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Abstract A high‐order improved model free adaptive control method based on iterative learning is designed to address the problem that primary permanent magnet linear motor has poor control performance, susceptibilities to load disturbances and other nonlinear disturbances during operation. The proposed algorithm adopts an improved dynamic linearization model and high‐order pseudo partial derivative estimation algorithm, which improves the data utilization of the data‐driven control algorithm, makes the algorithm better to describe the dynamic behaviour of the primary permanent magnet linear motor direct thrust force control system and improves the speed tracking accuracy and anti‐interference ability of the system. In addition, iterative learning control was adopted as feedforward compensation to further improve the control performance of the system and the stability of the closed‐loop system was analysed analytically. The simulation results show that the proposed control algorithm can improve the control accuracy of the system and suppress load disturbances and other nonlinear disturbances.

A high‐order improved model free adaptive control method based on iterative learning is designed to address the problem that primary permanent magnet linear motor has poor control performance, susceptibilities to load disturbances and other nonlinear disturbances during operation. The proposed algorithm adopts an improved dynamic linearization model and high‐order pseudo partial derivative estimation algorithm, which improves the data utilization of the data‐driven control algorithm, makes the algorithm better to describe the dynamic behaviour of the primary permanent magnet linear motor direct thrust force control system and improves the speed tracking accuracy and anti‐interference ability of the system. In addition, iterative learning control was adopted as feedforward compensation to further improve the control performance of the system and the stability of the closed‐loop system was analysed analytically. The simulation results show that the proposed control algorithm can improve the control accuracy of the system and suppress load disturbances and other nonlinear disturbances. [ABSTRACT FROM AUTHOR]

A dynamic system is considered where the regulating impact is the product of the control signal on the output variable of a linear dynamic system driven by the same applied control. The essence of the proposed method consists in the dynamic linearization of a nonlinear control operator, which makes it possible to guarantee a desired regulating impact. In a particular case, this approach corresponds to vector (field-oriented) control. It is shown that dynamic linearization based on the internal model method makes it possible to decompose a nonlinear system into a cascade of two subsystems. The proposed regulator consists of two blocks connected in series where the first block solves the problem of regulation with the Luenberger observer, and the second block compensates for a nonlinear dynamic operator. To demonstrate the effectiveness of the proposed approach, an example of numerical modeling of a neutrally stable plant with an output adaptive control is given. In practice, this method may be in demand in the tasks of controlling induction and synchronous motors and multi-link robotic manipulators.

This paper proposes a data‐driven bipartite leader‐following consensus strategy for a class of nonlinear multi‐agent systems (MASs) under external disturbances and hybrid attacks, which are composed of denial‐of‐service attacks and false data injection attacks. This data‐driven algorithm incorporates no system dynamics and only utilizes the input and output data generated by the controlled plant. First, the nonlinear MAS with external disturbances can be transformed into an equivalent linear data model by applying a revised dynamic linearization method. Second, a hybrid‐attack compensation mechanism is proposed to alleviate the adverse impact of data dropout caused by hybrid attacks. Then, based on the compensation mechanism, an extended state observer is designed that can mitigate the negative influence induced by external disturbances and improve the control performance even though the MAS is threatened by hybrid attacks. The systems under hybrid attacks and external disturbances can still remain stable with the proposed data‐driven strategy. Finally, simulation examples demonstrate the validity of the data‐driven strategy, and the bipartite consensus error can be reduced to a small range. [ABSTRACT FROM AUTHOR]

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The regulation of wastewater treatment plants (WWTPs) is a challenge due to their complex biological and chemical characteristics and their accurate mathematical model is generally not accessible because of the limitation of available measurements. To overcome such challenges, in this paper, a novel model-free adaptive nonsingular fast integral terminal sliding mode control (MFA-NFITSMC) is proposed. Firstly, based on the concept of dynamic linearization, a compact format dynamic linearized (CFDL) data model for the WWTP is established. Secondly, a novel fast integral terminal sliding mode surface is proposed to accelerate the convergence of tracking error and a discrete-time MFA-NFITSMC is created using the CFDL model as a basis; then, its stability is proved by theoretical analysis. Finally, the experimental verification is conducted based on the Benchmark Simulation Model No. 1 and the results show that the proposed method has a higher tracking accuracy and stronger robustness than other methods in the control of WWTPs. [ABSTRACT FROM AUTHOR]

