Intelligent control of nonlinear systems with actuator saturation using neural networks

Common actuator nonlinearities such as saturation, deadzone, backlash, and hysteresis are unavoidable in practical industrial control systems, such as computer numerical control (CNC) machines, xy-positioning tables, robot manipulators, overhead crane mechanisms, and more. When the actuator nonlinearities exist in control systems, they may exhibit relatively large steady-state tracking error or even oscillations, cause the closed-loop system instability, and degrade the overall system performance. Proportional-derivative (PD) controller has observed limit cycles if the actuator nonlinearity is not compensated well. The problems are particularly exacerbated when the required accuracy is high, as in micropositioning devices. Due to the non-analytic nature of the actuator nonlinear dynamics and the fact that the exact actuator nonlinear functions, namely operation uncertainty, are unknown, the saturation compensation research is a challenging and important topic with both theoretical and practical significance. Adaptive control can accommodate the system modeling, parametric, and environmental structural uncertainties. With the universal approximating property and learning capability of neural network (NN), it is appealing to develop adaptive NN-based saturation compensation scheme without explicit knowledge of actuator saturation nonlinearity. In this dissertation, intelligent anti-windup saturation compensation schemes in several scenarios of nonlinear systems are investigated. The nonlinear systems studied within this dissertation include the general nonlinear system in Brunovsky canonical form, a second order multi-input multi-output (MIMO) nonlinear system such as a robot manipulator, and an underactuated system-flexible robot system. The abovementioned methods assume the full states information is measurable and completely known. During the NN-based control law development, the imposed actuator saturation is assumed to be unknown and treated as the system input disturbance. The schemes that lead to stability, command following and disturbance rejection is rigorously proved, and verified using the nonlinear system models. On-line NN weights tuning law, the overall closed-loop performance, and the boundedness of the NN weights are rigorously derived and guaranteed based on Lyapunov approach. The NN saturation compensator is inserted into a feedforward path. The simulation conducted indicates that the proposed schemes can effectively compensate for the saturation nonlinearity in the presence of system uncertainty

Adaptive Control

Adaptive control has been a remarkable field for industrial and academic research since 1950s. Since more and more adaptive algorithms are applied in various control applications, it is becoming very important for practical implementation. As it can be confirmed from the increasing number of conferences and journals on adaptive control topics, it is certain that the adaptive control is a significant guidance for technology development.The authors the chapters in this book are professionals in their areas and their recent research results are presented in this book which will also provide new ideas for improved performance of various control application problems

Adaptive neural control of nonlinear systems with hysteresis

Ph.DDOCTOR OF PHILOSOPH

On the adaptive controls of nonlinear systems with different hysteresis model representations

The hysteresis phenomenon occurs in diverse disciplines ranging from physics to biology, from material science to mechanics, and from electronics to economics. When the hysteresis nonlinearity precedes a controlled system, the nonlinearity usually causes the overall closed-loop system to exhibit inaccuracies or oscillations, even leading to instability. Control techniques to mitigate the unwanted effects of hysteresis have been studied for decades and have recently once again attracted significant attention. In this thesis, several adaptive control strategies are developed for systems with different hysteresis model representations to guarantee the basic stability requirement of the closed-loop systems and to track a desired trajectory with a certain precision. These proposed strategies to mitigate the effects of hysteresis are as follows: i). With the classical Duhem model, an observer-based adaptive control scheme for a piezoelectric actuator system is proposed. Due to the unavailability of the hysteresis output, an observer-based adaptive controller incorporating a pre-inversion neural network compensator is developed for the purpose of mitigating the hysteretic effects; ii). With the Prandtl-Ishlinskii model, an adaptive tracking control approach is developed for a class of nonlinear systems in p-normal form by using the technique of adding a power integrator to address the challenge of how to fuse this hysteresis model with the control techniques to mitigate hysteresis, without necessarily constructing a hysteresis inverse; iii). With a newly proposed hysteresis model using play-like operators, two control strategies are proposed for a class of nonlinear systems: one with sliding mode control and the other with backstepping technique

