Neural network-based adaptive dynamic surface control for permanent magnet synchronous motors

Composite control based on FNTSMC and adaptive neural network for PMSM system

In this paper, a novel fixed-time non-singular terminal sliding mode control (NFNTSMC) method with an adaptive neural network (ANN) is proposed for permanent magnet synchronous motor (PMSM) system to improve PMSM performance. For nominal PMSM system without disturbance, a novel fixed-time non-singular terminal sliding mode control is designed to achieve fixed-time convergence property to improve the dynamic performance of the system. However, parameters mismatch and external load disturbances generally exist in PMSM system, the controller designed by NFNTSMC requires a large switching gain to ensure the robustness of the system, which will cause high-frequency sliding mode chattering. Therefore, an adaptive radial basis function (RBF) neural network is designed to approximate the unknown nonlinear lumped disturbance including parameters mismatch and external load disturbances online, and then the output of the neural network can be compensated to the NFNTSMC controller to reduce the switching gain and sliding mode chattering. Finally, the fixed-time convergence property and stability of the system are proved by Lyapunov method. The simulation and experimental results show that the presented strategy possesses satisfactory dynamic performance and strong robustness for PMSM system. And the proposed control scheme also provides an effective and systematic idea of the controller design for PMSM.

An Adaptive Control Scheme Based on Non-Interference Nonlinearity Approximation for a Class of Nonlinear Cascaded Systems and Its Application to Flexible Joint Manipulators

Control design for the nonlinear cascaded system is challenging due to its complicated system dynamics and system uncertainty, both of which can be considered some kind of system nonlinearity. In this paper, we propose a novel nonlinearity approximation scheme with a simplified structure, where the system nonlinearity is approximated by a steady component and an alternating component using only local tracking errors. The nonlinearity of each subsystem is estimated independently. On this basis, a model-free adaptive control for a class of nonlinear cascaded systems is proposed. A squared-error correction procedure is introduced to regulate the weight coefficients of the approximation components, which makes the whole adaptive system stable even with the unmodeled uncertainties. The effectiveness of the proposed controller is validated on a flexible joint system through numerical simulations and experiments. Simulation and experimental results show that the proposed controller can achieve better control performance than the radial basis function network control. Due to its simplicity and robustness, this method is suitable for engineering applications.

Distributed convex optimization of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints

This article investigates a penalty-based distributed optimization algorithm of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints. The proposed method addresses the distributed optimization problem by designing a penalty function in the form of a quadratic function, which is the sum of the global objective function and the consensus constraint. Moreover, the observer is presented to address the unmeasurable state of each agent. Radial basis function neural networks (RBFNN) are employed to approximate the unknown nonlinear functions. Then, by integrating RBFNN and dynamic surface control (DSC) techniques, an adaptive backstepping controller based on the barrier Lyapunov function (BLF) is proposed. Finally, the effectiveness of the suggested control strategy is verified under the condition that the state constraints are not broken. Simulation results indicate that the output trajectories of all agents remain within the upper and lower boundaries, converging asymptotically to the global optimal signal.

Nonsmooth funnel transformation function-based discrete-time sliding-mode control with deterministic performance margin for servo systems

This paper proposes a nonsmooth funnel transformation function-based discrete-time sliding-mode control strategy for the discrete-time servo systems with unknown frictions and disturbances. For obtaining a more accurate discrete-time system model, a filter-based adaptive identification algorithm (FAIA) is introduced, where the unknown measurement noises are considered. Based on the identified system model and a novel discrete-time nonsmooth funnel transformation function (improving the tracking performances), a discrete-time sliding-mode surface is designed to confine the tracking error to a smaller funnel region compared with the predefined one, which has a deterministic performance margin related to the upper bound of the lumped disturbance. Furthermore, selections of steady-state funnel boundary and sliding-mode surface parameter can be guided theoretically according to the upper bound of the lumped disturbance. Experimental results show that the tracking error is guaranteed in the predefined funnel with a deterministic performance margin by using the proposed control strategy.