Model‐free adaptive control (MFAC) is an effective data‐driven control method to deal with nonlinear and nonaffine systems. In this article, a data‐driven set‐point tuning (DDST) approach is proposed for MFAC to enhance its control performance. The proposed data‐driven set‐point tuning based MFAC (DDST‐MFAC) system consists of two control loops. The inner control loop takes the MFAC as the feedback controller where a virtual reference error signal is adopted in the control input. The DDST in the outer loop is derived from an ideal nonlinear set‐point tuning (NST) law, which exists in theory, to meet the control target. To realize the theoretically existing NST, a dynamic linearization (DL) technique is introduced. Virtually, the ideal NST law is independent of any controlled system, regardless linear or nonlinear, having an exact model or not. Since the nonlinear system considered in this work does not have any model information available to the designers, the parameter estimation law of the DDST is designed by using the DL method to transfer the original nonlinear system into a linear data model (LDM) with a projection algorithm to estimate the unknown parameters in the LDM. The convergence of tracking error is proved for a regulation scenario. Simulation study is provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

The current study presents a data-driven integral sliding mode predictive control method for a category of discrete-time repetitive nonlinear systems. At first, a compact form of iterative dynamic linearization (IDL) technology is utilized to establish an IDL data model. Then, considering the time and iterative domain simultaneously, an iterative integral sliding mode surface is constructed to establish an iterative integral sliding mode controller. The stability of the presented control strategy is then demonstrated through a precise mathematical analysis. Furthermore, to further reduce the control error, an iterative integral sliding mode predictive control strategy is established using the model predictive control. Since the proposed method is a data-driven control scheme, it only employs the online I/O data for parameter estimation and controller design. The effectiveness and monotonic convergence of the proposed schemes are evaluated through simulations. Comparative results with the data-driven optimal iterative learning controller (DDOILC) and the enhanced DDOILC indicate that the presented controller can provide a faster convergence and less tracking error. [ABSTRACT FROM AUTHOR]

The regulation of wastewater treatment plants (WWTPs) is a challenge due to their complex biological and chemical characteristics and their accurate mathematical model is generally not accessible because of the limitation of available measurements. To overcome such challenges, in this paper, a novel model-free adaptive nonsingular fast integral terminal sliding mode control (MFA-NFITSMC) is proposed. Firstly, based on the concept of dynamic linearization, a compact format dynamic linearized (CFDL) data model for the WWTP is established. Secondly, a novel fast integral terminal sliding mode surface is proposed to accelerate the convergence of tracking error and a discrete-time MFA-NFITSMC is created using the CFDL model as a basis; then, its stability is proved by theoretical analysis. Finally, the experimental verification is conducted based on the Benchmark Simulation Model No. 1 and the results show that the proposed method has a higher tracking accuracy and stronger robustness than other methods in the control of WWTPs.