Discrete Modeling and Sliding Mode Control of Piezoelectric Actuators

With the ability to generate fine displacements with a resolution down to sub-nanometers, piezoelectric actuators (PEAs) have found wide applications in various nano-positioning systems. However, existence of various effects in PEAs, such as hysteresis and creep, as well as dynamics can seriously degrade the PEA performance or even lead to instability. This raises a great need to model and control PEAs for improved performance, which have drawn remarkable attention in the literature. Sliding mode control (SMC) shows its potential to the control of PEA, by which the hysteresis and other nonlinear effects can be regard as disturbance to the dynamic model and thus rejected or compensated by its switching control. To implement SMC in digital computers, this research is aimed at developing novel discrete models and discrete SMC (DSMC)-based control schemes for PEAs, along with their experimental validation. The first part of this thesis concerns with the modeling and control of one-degree of freedom (DOF) PEA, which can be treated as a single-input-single-output (SISO) system. Specifically, a novel discrete model based on the concept of auto-regressive moving average (ARMA) was developed for the PEA hysteresis; and to compensate for the PEA hysteresis and improve its dynamics, an output tracking integrated discrete proportional-integral-derivative-based SMC (PID-SMC) was developed. On this basis, by making use of the availability of PEA hysteresis models, two control schemes, named “the discrete inversion feedforward based PID-SMC” and “the discrete disturbance observer (DOB)-based PID-SMC”, were further developed. To illustrate the effectiveness of the developed models and control schemes, experiments were designed and conducted on a commercially available one-DOF PEA, as compared with the existing ones. The second part of the thesis presents the extension of the developed modeling and control methods to multi-DOF PEAs. Given the fact that details with regard to the PEA internal configurations is not typically provided by the manufacturer, a state space model based on the black box system identification was developed for the three-DOF PEA. The developed model was then integrated in the output tracking based discrete PID-SMC, with its effectiveness verified through the experiments on a commercially available three-DOF PEA. The superiority of the proposed control method over the conventional PID controller was also experimentally investigated and demonstrated. Finally, by integrating with a DOB in the discrete PID-based SMC, a novel control scheme is resulted to compensate for the nonlinearities of the three-DOF PEA. To verify its effectiveness, the discrete DOB based PID-SMC was applied in the control experiments and compared with the existing SMC. The significance of this research lies in the development of the discrete models and PID-based SMC for PEAs, which is of great help to improve their performance. The successful application of the proposed method in the control of multi-DOF PEA allows the application of SMC to the control of complicated multi-inputs-multi-outputs (MIMO) systems without details regarding the internal configuration. Also, integration of the inversion based feedforward control and the DOB in the SMC design has been proven effective for the tracking control of PEAs

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

Modeling and Control of Magnetostrictive-actuated Dynamic Systems

Magnetostrictive actuators featuring high energy densities, large strokes and fast responses appear poised to play an increasingly important role in the field of nano/micro positioning applications. However, the performance of the actuator, in terms of precision, is mainly limited by 1) inherent hysteretic behaviors resulting from the irreversible rotation of magnetic domains within the magnetostrictive material; and 2) dynamic responses caused by the inertia and flexibility of the magnetostrictive actuator and the applied external mechanical loads. Due to the presence of the above limitations, it will prevent the magnetostrictive actuator from providing the desired performance and cause the system inaccuracy. This dissertation aims to develop a modeling and control methodology to improve the control performance of the magnetostrictive-actuated dynamic systems. Through thorough experimental investigations, a dynamic model based on the physical principle of the magnetostrictive actuator is proposed, in which the nonlinear hysteresis effect and the dynamic behaviors can both be represented. Furthermore, the hysteresis effect of the magnetostrictive actuator presents asymmetric characteristics. To capture these characteristics, an asymmetric shifted Prandtl-Ishlinskii (ASPI) model is proposed, being composed by three components: a Prandtl-Ishlinskii (PI) operator, a shift operator and an auxiliary function. The advantages of the proposed model are: 1) it is able to represent the asymmetric hysteresis behavior; 2) it facilitates the construction of the analytical inverse; 3) the analytical expression of the inverse compensation error can also be derived. The validity of the proposed ASPI model and the entire dynamic model was demonstrated through experimental tests on the magnetostrictive-actuated dynamic system. According to the proposed hysteresis model, the inverse compensation approach is applied for the purpose of mitigating the hysteresis effect. However, in real systems, there always exists a modeling error between the hysteresis model and the true hysteresis. The use of an estimated hysteresis model in deriving the inverse compensator will yield some degree of hysteresis compensation error. This error will cause tracking error in the closed-loop control system. To accommodate such a compensation error, an analytical expression of the inverse compensation error is derived first. Then, a prescribed adaptive control method is developed to suppress the compensation error and simultaneously guaranteeing global stability of the closed loop system with a prescribed transient and steady-state performance of the tracking error. The effectiveness of the proposed control scheme is validated on the magnetostrictive-actuated experimental platform. The experimental results illustrate an excellent tracking performance by using the developed control scheme