Inverse Multiplicative Structure Research Articles

Hysteresis Modeling and Compensation for Tendon-Sheath Mechanisms in Robot-Assisted Endoscopic Surgery Based on the Modified Bouc-Wen Model With Decoupled Model Parameters

The tendon-sheath mechanism (TSM) has been widely applied in flexible endoscopy (FE) and natural orifice transluminal endoscopic surgery (NOTES) owing to its advantages of remote force and displacement transmission, size reduction, compactness, and convenient implementation. However, the positioning accuracy of TSMs is highly restrained by the motion hysteresis due to the complex friction condition between the tendon and sheath. The hysteresis phenomenon has posed significant challenges for modeling and controlling TSMs. This paper proposes a modified Bouc-Wen-based mathematical model to characterize the asymmetric hysteresis loop with distinct inflection points. The model parameters are decoupled, facilitating identification and reducing computational costs. Moreover, the model has retained the Bouc-Wen model structure, allowing for efficient derivation of the feedforward compensator based on the inverse multiplicative structure. The compensator was derived and cascaded with the TSM system to suppress the hysteresis phenomenon. Totally 120 trials of experiments were conducted to validate the proposed model and the feedforward control scheme on the two TSMs with different accumulated curvatures of 180∘ and 360∘. The results indicated that the proposed method achieved a 25.5% and 43.9% lower estimation and compensation error than the classical Bouc-Wen model. Further, it is worth noting that the model parameter identification time consumption has been significantly reduced to 5.8ms. The proposed model and the feedforward compensator can effectively linearize the TSM system and further facilitate delicate operations in robot-assisted surgical procedures.

A new composite controller for trajectory tracking control of a piezo-driven bridge displacement amplifier

In this paper, a new composite controller (feedforward + feedback) is proposed for the trajectory tracking control of a piezo-driven bridge displacement amplifier. A hysteresis model considering dynamic effects is established based on the modified Bouc–Wen (MBW) model, which can describe the asymmetry and frequency-dependence behaviors. The effectiveness of the modified model is verified by the experimental comparison. A feedforward controller is designed to compensate for hysteresis nonlinearity based on the inverse multiplicative structure of the modified model. A feedback controller with the Kalman observer is designed based on a modified model predictive control (MMPC). The proportional term and integral term of feedback error are introduced into the MPC control law to improve the response speed and reduce the steady-state error. The proposed MBW + MMPC is compared with MBW + proportional–integral–derivative (PID), and MBW + MPC. The experimental tracking results of continuously differentiable signals and non-differentiable signals verify MBW + MMPC feasibility and show that it can improve tracking performance.

Recurrent-Neural-Network-Based Rate-Dependent Hysteresis Modeling and Feedforward Torque Control of the Magnetorheological Clutch

The complicated rate-dependent hysteresis due to the input current and rotation speed of the magnetorheological clutch (MRC) greatly hinders its applications in robotics. In this article, it is first proved that the Preisach model is a special diagonal recurrent neural network (dRNN) with a binary step activation function. Motivated by this, the condition and the internal knowledge of the classical dRNN in modeling the rate-dependent hysteresis are investigated and validated. To guarantee that such a condition holds in dRNN training, a new loss function is proposed. The coupled rate-dependent hysteresis of an MRC prototype is, then, precisely modeled by the dRNN with the current input and speed input. By employing the trained dRNN model, the MRC torque is controlled using the feedforward scheme with no external torque sensors. Taking the advantage of being free-of-parameter tuning for the classical inverse multiplicative structure control (IMSC), a dRNN-based IMSC is proposed by finding the best feasible neuron and solving a nonlinear function. Various experiments validate much better control accuracy and higher bandwidth of the IMSC over the model-based proportional–integral–derivative control.

Generalized Inverse Multiplicative Structure for Differential-Equation-Based Hysteresis Models

In this article, a generalized inverse multiplicative structure (GIMS) is developed for the purpose of compensating for the hysteresis effect represented by the differential-equation-based hysteresis model. The GIMS approach is an approximate inverse compensation approach, and it does not require the analytical solution of the differential equations. The novelty of the proposed GIMS is that it extends the classical inverse multiplicative structure and it can be applied to construct the inverse compensator for differential-equation-based hysteresis models that can be written into the proposed unified expression. The LuGre model and the backlash-like model are employed as examples in the simulations and experiments. Both results validate the effectiveness of the proposed compensation approach.

