Sign Gradient Descent Algorithms for Kinetostatic Protein Folding

This paper proposes a sign gradient descent (SGD) algorithm for predicting the three-dimensional folded protein molecule structures under the kinetostatic compliance method (KCM). In the KCM framework, which can be used to simulate the range of motion of peptide-based nanorobots/nanomachines, protein molecules are modeled as a large number of rigid nano-linkages that form a kinematic mechanism under motion constraints imposed by chemical bonds while folding under the kinetostatic effect of nonlinear interatomic force fields. In a departure from the conventional successive kinetostatic fold compliance framework, the proposed SGD-based iterative algorithm in this paper results in convergence to the local minima of the free energy of protein molecules corresponding to their final folded conformations in a faster and more robust manner. KCMbased folding dynamics simulations of the backbone chains of protein molecules demonstrate the effectiveness of the proposed algorithm.Comment: 6 pages, Accepted in 2023 International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS 2023

Generalized Prandtl-Ishlinskii hysteresis model and its analytical inverse for compensation of hysteresis in smart actuators

Smart actuators such as piezoceramics, magnetostrictive and shape memory alloy actuators, invariably, exhibit hysteresis, which has been associated with oscillations in the open-loop system's responses, and poor tracking performance and potential instabilities of the close-loop system. A number of phenomological operator-based hysteresis models such as the Preisach model, Krasnosel'skii-Pokrovskii model and Prandtl-Ishlinskii model, have been formulated to describe the hysteresis nonlinearities and to seek compensation of the hysteresis effects. Among these, the Prandtl-Ishlinskii model offers greater flexibility and unique property that its inverse can be attained analytically. The Prandtl-Ishlinskii model, however, is limited to rate-independent and symmetric hysteresis nonlinearities. In this dissertation research, the unique flexibility of the Prandtl-Ishlinskii model is explored for describing the symmetric as well as nonlinear hysteresis and output saturation properties of smart actuators, and for deriving an analytical inverse for effective compensation. A generalized play operator with dissimilar envelope functions is proposed to describe asymmetric hysteresis and output saturation nonlinearities of different smart actuators, when applied in conjunction with the classical Prandtl-Ishlinskii model. Dynamic density and dynamic threshold functions of time rate of the input are further proposed and integrated in the classical model to describe rate-dependent symmetric and asymmetric hysteresis properties of smart actuators. A fundamental relationship between the thresholds of the classical and the resulting generalized models is also formulated to facilitate parameters identification. The validity of the resulting generalized Prandtl-Ishlinskii models is demonstrated using the laboratory-measured data for piezoceramic, magnetostrictive and SMA actuators under different inputs over a broad range of frequencies. The results suggest that the proposed generalized models can effectively characterize the rate-dependent as well as rate-independent hysteresis properties of a broad class of smart actuators with output saturation. The properties of the proposed generalized models are subsequently explored to derive its inverse to seek an effective compensator for the asymmetric as well as rate-dependent hysteresis effects. The resulting inverse is applied as a feedforward compensator and simulation results are obtained to demonstrate its effectiveness in compensating the symmetric as well as asymmetric hysteresis of different smart actuators. The effectiveness of the proposed analytical inverse model-based real-time compensator is further demonstrated through its implementation in the laboratory for a piezoceramic actuator. Considering that the generalized Prandtl-Ishlinskii model provides an estimate of the hysteresis properties and the analytical inverse is a hysteresis model, the output of the inverse compensation is expected to yield hysteresis, although of a considerably lower magnitude. The expected compensation error, attributed to possible errors in hysteresis characterization, is analytically derived on the basis of the generalized model and its inverse. The design of a robust controller is presented for a system preceded by the hysteresis effects of an actuator using the proposed error model. The primary purpose is to fuse the analytical inverse compensation error model with an adaptive controller to achieve to enhance tracking precision. The global stability of the chosen control law and the entire closed-loop system is also analytically established. The results demonstrated significantly enhanced tracking performance, when the inverse of the estimated Prandtl-Ishlinskii model is considered in the closed-loop control system

Hysteresis modeling and experimental verifications of piezoelectric ceramics based actuators