In this paper, a distributed control algorithm based on a data-driven approach is developed to solve the consensus control of heterogeneous nonlinear Multi-Agent Systems (MAS). The consensus obtained from the solution of the Hamilton–Jacobi–Bellman (HJB) equation is challenging for unknown nonlinear systems. To address this issue, improved online reinforcement learning (RL) is employed to generate an approximate solution for each agent to achieve consensus. Unlike model-based RL and traditional algorithms, this method leverages I/O data to guide the learning of policies without any prior knowledge of agent dynamics. Furthermore, the adaptability of algorithm to heterogeneous nonlinear agents is enhanced by implementing online updates to the control strategy and dynamic linearization (DL). The convergence analysis of the algorithm is provided, along with the impact of the learning rate parameters on the consensus of MAS. By comparing with other data-driven methods, simulations are conducted to verify the stability and adaptability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this study a robust adaptive model-free depth tracking control scheme for the under-actuated lightweight autonomous underwater vehicle (LAUV) with guidance compensation and disturbance rejection, is presented. The proposed scheme includes a double-layer architecture including a kinematic guidance layer and a dynamic control layer. On the kinematic layer, the adaptive line-of-sight guidance with angle of attack compensation is employed to convert depth error into pitch error to address the under-actuated control issue. Additionally, a tracking differentiator is implemented to adjust the desired input parameters and to improve transient performance. On the kinetic layer, an improved model-free adaptive tracking algorithm based on I/O data-driven approaches is provided. The mathematical model is replaced by an approximate data model derived through dynamic linearization. In the proposed tracking scheme, an extended state observer in discrete time form is also incorporated to predict and compensate higher-order unmodeled dynamics and external disturbances. The proposed scheme has been validated through experimental results obtained from LAUV underwater maneuvering tests conducted in a towing tank. These results validate the algorithm's superiority and efficacy in achieving depth tracking control of LAUV, particularly in less accurate, complex and challenging modeling scenarios. • Improved adaptive tracking scheme without models is proposed for LAUV depth tracking. • Kinematic errors are estimated and compensated through ALOS guidance. • Residual terms based on the data model are estimated and compensated through DESO. • Simulation and experimental comparison results of several methods are provided. [ABSTRACT FROM AUTHOR]

This paper presents a new data driven control for a class of discrete-time multiple input and multiple output nonlinear systems which uses the principles of model-free adaptive control and the tensor product. The design of a linearization model using the notion of the tensor product overcomes reset problems in the calculation of the pseudo partial derivative and also improves control performance. The stability of the proposed method is guaranteed by theoretical analysis. Numerical simulation results and an experimental trial are presented to validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper the distributed leader-follower consensus tracking problem is investigated for unknown nonlinear non-affine discrete-time multi-agent systems. Via a dynamic linearization method both for the agent system and the local ideal distributed controller, a distributed adaptive control scheme is proposed in this paper using the Newton-type optimization method. The proposed approach is data-driven since only the local measurement information among neighboring agents is utilized in the control system design. The consensus tracking stabilities of the proposed approach are rigorously guaranteed in the cases of fixed and switching communication topologies. The simulations are conducted to verify the effectiveness of the proposed approach.

A forgetting factor based data-driven optimal iterative learning control method is proposed for a class of nonlinear nonaffine discrete-time systems running repeatedly in finite time. First, an iterative dynamic linearization method is introduced to transform the nonlinear system into a linear input and output incremental form. Second, the main problems of the optimal iterative learning method are analyzed. To solve the problem that the control input cannot respond in time due to the accumulation effect of historical information, an adaptive forgetting factor is designed to make the method more controllable and flexible. The proposed control method is a data-driven control approach, and the design and analysis process only depends on the input and output data of the system and does not contain any explicit model information. Finally, the effectiveness of the proposed method is verified by simulation results. [ABSTRACT FROM AUTHOR]

The linear motor tool feed system is an important part in noncircular turning. In this paper, the compact form dynamic linearization based model-free adaptive iterative control scheme (CFDL-MFAILC) and the full form dynamic linearization based model-free adaptive iterative control method scheme (FFDL-MFAILC) are designed for a complex nonlinear tool feed system. Theoretical analysis shows that the proposed scheme guarantees the output tracking error monotonic convergence along the iteration axis, and the FFDL-MFAILC is a complement and improvement to the CFDL-MFAILC. The designed control schemes are compared with PID and iterative learning feedforward and model-free adaptive predictive control feedback combination scheme (ILC-MFAPC) by simulations and experiments. Simulation results show that the proposed scheme can greatly decrease linear motor position error as iteration time increase, and has better position control advantages then other algorithms, the FFDL-MFAILC has faster convergence speed and smaller steady-state error than the CFDL-MFAILC. Experiment results prove that the proposed scheme is effective in linear motor tool feed system position control.