Inverse Compensator for A Simplified Discrete Preisach Model Using Model-Order Reduction Approach

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.

A Model Prediction Control Design for Inverse Multiplicative Structure Based Feedforward Hysteresis Compensation of a Piezo Nanopositioning Stage

The inherent hysteresis nonlinearity of piezoelectric actuators seriously deteriorates the tracking performance of piezo-actuated nanopositioning stage, especially in large stroke applications. Usually, the model of piezo-actuated stage is given by cascading a rate-independent hysteresis submodel with a linear dynamics submodel. This paper develops a composite model predictive control (MPC) with feedforward hysteresis compensation based on the inverse multiplicative structure. The feedforward controller has the merit of non-inverse requirement. The linear MPC is utilized as a feedback controller with the feature of simple solution for the feedforward compensation system. Experimental tracking results of sinusoidal signals at different frequencies as well as complex signals show that the proposed method can improve the tracking performance of the piezo-actuated stage, verifying its effectiveness.

Inverse Compensation of Hysteresis Using Krasnoselskii-Pokrovskii Model

The Krasnoselskii-Pokrovskii (KP) model, as one of the popular operator-based hysteresis models, is commonly used to describe the hysteresis nonlinearities, especially in the smart materials-based actuators. Due to the complex formulation of the KP model, it is a great challenge to construct the inverse for the KP model. In this paper, an inverse multiplicative structure (IMS) is employed to find the inverse of the KP model. The merit of IMS is that this approach is simple to implement and the detailed knowledge of the hysteresis model is not required. However, the IMS technique cannot be directly applied to construct the inverse compensator for the KP model due to its complexity. Toward this problem, a new expression of the KP model is developed, where the input variable is expressed explicitly. With this new expression, the KP model can fit into IMS. Experiments are conducted to validate the effectiveness of the developed inverse compensator on a piezoelectric platform.

Internal model-based feedback control design for inversion-free feedforward rate-dependent hysteresis compensation of piezoelectric cantilever actuator

This study proposes a new rate-dependent feedforward compensator for compensation of hysteresis nonlinearities in smart materials-based actuators without considering the analytical inverse model. The proposed rate-dependent compensator is constructed with the inverse multiplicative structure of the rate-dependent Prandtl–Ishlinskii (RDPI) model. The study also presents an investigation for the compensation error when the proposed compensator is applied in an open-loop feedforward manner. Then, an internal model-based feedback control design is applied with the proposed feedforward compensator to a piezoelectric cantilever actuator. The experimental results illustrate that the proposed feedforward–feedback control scheme can be used in micro-positioning motion control applications to enhance the tracking performance of the piezoelectric cantilever actuator under different operating conditions.

Multivariable classical Prandtl–Ishlinskii hysteresis modeling and compensation and sensorless control of a nonlinear 2-dof piezoactuator

A multivariable approach of modeling and feedforward control of rate-independent hysteresis in multi-dof piezoelectric actuators is proposed in this paper. For that, the classical Prandtl–Ishlinskii (CPI) hysteresis model is extended into multivariable. Then, based on the inverse multiplicative structure and on the multivariable CPI model, a compensator is suggested. The proposed compensator does not require an extra-calculation: As soon as the model is identified, the compensator is obtained by structure. Furthermore, inversion of the model is avoided. Additionally to the hysteresis suppression, the multivariable compensator permits to reduce the cross-couplings between the axes which is not possible with standard techniques. The modeling and the inversion-free compensator are afterward applied to a two-degrees-of-freedom (2-dof) piezoactuator. The extensive investigated experimental tests demonstrate that the strong cross-couplings and the strong hysteresis in the two axes can be substantially reduced and linearized, respectively.