There is an increasing usage of piezoceramic actuators in micropostioning applications, because they offer many desirable properties, such as fast response, high stiffness, and no backlash. Since piezoceramic materials are ferroelectric, they are fundamentally nonlinear in their response to an applied electric field, exhibiting a hysteresis effect between the electric field and the displacement. This usually causes undesirable inaccuracy or oscillations and even instability, which may severely limit the performance of the piezoceramic actuator system. One way to compensate hysteresis into set up a model that adequately describes the hysteresis and use it in a control loop. Focusing on a piezoelectric actuator from Physik Instrument Company, this thesis concentrates on modeling of hysteresis by using both the Preisach model and Prandtl-Ishlinskii model. The experiment on the hysteresis behavior of the piezoelectric actuator is carried out. Based on the measured data, a detailed discussion on the parameters identification for the two models is given and two models for the given piezoelectric actuator are therefore obtained. The validity of the two models is verified by comparing the actual and the model response of the piezoelectric actuator. The validity of the models is tested by comparing the actual and predicted response of the stacked piezoceramic actuator to input voltages

An RST control design based on interval technique for piezomicropositoning systems with rate-dependent hysteresis nonlinearities

We propose a feedforward-feedback con-trol of piezomicropositioing systems devoted to pre-cise positioning over different operating conditions. Such systems exhibit rate-dependent hysteresis non-linearities and badly damped oscillations character-istics. First, we introduce a rate-dependent Prandtl-Ishlinskii (RDPI) inverse model for feeforward com-pensation of hysteresis. This yields to compensation that can be characterized by an uncertain linear model with disturbances. To model the uncertainties, we suggest to use intervals then we propose a new interval design for a RST structured feedback controller. The proposed design method permits to satisfy prescribed performances. Simulation and experiments on a piezo-electric tube actuator are carried out and demonstrate the efficiency of the proposed control design

On hysteresis modeling of a piezoelectric precise positioning system under variable temperature

We propose the modeling of hysteresis nonlinearities in a piezoelectric material-based tube actuator classically employed in precise positioning applications under different sur-rounding temperatures. Beyond the voltage-to-displacement hysteresis nonlinearities they exhibit, these actuators are sensitive to the surrounding temperature. Therefore, contrary to the existing works in the literature where the two phenomena were treated individually,this paper suggests to model the hysteresis nonlinearities and the temperature effects si-multaneously. First an experimental study was performed to investigate the effects of the surrounding temperature on the voltage-to-displacement hysteresis loops of the piezoelectric tube actuators. The experimental results show that increasing the input surrounding temperature contributes an increase in the voltage-to-displacement sensitivity of the piezoelectric tube actuator under the input voltage range considered in the experimental tests. Then, two different nonlinear temperature-dependent hysteresis models a temperature-dependent (TD) electromechanical model and a temperature-dependent Prandtl-Ishlinskii model (TD-PI) were proposed to account the temperature effects on the hysteresis nonlinearity. In first, the mathematical formulation of TD-electromechanical model was presented to describe the electrical and mechanical properties of piezoelectric tube actuator. This model integrates the temperature dependent electromechanical coupling factor to model the temperature effects, the Simscape library in MATLAB-Simulink software was used to develop a physical simulation for the TD-electromechanical model. In a second time, a TD-PI model was proposed to describe the voltage-to-displacement characteristic of piezoelectric tube actuator using a proposed temperature shape function. The parameters of the two proposed models were estimated using proposed optimization algorithms based on Grey Wolf Optimizer (GWO). The modeling results demonstrate that the two proposed models can account for the hysteresis nonlinearities of the piezoelectric tube actuators under different levels of the surrounding temperatures. Finally, the analytical inverse of TD-PI model was derived and applied in feed forward manner to compensate the hysteresis nonlinearities under different levels of the surrounding temperatures

Temperature dependent hysteresis modeling of a piezoelectric tube using Elman neural network

In this study, the hysteresis nonlinearities of a piezotube actuator are investigated under different levels of surrounding temperature. The experimental results show that increasing of the surrounding temperature contributes to an increase in the output displacement of the piezotube actuator under the input range that is considered in the experimental tests. In this study, we develop a hysteresis model integrates the dead-zone operator with Elman Neural Network (ENN) to model the temperature-dependent hysteresis nonlinearities. The simulation results show that the proposed temperature-dependent hysteresis model accounts for the temperature effects on the voltage-to-displacement hysteresis nonlinearities. The results show that the proposed model can characterize the voltage-to-displacement hysteresis loops over different levels of surrounding temperature