Adaptive Resilient Neural Control of Uncertain Time-Delay Nonlinear CPSs with Full-State Constraints under Deception Attacks

This paper focuses on the adaptive control problem of a class of uncertain time-delay nonlinear cyber-physical systems (CPSs) with both unknown time-varying deception attacks and full-state constraints. Since the sensors are disturbed by external deception attacks making the system state variables unknown, this paper first establishes a new backstepping control strategy based on compromised variables and uses dynamic surface techniques to solve the disadvantages of the huge computational effort of the backstepping technique, and then establishes attack compensators to mitigate the impact of unknown attack signals on the control performance. Second, the barrier Lyapunov function (BLF) is introduced to restrict the state variables. In addition, the unknown nonlinear terms of the system are approximated using radial basis function (RBF) neural networks, and the Lyapunov-Krasovskii function (LKF) is introduced to eliminate the influence of the unknown time-delay terms. Finally, an adaptive resilient controller is designed to ensure that the system state variables converge and satisfy the predefined state constraints, all signals of the closed-loop system are semi-globally uniformly ultimately bounded under the premise that the error variables converge to an adjustable neighborhood of origin. The numerical simulation experiments verify the validity of the theoretical results.

Adaptive Neural Network Control Using Nonlinear Information Gain for Permanent Magnet Synchronous Motors

In this study, an adaptive neural network (NN) control using nonlinear information (NI) gain for permanent magnet synchronous motors (PMSMs) is proposed to improve control and estimation performance. The proposed method consists of a nonlinear controller, a three-layer NN approximator, and NI gain. The nonlinear controller is designed via a backstepping procedure for position tracking. The commutation scheme is designed to implement the PMSM control without the direct-quadrature (DQ) transform. The three-layer NN approximator is designed to estimate the unknown complex function generated by the recursive backstepping process. The NI gains are designed to enhance the control and estimation performance according to the increased tracking errors owing to the load torque and the desired position variations. All of signals in the closed-loop system guarantee the semiglobal uniformly ultimately boundness (UUB) using the Lyapunov stability theorem and the input-to-state stability (ISS) property. The performance of the proposed method was validated by experiments performed using a PMSM testbed.

Linear-Nonlinear Switching Active Disturbance Rejection Speed Controller for Permanent Magnet Synchronous Motors

To combine the advantages of linear active disturbance rejection control (LADRC) and nonlinear active disturbance rejection control (NLADRC) and improve the contradiction between the response speed and control precision caused by the limitation of parameter α in NLADRC, a linear-nonlinear switching active disturbance rejection control (SADRC) strategy based on linear-nonlinear switching extended state observer (SESO) and linear-nonlinear switching state error feedback control law (SSEF) is proposed in this paper. First, the reasons for the performance differences between LADRC and NLADRC are analysed from a theoretical point of view, then a linear-nonlinear switching function (SF) that can change the switching point by adjusting its parameters is constructed and then propose SESO and SSEF based on this function. Subsequently, the convergence range of the observation error of the SESO is derived, and the stability of the closed-loop system with the application of SSEF is also demonstrated. Finally, the proposed SADRC control strategy is applied to a 707 W permanent magnet synchronous motor (PMSM) experimental platform, and both the dynamic and static characteristics of SADRC are verified. The experimental results show that the proposed SADRC control strategy can well combine the performance advantages of LADRC and NLADRC and can better balance the response speed and control precision and has a better capacity for disturbance rejection, which has potential application in engineering practise.

Neuroadaptive dynamic surface control for induction motors stochastic system based on reduced-order observer

This paper studies an observer-based neural network position tracking control scheme for induction motors system operating under a field-oriented control scheme with the problem of stochastic disturbance. Firstly, the angular velocity is estimated by the constructed reduced-order observer. Then, the nonlinear functions are approximated by the neural networks and the stochastic Lyapunov functions are chosen to analyze the stability of the system. Besides, the "complexity of computation" existed in traditional backstepping control is solved by using the dynamic surface control technique. At last, the results of the comparison simulation experiments show that the proposed control scheme can reduce the influence of stochastic disturbance, and have faster tracking speed smaller tracking error. The designed observer can estimate the signals effectively.

