This paper proposes a deep neural network (DNN)-augmented inverse optimal adaptive control for stabilizing stochastic interconnected systems, focusing on challenges posed by unmodeled dynamics and uncertainties. A structured small-gain framework is developed to address the mutual dependencies among interconnected subsystems and to ensure the input-to-state practical stability in probability. To approximate unmodeled nonlinearities, a DNN-based identifier is integrated into each subsystem, allowing real-time estimation of uncertain dynamics while preserving the analytical tractability of the controller. Through this idea, we develop an adaptive controller that guarantees uniform boundedness of the interconnected system and ensures state convergence within a small neighborhood of the origin while optimizing overall system performance. Finally, an automobile suspension system is presented to demonstrate how the proposed approach effectively achieves closed-loop stability for stochastic interconnected systems while incorporating inverse optimal control design.

This paper introduces a novel framework for reactive control in dual-arm cooperative robotic systems, addressing the significant challenges posed by high-dimensional, non-convex optimization demands, intricate kinematic, multi-modal distribution, the need for precise, and synchronized coordination. The core of our approach is a two-stage sampling-based model predictive control, which integrates k-means, dual quaternion, and null space into a cohesive system. This integration enhances the system's ability to manage complex coordination tasks, such as obstacle avoidance and holding a water cup, while mitigating risks associated with local optima and reducing control jitter. Our framework not only improves performance and reliability, but also overcomes the traditional computational bottlenecks inherent in dual-arm coordination. These advancements are validated through extensive simulations and experiments, demonstrating the robustness and efficiency of our proposed methodology.

Accurate modeling of dynamic systems is essential for robotics, enhancing system perception and control performance. This work tackles causal modeling challenges for mobile robots under complex uncertainties, including internal model inaccuracies and external environmental disturbances. Unlike first-principle or purely data-driven methods, we propose Pet-NODE, an advanced Neural Ordinary Differential Equation (NODE) framework that integrates physical priors with temporal features for high-fidelity system modeling. To further embed domain knowledge, we introduce a novel loss function with self-prediction objectives, ensuring adherence to physical principles. Extensive experiment evaluations, including ablation studies and comparisons against Nominal model, K-NODE and PI-TCN methods, demonstrate Pet-NODE’s robustness, interpretability, and superior localization accuracy on a self-collected wheeled robot dataset.

Unmanned Aerial Vehicles (UAVs) are gaining attention for inspections due to their improved safety, efficiency, and accuracy, alongside reduced costs and environmental risks. Visual servoing is crucial for autonomous UAV flight in GPS-degraded environments, guiding the UAV by minimizing errors between observed and desired visual features. This study focuses on Image-Based Visual Servoing (IBVS) control for quadrotor UAVs under complex dynamics and environmental disturbances. A nonlinear model predictive control (MPC) framework is first integrated with visual servoing to handle dynamics nonlinearity, control optimality, and constraints. To address uncertainties and disturbances, a Generalized Extended State Observer (GESO) is incorporated into the MPC, forming the Disturbance-Resilient (DR-) MPC. The GESO estimates the lumped disturbance to improve model predictions within the MPC horizon. The proposed algorithm is validated in a realistic Gazebo environment for UAV pipeline inspection in 3D scenarios, showing better control accuracy and reduced inspection time compared to three baseline methods: IBVS, IBVS-MPC(K) with kinematics, and IBVS-MPC(D) with dynamics.1

Model Predictive Path Integral (MPPI) controllers are drawing increasing attention for their ability to efficiently handle complex systems by leveraging GPU acceleration while with flexible prediction models and cost functions. However, their performance generally degrades with low-quality prediction models and unknown external disturbances. Existing methods that rely solely on feedforward disturbance compensation are limited by the assumption of matched disturbances, which rarely holds in practice due to the complex lumped disturbances. To this end, we propose a novel Disturbance-Aware (DA-) MPPI framework, which seamlessly integrates an Extended high-order Sliding Mode Observer (ESMO) into MPPI. The ESMO provides accurate estimates of uncertainties and external disturbances, which are directly incorporated into the MPPI rolling dynamics to improve prediction and therefore tracking control performance. The proposed algorithm is verified against the baseline MPPI in AirSim simulation environment by stochastic simulation. Comparatively statistical experiments show that incorporating ESMO within the MPPI framework significantly enhances tracking performance, with the RMSE reduction in term of mean by 8.0%, 17.7%, 6.17%, 12.9% and in term of standard variance by 11.5%, 26.0%, 10.4%, and 9.2% in four representative scenarios. The effects of target velocity and prediction horizon on control performance are also systematically evaluated. These results validate the robustness and accuracy of the DA-MPPI controller in complex and uncertain environments.1