Kinodynamic Generation of Wafer Scanners Trajectories Used in Semiconductor Manufacturing

The operation time of an ideal reliable wafer scanner model is defined at the die level where the actual exposure process takes place as the time unit per die, or at the wafer substrate level as the time unit per wafer substrate. Therefore, the machine throughput is given as the reciprocal of the operation time. The involved motion profiles of a machine, namely the step-and-scan trajectories, function as the heartbeats that drive its multidisciplinary elements, which suggests that a multidisciplinary design optimization should be involved when such profiles are selected or designed. This is also true when considering the traverse motion profiles among rows and columns within the wafer substrate. The step-and-scan trajectories affect the machine throughput, performance, and die yield. The effects of tracking such profiles appear as structural vibration, tracking errors, and thermal loading at various machine elements such as the actuators, the reticle, the wafer, and the projection elements specifically when the exposure high-energy duration and frequency are not taken into consideration while designing the reference motion. From the dynamics perspective, having a reference motion with nonzero and bounded higher-order derivatives is recommended since it enhances the tracking performance of the machine, however, its ability to increase the operation time is usually overlooked. In an attempt to understand such effects, we present a case study that outlines the aforementioned aspects using three step-and-scan profiles of mainly $3^{rd}$ -order. Taking the dynamics of the driven stage into consideration through input shaping, both the step-and-scan and traverse motion profiles are analyzed. We provide analytical expressions that can be used to generate both types of motion profiles on the fly without additional optimization. A simulation example of a simplified wafer scanner machine shows the usefulness of the proposed framework. Note to Practitioners - Choosing the most suitable operating conditions of a lithography machine is challenging. These conditions affect machine productivity, profit margin, and maintenance. In this paper, we reveal the relation between the selection of operating conditions based on several decision variables- and the kinodynamic step-and-scan trajectory generation based on specific machine parameters and clients' requirements. Being chart-based, the selection process of an operating point can be less practical at some points. However, using appropriate curve fitting tools, the information provided in the optimal operating charts can be put into suboptimal closed-form expressions that facilitate the selection process. Therefore, the designed trajectories parameters can be easily saved in lookup tables for ease of evaluation and future use. This helps in accommodating changes in the operation plans and flexible manufacturing systems. Also, starting with a given set of machine parameters, it is possible to calculate the optimal machine operating point when the input shaping technique is used, as illustrated in this paper.</p

Adaptive Control of Uncertain Hammerstein Systems with Hysteretic Nonlinearities

Abstract-We numerically investigate the sense in which an adaptive control law achieves internal model control of Hammerstein plants with Prandtl-Ishlinskii hysteresis. We apply retrospective cost adaptive control (RCAC) to a commandfollowing problem for uncertain Hammerstein systems with hysteretic input nonlinearities. The only required modeling information of the linear plant is a single Markov parameter. Describing functions are used to determine whether the adaptive controller inverts the plant at the exogenous frequencies

Inversion-Free Adaptive Control of Uncertain Systems with Shape-Memory-Alloy Actuation

Abstract-We apply retrospective cost adaptive control (RCAC) to a command-following problem for an uncertain shape-memory-alloy (SMA) actuator. The SMA actuator is characterized by a Wiener model consisting of linear dynamics that convert the input voltage or current to a temperature, and a hysteresis model that characterizes the relationship between the temperature and the output displacement. We use the generalized Prandtl-Ishlinskii model to characterize the inputoutput relationship between the temperature and the output displacement in the SMA actuator

Enhancement of Micro-positioning Accuracy of a Piezoelectric Positioner by Suppressing the Rate-Dependant Hysteresis Nonlinearities

Abstract-Compensation of rate-dependent hysteresis nonlinearities of a Piezoelectric positioner is carried out by integrating the inverse of the ratedependent Prandtl-Ishlinskii model as a feedforward compensator. The proposed compensator was subsequently implemented to the positioner hardware in the laboratory to study its potential for ratedependent hysteresis compensation on a real-time basis. The experimental results obtained under different excitation frequencies revealed that the integrated inverse compensator can substantially suppress the hysteresis nonlinearities in the entire frequency range considered in the study. The proposed inverse model compensates for the rate-dependent hysteresis nonlinearities without using the feedback control techniques