Neuroadaptive Finite-Time Control for Nonlinear MIMO Systems With Input Constraint

This article considers the problem of finite-time (FT) tracking control for a class of uncertain multi-input-multioutput (MIMO) nonlinear systems with input backlash. A modified FT command filter is designed in each step of backstepping, which ensures the output of the filter can faster approximate the derivatives of virtual signals, suppress chattering, and relax the input signal limit of the Levant differentiator. Then, the corresponding improved FT error compensation mechanism is adopted to reduce the negative impact of filtering errors. Furthermore, a neural-network-adaptive technology is proposed for MIMO systems with input backlash via FT convergence. It is shown that desired tracking performance can be implemented in finite time. The simulation example is presented to illustrate the effectiveness and advantages of the new design method.

Neuroadaptive control of information-poor servomechanisms with smooth and nonsmooth uncertainties

For motion control of uncertain servomechanisms, nonlinear dynamics including smooth and nonsmooth types, external disturbances, signal measurement noises, asymmetric input saturation, and so on seriously hinder the further development of high-performance closed-loop control algorithms. However, already existing control strategies cannot address the above-mentioned issues at the same time. It greatly increases the difficulty of controller design especially when some states are not measurable. Inspired by above motivations, this paper exploits neural networks to deal with nonlinear dynamics including discontinuous types, and combines extended state observers to estimate disturbances and unmeasurable states for uncertain nonlinear servomechanisms. Meanwhile, the desired-command-based model compensation approach is integrated into the controller design. It is worth noting that the neural network weights are updated by the combination of the estimation error and tracking error to acquire better approximation accuracy. According to above technologies, a novel extended-state-observer-based neural network adaptive motion control algorithm will be synthesized. The bounded stability of the whole closed-loop system is proved strictly. In addition, the comparisons of the application results on an electro-hydraulic servo system verify the availability and superiority of the developed control algorithm.

Control Algorithm of Permanent Magnet Direct Drive Belt Conveyor System for Mining Based on Reduced Order Model

Over the decades, permanent magnet synchronous motor (PMSM) has been widely used in coal mine production. In this paper, an optimized neural network predictive controller (NNPC) of permanent magnet direct drive belt conveyor system (BCS) for mining based on reduced order model (ROM) is established. First, in order to establish the full order model of the permanent magnet direct drive BCS, CEMA is used for dynamic analysis, and the dynamic equation of the permanent magnet direct drive BCS is established. Second, the Proper Orthogonal Decomposition (POD) method is used to reduce the order in this paper. Finally, the NNPC of permanent magnet direct drive BCS based on the ROM is proposed. The simulation result shows that the order of BCS model is effectively reduced by the POD method. The NNPC based on the ROM has a good performance in the control of permanent magnet direct drive BCS, and the error between of the full order model and the ROM is 0.19[Formula: see text]m/s.

Neural Network Command Filtered Control of Fractional-Order Chaotic Systems

An adaptive neural network (NN) backstepping control method based on command filtering is proposed for a class of fractional-order chaotic systems (FOCSs) in this paper. In order to solve the problem of the item explosion in the classical backstepping method, a command filter method is adopted and the error compensation mechanism is introduced to overcome the shortcomings of the dynamic surface method. Moreover, an adaptive neural network method for unknown FOCSs is proposed. Compared with the existing control methods, the advantage of the proposed control method is that the design of the compensation signals eliminates the filtering errors, which makes the control effect of the actual system improve well. Finally, two examples are given to prove the effectiveness and potential of the proposed method.

Disturbance rejection control for PMSM using integral sliding mode based composite nonlinear feedback control with load observer

The low-speed high-torque permanent magnet synchronous motor (PMSM) drive system is a kind of typical nonlinear, strong-coupling and easy-parameter perturbation electromechanical coupling system. The control system is uncertainties and subject to unknown external interferences as well. In this paper, a disturbance rejection control method combining robust speed controller and load observer is proposed for low-speed high-torque PMSM. The robust speed controller combines the composite nonlinear feedback (CNF) which has advantage in improving the transient responsive performance and the integral sliding mode (ISM) advancing in improving system robustness. Subsequently, the effects of unknown external interferences are avoided by using a sliding mode observer (SMO), in which the chattering is reduced by introducing fuzzy control, and the observation is used for feed-forward compensation. The proposed robust speed controller solves the contradiction between the rapidity and overshoot of the traditional control method, and combines the load observer to compensate the influence of the load mutations and wide range of the load changes on the control system. Finally, the numerical simulation and experiments demonstrate that the proposed speed control method is able to achieve good transient performance in inhibiting system overshoot and reducing stable state error. Additionally, it successfully suppresses the influence of load disturbances and mutations, and shows the proposed method has better robustness.