This work explores a model-free adaptive PID (MFA-PID) control for nonlinear discrete-time systems with rigorous mathematical analysis under a data-driven framework. An improved compact form dynamic linearization (iCFDL) is proposed to transfer the original nonlinear system into an affined linear data model including a nonlinear residual term. Both a time-difference estimator and a gradient parameter estimator are designed to estimate the nonlinear residual uncertainties and the unknown parameters in the iCFDL model. Subsequently, a novel improved CFDL based MFA-PID (iCFDL-MFA-PID) control is proposed by incorporating these two estimators. The results are extended by the use of improved partial format dynamic linearization (iPFDL) and full format dynamic linearization (iFFDL). The theoretical results are shown using contraction mapping principle-based mathematical analysis, as well as simulations. [ABSTRACT FROM AUTHOR]

• A linear data model of the nonlinear nonaffine system is derived to describe the linear I/O relationship of the system. • A new RLS identification method is proposed to predict system output by estimating the parameters in linear data model. • The number of unknown parameters in the linear data model can be tuned flexibly to reduce computation complexity. Aiming at identifying nonlinear systems, one of the most challenging problems in system identification, a class of data-driven recursive least squares algorithms are presented in this work. First, a full form dynamic linearization based linear data model for nonlinear systems is derived. Consequently, a full form dynamic linearization-based data-driven recursive least squares identification method for estimating the unknown parameter of the obtained linear data model is proposed along with convergence analysis and prediction of the outputs subject to stochastic noises. Furthermore, a partial form dynamic linearization-based data-driven recursive least squares identification algorithm is also developed as a special case of the full form dynamic linearization based algorithm. The proposed two identification algorithms for the nonlinear nonaffine discrete-time systems are flexible in applications without relying on any explicit mechanism model information of the systems. Additionally, the number of the parameters in the obtained linear data model can be tuned flexibly to reduce computation complexity. The validity of the two identification algorithms is verified by rigorous theoretical analysis and simulation studies. [ABSTRACT FROM AUTHOR]

This study proposes a data-driven adaptive filtering method for the fault diagnosis (DDAF-FD) of discrete-time nonlinear systems and provides a simultaneous online estimation of actuator and sensor faults. First, dynamic linearization was adopted to transform the nonlinear system into a quasi-linear model, which facilitated accurate modeling of the nonlinear system. Second, a data-driven adaptive fault diagnosis method was designed under the framework of data-driven filtering and the recursive least-squares algorithm using system I/O data only, and accurate real-time estimation of two fault factors was achieved. In addition, the simulation results demonstrate the effectiveness of the proposed method. The stability was verified via the Lyapunov method.

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Conventional model-based prediction (MBP) methods for spindle thermal errors have three serious contradictions: those between unmodeled dynamics and robustness, between model precision and model complexity, and between partial linearization and overall complexity. To avoid these contradictions, a new data-driven prediction (DDP) approach is applied to the dynamic linearization modeling for spindle thermal errors. In this model, the current thermal errors are predicted by history temperature data without the information of physical mechanisms. Four points along the spindle front bearing circle (left, right, front and back sides) are selected, whose temperatures are recorded in real time via thermocouples, and the average values are calculated. Then the temperature gradients of these four points are selected as the input to predict the axial and radial offsets and the tilt angle errors. The hysteresis phenomenon between temperature and deformation is determined via thermal characteristic tests, and the time interval for data input is identified . Furthermore, sufficient experimental tests verify that the DDP model is significantly better than the general model-based method in terms of accuracy and robustness. [ABSTRACT FROM AUTHOR]

