Feedforward Control of Shape Memory Alloy Actuators Using Fuzzy-Based Inverse Preisach Model

Inverse hysteresis model with magnetic flux density and magnetic field intensity as input and output, respectively, is more preferred, compared with the forward one, for resolving the electromagnetic issues of electrical equipment in terms of magnetic vector potential or with voltage sources. And an inverse hysteresis model with high accuracy and high computation speed has a broader range of applications. However, the well-known classical Preisach hysteresis model is formulated with the forward form, and has the double integration of its distribution function, making it inconvenient and impractical in electrical engineering. In this article, an analytical inverse Preisach model is proposed for the first time. First, the analytical expressions of permeability of the initial magnetization curve, descending and ascending branches of the hysteresis loop are derived using one closed form of the Everett integral function. Subsequently, the analytical inverse Preisach model is derived by the difference method, considering the reversible magnetization component that the classical Preisach model cannot simulate with an odd function analytically. The experiment of one grain-oriented silicon steel sample and one non-oriented silicon steel sample, under different magnetic excitation levels, is conducted, and the accuracy and efficiency of the proposed analytical inverse Preisach model are confirmed by comparing its simulated hysteresis loops with the experimental ones and that computed with the widely used inverse Jiles–Atherton (J–A) hysteresis model.

This paper presents the classical Preisach hysteresis modeling and tracking control of a curved pre-stressed piezoceramic patch actuator system with severe hysteresis. The actuator is also flexible with very small inherent damping. It has potential applications in active antennas. A series of tests are conducted to study the hysteresis properties of the piezoceramic actuator system. The numerical expressions of the classical Preisach model for different input variations are presented. The classical Preisach model is applied to simulate the static hysteresis behavior of the system. Higher order hysteresis reversal curves predicted by the classical Preisach model are verified experimentally. The good agreement found between the measured and predicted curves showed that the classical Preisach model is an effective mean for modeling the hysteresis of the piezoceramic actuator system. Subsequently, the inverse classical Preisach model is established and applied to cancel the hysteresis the piezoceramic actuator system for the real-time microposition tracking control. In order to improve the control accuracy and to increase damping of the actuator system, a cascaded PD/lead-lag feedback controller is designed with consideration of the dynamics of the actuator. In the experiments, two cases are considered, control with major loop hysteresis compensation, and control with minor loop hysteresis compensation. Experimental results show that RMS tracking errors are reduced by 50% to 70% if the hysteresis compensation is added in the feedforward path in both cases. Therefore, hysteresis compensation with the feedback controller greatly improves the tracking control accuracy of the piezoceramic actuator.

In a controller design process, it is interesting to find the inverse model, in which the desired input signal of the system is determined by using a desired output of the system. In many cases, the inverse model problem is very difficult, and sometimes impossible to determine and implement. There are some methods to make an inverse dynamic model, such as computed torque control, which had been studied in the previous Chapters. The capability of the NNs to learn the inverse model of the plant has been investigated for many years; the NN can be used to learn an approximate inverse system. In this approach, the desired output of the dynamic system should be known, and the NN can be trained by the desired output of the dynamic system to obtain the inverse dynamic model. In early studies of adaptive learning control using an NN model, Barto et al. [1], Jordan [2], Miller et al. [3] and Psaltis et al. [4] addressed the problem of how to obtain the error signal for training the NN controller. Generally, the cost function, consisting of the squared norm of the output reference errors, can not correctly train the NN controller as an inverse dynamic model. Therefore, Jordan [2] proposed a forward-inverse-modeling, and Albus [5], Atkeson and Reinkensmeyer [6], Psaltis et al. [4], and Kuperstein and Rubinstein [7] used a direct-inverse-modeling to obtain the command-error for forming the inverse dynamic model as a feedforward controller. Moreover, Watanabe et al. [8] proposed a linear NN using feedforward NNs with two layers and a linear unit function in the output-layer. Kawato [9] proposed a learning method to obtain a feedforward controller, which uses the output of a feedback controller as the error for training an NN model. The conventional feedback controller is configured in parallel to the NN controller, in the same manner as reported by Gomi and Kawato [10], and Miyamoto et al. [11], but with a different SF and learning algorithm. In another work, Wada and Kawato [12] used a feedforward NN as an inverse dynamic model.

Chapter 2 - Generalized Scalar Preisach Models of Hysteresis

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.