Dual-Motor Synchronization Control Design Based on Adaptive Neural Networks Considering Full-State Constraints and Partial Asymmetric Dead-Zone

This paper proposes a command filtering backstepping (CFB) scheme with full-state constraints by leading into time-varying barrier Lyapunov functions (T-BLFs) for a dual-motor servo system with partial asymmetric dead-zone. Firstly, for the convenience of the controller design, the conventional partial asymmetric dead-zone model was replaced with a new smooth differentiable model owing to its non-smoothness. Secondly, neural networks (NNs) were utilized to approximate the nonlinearity that exists in the dead-zone model, improving the control performance. In addition, CFB was utilized to deal with the inherent computational explosion problem of the traditional backstepping method, and an error compensation mechanism was introduced to further reduce the filtering errors. Then, by applying the T-BLF to the CFB process, the states of the system never violated the prescribed constraints, and all signals in the dual-motor servo system were bounded. The tracking error and synchronization error could converge to a small desired neighborhood of the origin. In the end, the effectiveness of the proposed control scheme was verified through simulations.

Memory-Based Integral Sliding-Mode Control for T-S Fuzzy Systems With PMSM via Disturbance Observer

In this article, the disturbance observer (DOB)-based memory integral sliding-mode control (ISMC) is designed for the permanent magnet synchronous motor (PMSM) model subject to mismatched disturbance through the Takagi-Sugeno (T-S) fuzzy approach. Different from the previous studies, a memory-based ISMC scheme that has a constant delay is taken for the first time to design the ISMC for the T-S fuzzy systems. The DOB is given to estimate the disturbances, which are incorporated in the controller design to counteract the disturbance. To fully abide by the model characteristics of the PMSM-based T-S fuzzy systems and DOB, an integral-type fuzzy switching surface function (IFSSF), which involves state-dependent input matrix and memory parameter simultaneously, is defined. From the IFSSF, the fuzzy ISMC is designed to ensure the reachability condition in finite time. Besides that, the designed fuzzy ISMC can effectively attenuate the mismatched disturbances based on the H_∞ control theory. Also, a set of sufficient conditions is derived to ensure the global asymptotic stability for the sliding-mode dynamics by the proposed controller. Finally, the applicability of designed DOB-based memory fuzzy ISMC methodology is demonstrated by a controller design for the PMSM model.

Finite-Time Tracking Control for Nonlinear Systems via Adaptive Neural Output Feedback and Command Filtered Backstepping

This article is concerned with the tracking control problem for uncertain high-order nonlinear systems in the presence of input saturation. A finite-time control strategy combined with neural state observer and command filtered backstepping is proposed. The neural network models the unknown nonlinear dynamics, the finite-time command filter (FTCF) guarantees the approximation of its output to the derivative of virtual control signal in finite time at the backstepping procedure, and the fraction power-based error compensation system compensates for the filtering errors between FTCF and virtual signal. In addition, the input saturation problem is dealt with by introducing the auxiliary system. Overall, it is shown that the designed controller drives the output tracking error to the desired neighborhood of the origin at a finite time and all the signals in the closed-loop system are bounded at a finite time. Two simulation examples are given to demonstrate the control effectiveness.

