressing multi-modal vibrations.

The design of a linear, reduced-order, continuous or discrete-time feedforward controller (FFC) is presented. The FFC is located in the reference value branch of a linear feedback system of any order which is designed according to the damping optimum. The aim of the FFC is to decrease the control system reference response time, while retaining a low overshoot and a well-damped form of the reference step response. This is achieved by locating the FFC zeros with the aid of the extended magnitude optimum, which is provided in the continuous or discrete-time variant. The influence of a suboptimally designed feedback system with a reduced-order feedback controller on feedforward control is analyzed. Reduced and full-order FFCs are compared.

Flexure-guided fast tool servo (FTS) driven by piezoelectric actuator (PEA) has the advantages of high accuracy and high speed, which makes it has been widely applied in the microstructure surface processing. Unfortunately, PEA has complicated hysteresis nonlinearity, which will greatly reduce the processing accuracy. The common PID and other traditional control methods are hard to handle complex hysteresis nonlinearity issue. As a classic method of intelligent hysteresis modeling, the traditional artificial neural network (TANN) algorithm can model the hysteresis nonlinearity accurately, however, the high-frequency dynamic hysteresis modeling based on TANN is difficult to be achieved on-line. Therefore, a novel on-line sequential extreme learning machine (OS-ELM) modeling method is proposed in this work. A compound control strategy consists of the OS-ELM model and PID feedback (OSEP) controller is proposed. A series of validation experiments are successfully carried out. The parameter identification results show that the training speed of the OS-ELM model is 836 times faster than that of the TANN model, and the identification accuracy is improved by 475 times. The closed-loop control results show that the positioning accuracy with OS-ELM hysteresis compensation is 13 times higher than with TANN model. It proves that the FTS system can achieve a satisfactory performance (stroke: $\pmb{120}\mu \mathbf{m}$ , average linearity: 0.54%) under high closed-loop bandwidth 200Hz.