Bouc–Wen Modeling and Feedforward Control of Multivariable Hysteresis in Piezoelectric Systems: Application to a 3-DoF Piezotube Scanner

This paper is concerned with multivariable coupled hysteretic systems. The traditional Bouc-Wen monovariable hysteresis model devoted to 1 degree of freedom (DoF) actuated systems is extended to model the hysteresis in systems with multiple DoF, which typify strong cross-couplings. The proposed approach is able to model and to compensate for known hysteresis nonlinearities that affect smart materials. First, after presenting the new multivariable hysteresis Bouc-Wen model, a procedure of identification of its parameters is proposed. Then, we propose a multivariable compensator for the hysteresis. The compensator is based on the combination of the inverse multiplicative structure with the model, which permits to avoid additional calculation of its parameters. Such advantage is essential when the number of DoF is high. All along this paper, the cases of underactuated, overactuated, and fully actuated hysteretic systems are discussed. Finally, the proposed method is used to model and to compensate for the hysteresis in a 3-DoF piezoelectric tube actuator. The experimental results demonstrate its efficiency to linearize the hysteresis in the direct transfers and to minimize the hysteresis of the cross-couplings.

Simultaneous compensation of hysteresis and creep in a single piezoelectric actuator by open-loop control for quasi-static space active optics applications

Owing to their excellent properties piezoelectric actuators are studied as embedded elements for the quasi-statically active shape control of spatial optical mirrors. However, unwanted nonlinear effects in piezoelectric actuators, i.e., hysteresis and creep, severely limit their performance. This paper aims at developing a control methodology to compensate hysteresis and creep in a piezoelectric actuator simultaneously for quasi-static space active applications. In the methodology developed, hysteresis and creep behaviors are successively compensated by open-loop control. First, a derivative Preisach model is proposed to accurately portray the hysteresis while requiring relatively few measurements and describing the detachment between major and minor loops. The inverse derivative Preisach model is derived and inserted in open-loop to achieve hysteresis compensation. Then, the creep in the hysteresis compensated piezoelectric actuator is described by the use of a nonlinear viscoelastic model and a low pass filter is suggested to eliminate the effect of the inverse derivative Preisach model on the step reference input. To invert the creep model, the concept of “input relaxation” is implemented and an inverse multiplicative structure allows identifying the parameters of the inverse model while circumventing the difficulty of a mathematical computation. Finally, by cascading the low pass filter, the inverse model of creep and the inverse derivative Preisach model one after the other with the single piezoelectric actuator, the simultaneous compensation of hysteresis and creep is achieved. Experimental results show that in the case of step-like reference signals the hysteresis and the creep in a piezoelectric actuator can be significantly reduced at the same time. It implies that the developed methodology is effective and feasible in space active optics applications for which quasi-static distortions need to be compensated.

Compensation of Hysteresis Nonlinearity in Magnetostrictive Actuators With Inverse Multiplicative Structure for Preisach Model

Compensation of hysteresis nonlinearities in smart material based actuators presents a challenging task for their applications. Many approaches have been proposed in the literature, including the inverse multiplicative scheme. The advantage for such a scheme is to avoid direct model inversions. However, the approach is mainly developed for the Bouc-Wen model. Focusing on the Preisach model which is utilized to describe magnetostrictive actuators, in this paper an inverse compensation approach for Preisach model using the inverse multiplicative structure is developed. Since the input signal is implicitly involved in the Preisach model, it imposes a great challenge to construct the inverse function of the model. To obtain an explicit expression of the input signal from its implicit form so that the inverse multiplicative technique can be applied, the Preisach model is decomposed into a non-memory part and memory part. Using this separation, it only requires to solve the inverse of the non-memory part to obtain an explicit expression of the input signal, thus avoiding constructing the inverse for entire complex dual integral formulation of the Preisach model. Experimental results for a magnetostrictive actuator demonstrate the effectiveness of the proposed approach.

Multivariable Generalized Bouc-Wen modeling, identification and feedforward control and its application to multi-DoF piezoelectric actuators

Abstract In the literature, the generalized Bouc-Wen model can track precisely asymmetric hysteresis nonlinearity. In this paper, we propose to extend this generalized model to multivariable hysteresis model that can track the nonlinearities in multi-degrees of freedom (multi-DoF) hysteretic actuated systems. In particular, these systems are typified by strong hysteresis couplings. Then, a method of identification of the multivariable hysteresis model is proposed. Finally, based on the inverse multiplicative structure, we propose a multivariable feedforward compensator of the nonlinearity. The proposed approach has been applied to a multi-DoF piezoelectric tube (piezotube) used in scanning probe microscopy and the experimental verification demonstrated its validity in terms of model precision and compensation efficiency.