Universal Control of Permanent Magnet Synchronous Motors with Uncertain Dynamics

This paper focuses on the universal control design of permanent magnet synchronous motors (PMSMs) with uncertain system dynamics. In vector control, classical proportional-integral (PI) controllers are used to control d-q axis currents and speed of the PMSM. This paper uses two control methods: conventional field-oriented vector control and simplified control. First, all the control gains are determined for numerous PMSMs with various power ratings using an empirical study and generalized mathematical expressions are derived for each of the gains. Then, these expressions are used for automatic gain calculation for various PMSMs with a wide power-rating range. In vector control, the control gains are determined using only the motor power ratings. In the simplified control, generalized control gain expressions are obtained using the number of pole pairs and the flux linkage. Compared to the vector control, the simplified control method provides much simpler generalized mathematical expressions. Validation is carried out in MATLAB/Simulink environment using various PMSMs from 0.2 HP to 10 HP, and results show accurate tracking of reference speed and d-q axis reference currents. Thus, the proposed gain scheduling approach is effective and can be used for self-commissioning motor drives.

Fuzzy Observer Constraint Based on Adaptive Control for Uncertain Nonlinear MIMO Systems With Time-Varying State Constraints

This article presents an adaptive output feedback approach of nonlinear multi-input-multi-output (MIMO) systems with time-varying state constraints and unmeasured states. An adaptive approximator is designed to approximate the unknown nonlinear functions existing in the state-constrained systems with immeasurable states. To deal with the tracking problem of such systems, a state observer with time-varying barrier Lyapunov functions (BLFs) is introduced in the controller design procedure. The backstepping design with time-varying BLFs is utilized to guarantee that all system states remain within the time-varying-constrained interval. The constant constraint is only the special case of the time-varying constraint which is more general in the real systems. The proposed control approach guarantees that all signals in the closed-loop systems are bounded and the tracking errors converge to a bounded compact set, and time-varying full-state constraints are never violated. A simulation example is given to confirm the feasibility of the presented control approach in this article.

Intelligent system for university legal education based on machine learning

University legal education is of great significance to the personal development and social stability of college students. At present, there are certain problems in the traditional teaching system, which has led to inefficient university legal education. In order to improve the legal teaching effect of the university, based on machine learning and neural networks, this paper integrates and optimizes the original hardware and software and operation process, and further highlights the functions of interconnection and sharing, automatic sensing, real-time recording, interactive feedback, dynamic supervision, and intelligent analysis, which greatly facilitates the evaluation of teaching at all levels. In particular, this study uses big data technology to conduct an intelligent analysis of data completeness, multimedia application rate, system execution, and average test scores, and scientifically evaluates the implementation of basic-level education systems and the effectiveness of education, which can effectively solve the problems of quantitative formalization and qualitative subjectivity of current education evaluation from a technical level. In addition, this study designs a control experiment to analyze the system performance. The research results show that the model proposed in this paper has a certain effect.

Sensorless Speed Tracking of a Brushless DC Motor Using a Neural Network

In this work, the sensorless speed control of a brushless direct current motor utilizing a neural network is presented. This control is done using a two-layer neural network that uses the backpropagation algorithm for training. The values provided by a Proportional, Integral, and Derivative (PID) control to this type of motor are used to train the network. From this PID control, the velocity values and their corresponding signal control (u) are recovered for different values of load pairs. Five different values of load pairs were used to consider the entire working range of the motor to be controlled. After carrying out the training, it was observed that the proposed network could hold constant load pairs, as well as variables. Several tests were carried out at the simulation level, which showed that control based on neural networks is robust. Finally, it is worth mentioning that this control strategy can be realized without the need for a speed sensor.

Adaptive Neural Command Filtering Control for Nonlinear MIMO Systems With Saturation Input and Unknown Control Direction

In this paper, the tracking control problem is considered for a class of multiple-input multiple-output (MIMO) nonlinear systems with input saturation and unknown direction control gains. A command filtered adaptive neural networks (NNs) control method is presented with regard to the MIMO systems by designing the virtual controllers and error compensation signals. First, the command filtering is used to solve the "explosion of complexity" problem in the conventional backstepping design and the nonlinearities are approximated by NNs. Then, the error compensation signals are developed to conquer the shortcoming of the dynamic surface method. In addition, the Nussbaum-type functions are utilized to cope with the unknown direction control gains. The effectiveness of the proposed new design scheme is illustrated by simulation examples.