The classical Preisach model has been unified using population dynamics, resulting in a bilinear product model. A practical numerical procedure has been devised for the calculation of the model parameters from measured magnetization data. Experimental magnetization curves have been analyzed by this method to obtain the material parameters and the modified Preisach density function for a sample of a recording tape, an iron wire, and a cold-rolled iron foil. Hysteresis curves and minor magnetization loops calculated from these data are compared with those measured. It is found that analysis using the bilinear product model can predict more general hysteresis loops than the classical Preisach model including reversible and noncongruent effects. The computation of the Preisach density function suffers from the same errors as the classical function, since it is also obtained by the method of second differences; however, the computation of the hysteresis loops smooths out the resulting noise.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Due to the high stiffness, high dynamic performance, the parallel manipulator presents great advantages in the industrial manufacture. However in the machining process, the external low frequency disturbance, e.g. the varying cutting force, has a significant effect on the control system of parallel manipulator, which presents a chatter phenomenon on the end-effector of manipulator. In this paper, a feed forward control strategy is proposed to eliminate the effect of the random external disturbance on the control system of parallel manipulator. By applying the external disturbance force on the inverse dynamic model, the compensation torque is calculated and fed forward into the manipulator driving joints to cancel out the effect of the disturbance acting on the manipulator end-effector. The key issue herein is to be able to establish the accurate dynamic model for the parallel manipulator. Furthermore, in order to guarantee the position precision of the manipulator, a feed forward model-based control strategy combined with the feedback loop PV (position and velocity) control has been developed based on the reference trajectory, which could relatively simplify the highly nonlinear control system of the parallel manipulator and obtain a stable tracking error model. The whole research has been carried out on a parallel manipulator named CaPaMan which has been built in the laboratory of robotics and mechatronics in university of Cassino and South Latium. The results show that the chatter phenomenon could be utterly depressed by the force compensation from the feed forward path of the external disturbance; meanwhile the model-based controller can guarantee the trajectory tracking accuracy within a stable error by choosing the suitable PV gains.

Atomic Force microscopy (AFM) is a powerful technology for observing and developing the micro/nano world, which has been bringing tremendous revolution opportunities to various fields. An AFM's maneuverability can be enhanced via modification into a nanorobotic system with its scanning probe working as the end-effector. The probe's spatial precision can easily reach to nanometer level, which is commonly actuated by smart materials, typically the piezoceramics. However, instinctive hysteretic characteristics ubiquitously exist in smart material actuators, which degrade their controllable positioning accuracy, especially for the open-loop cases. As common phenomena, input-output hysteretic relations of integrated AFM systems are generally complicated, caused by actuators' specific characteristics. Since the AFM based nanomanipulation requires slow operations to prevent damage from samples and the sharp probe itself, commonly only hysteresis at low frequency (typically less than 10Hz) need to be reduced. To precisely represent and further reduce generalized hysteretic effects at low frequency, this paper proposes the equivalent representation of the classical Preisach model with analytical inversion. The contributions of this paper are: it is the first time that the exact inversion is established for the Preisach model with generalized discrete representation; furthermore, while maintaining modeling accuracy, the new discrete Preisach model significantly reduces model complexity compared to the traditional Preisach model. Numerical verification was conducted to demonstrate the effectiveness of the proposed discrete Preisach model and its analytical inversion.

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.

Lead, Zirconate, Titanate ceramics undergo polarization switching under electric fields, resulting in polarization hysteresis and strain butterfly loops. In addition, compressive stress inputs lead to ferroelastic 90 degree(s) polarization switching which interacts with the ferroelectric switching under the combined electric fields and stress inputs. In this paper, the phenomenological scalar Preisach model is modified consistent with the above physical phenomena to simulate the polarization and strain loops under the combined electric field and stress inputs. The hysterons that are used in the classical Preisach model are modified to take into account the effect of stress inputs and the effect of polarization switching. Simulations are carried out and the model is suggested as a simulation tool for nonlinear transformations occurring in materials.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

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

This paper proposes a new feed-forward control strategy for a plant with non-minimum phase dynamics. A Feed-Forward controller is very essential for controlling plants with time-varying reference signals. However, designing this type of controller is a non-trivial problem in case the plant dynamics is non-minimum-phase. This is because, this controller design involves the concept of inversion of the plant model and inverse of a non-minimum-phase plant model is unstable or non-causal. For this problem, usually an approximate inversion of a plant model is applied. An approach with corrected-approximate-inverse (CAI) method is available for feed forward controller design. After analyzing the results and discussion of this CAI technique, it is seen that although it seems to be working perfectly for small duration of time but its performance is unsatisfactory in case of large span of time. Therefore, in this paper, a new feed-forward control strategy has been designed to erase the above said problem. This method has adopted a simple version of an internal plant-model structure in its time domain. The fixed-structure feed forward controller that is constructed using this method is usually a linear amalgamation of a reference trajectory and its time-derivatives with suitable weighting factors. This control strategy has been verified with appropriate simulation results applied to a studied plant and results are compared with that of the CAI technique.

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.

ABSTRACTThe considered transport systems, which possess an actuator with a spatial influence characteristic along the transport path, are used for the transport of material between different process stages and for the conditioning of the conveyed goods at the same time. The spatially acting input results in complex input/output behaviour of a Single-Input Single-Output (SISO) system with distributed delays. The feedforward control task under consideration is defined by a setpoint change of the subsequent process stage. For the feedforward controller design, an inversion-based approach in the frequency domain is investigated to steer the output of the transport system towards a predefined constant value. In order to compensate model uncertainties and reject unknown disturbances, the results of the inversion-based feedforward control are used to design a feedback controller.

This study proposed a combined predictive feedforward and feedback control strategy and used the predicted value as the reference value of the feedforward controller. In wind turbine with large changes in wind conditions, the pitch actuator had not changed in real time and the feedback control signal had the problem of hysteresis. The control strategy was the predictive feedforward controller combined with the feedback controller optimized by the distributed parallel firefly algorithm (DPFA). The variable pitch actuator changed pitch angle in advance to achieve the purpose of smooth power output of wind turbine. Finally, the algorithms and control strategies proposed in this article were applied to megawatt-level wind turbines and compared with traditional control strategies. The simulation results show that the predictive feedforward-feedback control strategy have a better control effect.