This paper presents a novel data-driven predictive iterative learning control (DDPILC) scheme based on a new dynamic linearization technique along the iteration axis for a class of repeatable multiple-input and multiple-output nonlinear discrete-time systems. The proposed DDPILC scheme combines iterative learning control with predictive control and the distinct feature of the scheme is that the controller design depends only on the measured input/output data without using any model information of the controlled plant. In addition, if the control system is subjected to input and output constraints, the constrained DDPILC scheme is also proposed. The theoretical analysis shows that with random initial operation conditions, the proposed unconstrained DDPILC scheme guarantees monotonic and pointwise convergence while the constrained DDPILC scheme guarantees the asymptotic and pointwise convergence. The applicability and effectiveness of the proposed DDPILC schemes are further verified through simulations. [ABSTRACT FROM AUTHOR]

In this paper, we develop an adaptive output trajectory tracking control (AOTTC) method for a class of affine nonlinear discrete-time systems. The controller designed by this AOTTC method can make real-system output track the given expected trajectory asymptotically. Our method has some advantages: 1) it requires relatively few assumptions about the system model; 2) it can simplify the control problem by dynamically linearizing the system model and designing and adjusting the feedback gain matrix to adaptively stabilize the system online; and 3) it can estimate the system parameters by using an optimization scheme without using vast amounts of sampled data. This designing and adjusting procedure of the feedback gain matrix has a clear physical meaning and is easily applied. We also give out the convergence condition of the AOTTC method. Then, a voltage-controllable permanent magnet linear motor system is employed for computer simulation, whose results demonstrate the feasibility of our control method. [ABSTRACT FROM PUBLISHER]

Piezoelectric actuators (PEAs) are widely used in high-precision positioning applications. However, the inherent hysteresis nonlinearity seriously deteriorates the tracking performance of PEAs. To deal with it, the compensation of the hysteresis by using its inverse model (called inversion-based) is the popular method in the literature. One major disadvantage of this method is that the tracking performance of PEAs highly relies on its inverse model. Meanwhile, the computational burden of obtaining the inverse model is overwhelming. In addition, the physical constraints of the input voltage of PEAs is hardly handled by the inversion-based method. This paper proposes an inversion-free predictive controller, which is based on a dynamic linearized multilayer feedforward neural network (MFNN) model. By the proposed method, the inverse model of the inherent hysteresis is not required, and the control law can be obtained in an explicit form. By using the technique of constrained quadratic programming, the proposed method still works well when dealing with the physical constraints of PEAs. Moreover, an error compensation term is introduced to reduce the steady-state error if the dynamic linearized MFNN cannot approximate the PEA's dynamical model satisfactorily. To verify the effectiveness of the proposed method, experiments are conducted on a commercial PEA. The experiment results show that the proposed method has a satisfactory tracking performance even with high-frequency references. Comparisons demonstrate that the proposed method outperforms some existing results. [ABSTRACT FROM PUBLISHER]

This paper describes the use of pseudo-partial derivative (PPD) to dynamically linearize a nonlinear system, and aggregation is applied to the predicted PPD, resulting in a model-free adaptive predictive control algorithm for a nonlinear system. The algorithm design is only based on the PPD derived online from the input/output data of the controlled process, however it does provide bounded input/output sequence and setpoint tracking without steady- state error. A detailed discussion on parameter selection is also provided. To show the capability of the algorithm, simulations of a time-delay plant and a pH neutralization process show that the proposed method is effective for system parameter perturbation and external disturbance rejection. [ABSTRACT FROM AUTHOR]

This study proposes a data-driven adaptive filtering method for the fault diagnosis (DDAF-FD) of discrete-time nonlinear systems and provides a simultaneous online estimation of actuator and sensor faults. First, dynamic linearization was adopted to transform the nonlinear system into a quasi-linear model, which facilitated accurate modeling of the nonlinear system. Second, a data-driven adaptive fault diagnosis method was designed under the framework of data-driven filtering and the recursive least-squares algorithm using system I/O data only, and accurate real-time estimation of two fault factors was achieved. In addition, the simulation results demonstrate the effectiveness of the proposed method. The stability was verified via the Lyapunov method. [ABSTRACT FROM AUTHOR]