Neural-Network-Based Adaptive Funnel Control for Servo Mechanisms With Unknown Dead-Zone

This paper proposes an adaptive funnel control (FC) scheme for servo mechanisms with an unknown dead-zone. To improve the transient and steady-state performance, a modified funnel variable, which relaxes the limitation of the original FC (e.g., systems with relative degree 1 or 2), is developed using the tracking error to replace the scaling factor. Then, by applying the error transformation method, the original error is transformed into a new error variable which is used in the controller design. By using an improved funnel function in a dynamic surface control procedure, an adaptive funnel controller is proposed to guarantee that the output error remains within a predefined funnel boundary. A novel command filter technique is introduced by using the Levant differentiator to eliminate the "explosion of complexity" problem in the conventional backstepping procedure. Neural networks are used to approximate the unknown dead-zone and unknown nonlinear functions. Comparative experiments on a turntable servo mechanism confirm the effectiveness of the devised control method.

Dynamic Surface Backstepping Control for Voltage Source Converter-High Voltage Direct Current Transmission Grid Side Converter Systems

This paper studies the coordination control of active and reactive power of the voltage source converter-high voltage direct current transmission (VSC-HVDC) grid side converter. Firstly, the high-order VSC-HVDC converter system is decomposed into three subsystems by using the backstepping control method, and the control laws are designed for each subsystem to realize the control of VSC-HVDC converter systems. Secondly, the dynamic surface control method is used to deal with the problem of “explosion of complexity” in the traditional backstepping control method. Finally, the simulation results demonstrate that the VSC-HVDC converter systems can provide a certain capacity of reactive power compensation under the proposed method in this paper. In addition, the control method proposed in this paper does not require the information of the second derivative of active power and reactive power.

Practical tracking control for a class of high-order switched nonlinear systems with quantized input

This paper concentrates on the global practical tracking problem for a class of high-order switched nonlinear systems under arbitrary switching, whose powers and nonlinearities count on the switching signal. The sector-bounded approach is utilized to dispose of the control input, which is quantized by a logarithmic quantizer. Firstly, through the medium of adding a power integrator approach, a homogeneous output feedback controller is designed for the nominal part of the switched systems. Then, by virtue of the homogeneous domination idea and a common change of coordinates, scaled homogeneous output feedback controllers are achieved to assure global boundedness of all the states in the whole system and ensure the tracking error to converge into an arbitrarily small neighborhood of origin in a finite time. Finally, two examples are provided to test the validity of the proposed method.

Adaptive Neural Network Learning Controller Design for a Class of Nonlinear Systems With Time-Varying State Constraints

This paper studies an adaptive neural network (NN) tracking control method for a class of uncertain nonlinear strict-feedback systems with time-varying full-state constraints. As we all know, the states are inevitably constrained in the actual systems because of the safety and performance factors. The main contributions of this paper are that: 1) in order to ensure that the states do not violate the asymmetric time-varying constraint regions, an adaptive NN controller is constructed by introducing the asymmetric time-varying barrier Lyapunov function (TVBLF) and 2) the amount of the learning parameters is reduced by introducing a TVBLF at each step of the backstepping. Based on the Lyapunov stability analysis, it can be proven that all the signals in the closed-loop system are the semiglobal ultimately uniformly bounded and the time-varying full-state constraints are never violated. Finally, a numerical simulation is given, and the effectiveness of this adaptive control method can be verified.

Controller Design for Different Electric Tail Rotor Operating Modes in Helicopters

The nonlinear aerodynamics and new kinds of operation associated with helicopter electric tail rotors (ETRs) make accurate speed tracking control under complex flight conditions a key challenge confronting designers. In this paper, we present an electric propulsion system for tail rotors that uses a high-power-density permanent magnet motor. The management of aerodynamic disturbance rejection and accurate speed control are aspects of ETR design that require particularly close attention. To this end, we have developed a speed controller that is based on an active disturbance rejection control (ADRC) technique that can handle fixed speed and adjustable pitch-angle modes. We have also applied a linear extended state observer (LESO) with a self-tuning bandwidth to estimate fluctuations in the drive system. For variable speeds, a simple controller combined with an adaptive radial basis function (RBF) observer and nonlinear state error feedback using ADRC was designed to replace LESO while avoiding any dependence on the system parameters. The stability of the controllers was analyzed and their effectiveness was verified using a simulation platform. Test results showed that the propulsion system is able to achieve fast dynamic response and aerodynamic disturbance rejection.

