This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

A survey on hysteresis modeling, identification and control

In this article, the adaptive fault-tolerant control (FTC) problem is solved for a switched resistance–inductance–capacitance (RLC) circuit system. Due to the existence of faults which may lead to instability of subsystems, the innovation of this article is that the unstable subsystems are taken into account in the frame of output constraint and unmeasurable states. Obviously, there are not any unstable subsystems in unswitched systems. The unstable subsystems will involve many serious consequences and difficulties. Since the system states are unavailable, a switched state observer is designed. In addition, the fuzzy-logic systems (FLSs) are employed to approximate unknown internal dynamics in the controller design procedure. Then, the barrier Lyapunov function (BLF) is exploited to guarantee that the system output satisfy its constrained interval. Moreover, by using the average dwell-time method, all signals in the resulting systems are proofed to be bounded even when faults occur. Finally, the proposed strategy is carried out on the switched RLC circuit system to show the effectiveness and practicability.

Barrier Lyapunov Function-Based Adaptive Fuzzy FTC for Switched Systems and Its Applications to Resistance–Inductance–Capacitance Circuit System

Application of neural network algorithm in fault diagnosis of mechanical intelligence

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.

Inverse Compensation of Hysteresis Using Krasnoselskii-Pokrovskii Model

Magnetic shape memory alloy (MSMA) based actuators are extensively applied in the fields of precision manufacturing and micro/nano technology. Nevertheless, the inherent hysteresis in the MSMA-based actuator severely hinders its further application. In this letter, the characteristics of hysteresis behavior under different input signals are investigated. Then, a nonlinear auto-regressive moving average with exogenous inputs (NARMAX) model based on a diagonal recurrent neural network (DRNN) is used to construct the rate-dependent hysteresis model. To improve the capability of characterizing the multi-valued mapping of the hysteresis loop, the play operator is adopted as the exogenous variable function of the NARMAX model. To verify the effectiveness of the proposed model, a series of comparisons are implemented. The experimental results show that the proposed NARMAX model based on the DRNN exhibits excellent modeling performance.

NARMAX Model-Based Hysteresis Modeling of Magnetic Shape Memory Alloy Actuators

Piezo-actuated stages are widely applied in the field of high-precision positioning. However, piezo-actuated stages produce hysteresis between the input voltage and the output displacement that negatively influences the positioning accuracy. In this paper, the Bouc–Wen model is established and identified using the bat-inspired optimization algorithm. Subsequently, based on the established hysteresis model, we propose a sliding mode control method with a new reaching law to suppress the hysteresis nonlinearity and achieve high-precision tracking control for the piezo-actuated stages. In addition, the proposed control method contains the perturbation estimation part, which can estimate online the modeling uncertainty and the unknown external disturbances. The stability of the proposed control method is demonstrated through the Lyapunov theory. Finally, to validate the effectiveness of the proposed control method, experiments are conducted on the piezo-actuated stages. Experimental results demonstrate that the proposed control method is superior to the feed-forward control and the conventional sliding mode control method.

Sliding Mode Tracking Control With Perturbation Estimation for Hysteresis Nonlinearity of Piezo-Actuated Stages

Piezo-actuated stages are widely applied in the high-precision positioning field nowadays. However, the inherent hysteresis nonlinearity in piezo-actuated stages greatly deteriorates the positioning accuracy of piezo-actuated stages. This paper first utilizes a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model based on the Pi-sigma fuzzy neural network (PSFNN) to construct an online rate-dependent hysteresis model for describing the hysteresis nonlinearity in piezo-actuated stages. In order to improve the convergence rate of PSFNN and modeling precision, we adopt the gradient descent algorithm featuring three different learning factors to update the model parameters. The convergence of the NARMAX model based on the PSFNN is analyzed effectively. To ensure that the parameters can converge to the true values, the persistent excitation condition is considered. Then, a self-adaption compensation controller is designed for eliminating the hysteresis nonlinearity in piezo-actuated stages. A merit of the proposed controller is that it can directly eliminate the complex hysteresis nonlinearity in piezo-actuated stages without any inverse dynamic models. To demonstrate the effectiveness of the proposed model and control methods, a set of comparative experiments are performed on piezo-actuated stages. Experimental results show that the proposed modeling and control methods have excellent performance.

https://iopscience.iop.org/article/10.1088/1361-665X/aaae28/pdf

A self-adaption compensation control for hysteresis nonlinearity in piezo-actuated stages based on Pi-sigma fuzzy neural network

A Bouc–Wen model is presented and identified based on the bat-inspired algorithm to describe the hysteresis of the piezo-actuated stage. Based on the established Bouc–Wen model, a sliding mode controller is proposed to suppress the hysteresis non-linearity of the piezo-actuated stages. In order to solve the buffeting problem in the process of control, the sign function is replaced by the sigmoid function. Experiment is performed to validate the effectiveness of the proposed sliding mode controller, and the results show that the maximum error of the motion tracking control of the piezo-actuated stage is 0.3264 μm.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/el.2016.3558

Sliding mode control with sigmoid function for the motion tracking control of the piezo-actuated stages

The typical characteristic of a magnetic shape memory alloy (MSMA) based actuator is rate-dependent and stress-dependent hysteresis. In addition, the hysteresis in an MSMA-based actuator includes memory, multi-valued mapping, and asymmetry properties, which seriously degrade the positioning accuracy. In this study, a feedforward neural network (FNN) based nonlinear autoregressive moving average with exogenous inputs (NARMAX) model is employed to describe the hysteresis in an MSMA-based actuator. Through a Taylor expansion, it is revealed how the FNN constructs the nonlinear function of the NARMAX model. For the controller implementation, an FNN-based iterative learning control (ILC) strategy is proposed to achieve the desired tracking performance. The contributions of this study include exploring the update rule of the FNN-based ILC and analyzing the convergence properties of the proposed controller when the initial state of the system varies. To verify the effectiveness of the proposed method, experiments on an MSMA-based actuator were conducted. The results illustrate that the proposed modeling and control methods achieve an excellent performance and that the theoretical results are correct.

Miaolei Zhou

Papers

NARMAX Model-Based Hysteresis Modeling of Magnetic Shape Memory Alloy Actuators

Sliding Mode Tracking Control With Perturbation Estimation for Hysteresis Nonlinearity of Piezo-Actuated Stages

A self-adaption compensation control for hysteresis nonlinearity in piezo-actuated stages based on Pi-sigma fuzzy neural network

Sliding mode control with sigmoid function for the motion tracking control of the piezo-actuated stages

Neural Network-based Iterative Learning Control for Hysteresis in Magnetic Shape Memory Alloy Actuator