Anti-disturbance speed control of low-speed high-torque PMSM based on second-order non-singular terminal sliding mode load observer

This paper presents an anti-disturbance speed control of low-speed high-torque permanent magnet synchronous motor (PMSM) based on the second-order non-singular terminal sliding mode load observer. According to the coordinate transformation theory, the mathematical model of PMSM is established. Subsequently, the second-order non-singular terminal sliding mode observer (SNTSMO) is designed to observe the changes of load disturbance in the PMSM system. The SNTSMO combines the advantages of both high-order sliding mode and non-singular terminal sliding mode to achieve the fast convergence and no chattering. Next, the sliding mode controller (SMC) is designed to achieve speed loop control of PMSM. Then, the anti-disturbance compound speed controller is established on the basis of SMC and SNTSMO, wherein the feed-forward compensation is used to reduce the disturbance from the load. Finally, the numerical simulations and experiments are presented according to the schematic diagram of the designed compound speed controller of PMSM. The results demonstrate that the designed SNTSMO can precisely estimate the load disturbance and suppress the effects of buffeting in the traditional sliding mode observer (SMO). Additionally, the designed compound speed controller of PMSM can achieve smooth speed control in the presence of load disturbance, achieve the purpose of anti-disturbance speed control and further improve the robustness of the control system.

Command filter based adaptive fuzzy bipartite output consensus tracking of nonlinear coopetition multi-agent systems with input saturation

This paper is concerned with the adaptive bipartite output consensus tracking problem of high-order nonlinear coopetition multi-agent systems with input saturation under a signed directed graph. A distributed fuzzy-based command filtered backstepping scheme is proposed, where the unknown nonlinear dynamics are approximated by the fuzzy logic system (FLS). The errors compensation mechanism is constructed to eliminate the errors caused by filters. Under the proposed control scheme, we only need to design one adaptive law for each agent, and it is proved that the bipartite output tracking errors converge into the desired neighborhood and all the closed-loop signals are bounded although the input saturation exists. Two numerical examples are included to verify the effectiveness of given scheme.

Fuzzy Finite-Time Command Filtered Control of Nonlinear Systems With Input Saturation

This paper considers the fuzzy finite-time tracking control problem for a class of nonlinear systems with input saturation. A novel fuzzy finite-time command filtered backstepping approach is proposed by introducing the fuzzy finite-time command filter, designing the new virtual control signals and the modified error compensation signals. The proposed approach not only holds the advantages of the conventional command-filtered backstepping control, but also guarantees the finite-time convergence. A practical example is included to show the effectiveness of the proposed method.

Observer-Based Adaptive Fault-Tolerant Tracking Control of Nonlinear Nonstrict-Feedback Systems

This paper studies an output-based adaptive fault-tolerant control problem for nonlinear systems with nonstrict-feedback form. Neural networks are utilized to identify the unknown nonlinear characteristics in the system. An observer and a general fault model are constructed to estimate the unavailable states and describe the fault, respectively. Adaptive parameters are constructed to overcome the difficulties in the design process for nonstrict-feedback systems. Meanwhile, dynamic surface control technique is introduced to avoid the problem of "explosion of complexity". Furthermore, based on adaptive backstepping control method, an output-based adaptive neural tracking control strategy is developed for the considered system against actuator fault, which can ensure that all the signals in the resulting closed-loop system are bounded, and the system output signal can be regulated to follow the response of the given reference signal with a small error. Finally, the simulation results are provided to validate the effectiveness of the control strategy proposed in this paper.

Command Filtering-Based Fuzzy Control for Nonlinear Systems With Saturation Input

In this paper, command filtering-based fuzzy control is designed for uncertain multi-input multioutput (MIMO) nonlinear systems with saturation nonlinearity input. First, the command filtering method is employed to deal with the explosion of complexity caused by the derivative of virtual controllers. Then, fuzzy logic systems are utilized to approximate the nonlinear functions of MIMO systems. Furthermore, error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. The developed method will guarantee all signals of the systems are bounded. The effectiveness and advantages of the theoretic result are obtained by a simulation example.