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as safety guarantees and decision-making. In this work, we introduceInput Concomitant Neural ODEs (ICODEs), which incorporate precise real-time input information into the learning process of the models, rather than treating the inputs as hidden parameters to be learned. The sufficient conditions to ensure the model’s contraction property are provided to guarantee that system trajectories of the trained model converge to a fixed point, regardless of initial conditions across different training processes. We validate our method through experiments on several representative real dynamics: Single-link robot, DC-to-DC converter, motion dynamics of a rigid body, Rabinovich-Fabrikant equation, Glycolytic-glycogenolytic pathway model, and heat conduction equation. The experimental results demonstrate that our proposed ICODEs efficiently learn the ground truth systems, achieving superior prediction performance under both typical and atypical inputs. This work offers a valuable class of neural ODE models for understanding physical systems with explicit external input information, with potentially promising applications in fields such as physics and robotics. Our code is available online at https://github.com/EEE-ai59/ICODE.git.

Considering the speed regulation problem of converter-driven motor systems (CDMS), a composite finite-time anti-disturbance control scheme is proposed in this paper. Firstly, the controller design process is mainly divided into two blocks according to block backstepping control techniques. Then, by constructing universal finite-time observers (UFTO), immeasurable system dynamics and multiple disturbances are estimated, simultaneously. Based on the estimated information, the integral terminal sliding mode control (ITSMC) strategies devised for the CDMS exhibit robust disturbance rejection capabilities. Compared with existing methods, the proposed composite control scheme is distinguished by its reliance solely on measured output, enhanced dynamic response speed, superior disturbance rejection capability, and a more streamlined controller design. Furthermore, a rigorous global finite-time stability analysis is presented for the closed-loop system. Finally, numerous experimental results are given to validate the effectiveness of the proposed control scheme.

This article investigates the problem of removing the peaking phenomenon in the stabilization of a class of nonlinear cascaded systems using linear partial state feedback within a quadratic program (QP) framework. By appropriately designing the QP and selecting its parameters, the inter-subsystem cascaded input terms are effectively constrained within a desirable control-invariant set, thereby eliminating undesirable transient peaks. Semi-global stabilization of the overall system is achieved through only minimal modifications to the nominal linear feedback controllers. Owing to the simplicity of the resulting controller structure and the real-time efficiency of QP solvers, the proposed method is readily applicable to practical systems. Numerical examples from previous studies are revisited to demonstrate the effectiveness and robustness of the proposed control strategy.

The high level of autonomy within autonomous systems demands new control strategies to achieve more complex objectives while ensuring both safety and robustness, rather than relying solely on a given reference. To this end, this article addresses the problem of temporal logic disturbance rejection control (TLDRC) for a class of nonlinear systems subject to disturbances. Signal temporal logic (STL) specifications are introduced for the representation of complex tasks. A control barrier function (CBF), composed of a monotonic function characterizing the temporal behavior of the system and a predicate function, is constructed to encode the STL specifications. To guarantee robustness against disturbances, generalized proportional integral observers (GPIOs) are introduced for higher-accuracy disturbance estimation. It is shown that by fully exploiting the constructed CBF and the disturbance estimate, the developed TLDRC strategy is able to ensure the STL specifications and compensate undesirable effects caused by unknown disturbances, even if they are fast-time-varying. A numerical example is presented to illustrate the effectiveness of the proposed strategy.

The complexity of coupled multivariate data in industrial settings often limits the effectiveness of principal component analysis (PCA) in revealing patterns and structures in the data. In this article, we propose a novel fault detection framework for industrial process time series data with temporal and spatial correlation. First, by applying graph theory, the framework captures the complex network structures inherent in industrial processes, enabling the discovery of hidden data associations from a topological perspective. Then, the proposed method integrates temporal and spatial correlations in the modeling process, ensuring a comprehensive and integrated analysis. Specifically, the time series data are divided into sliding window intervals, and then the graph convolution is embedded within each window. After the modeling optimization objectives are defined, the overall solution is derived. Finally, these components, which contain spatio–temporal information, are used to construct dynamic and static statistics. Experiments on a chemical dataset show that the proposed method can significantly reduce the false alarm rate and improve the fault detection rate compared with the dynamic internal PCA without considering spatial factors. In addition, by applying it to the actual hot rolling process of strip, the superiority of the method is further verified, and its practical value and robustness are highlighted.

The development of rigorous theoretical tools, such as feasibility and stability analysis, for finite-control-set model predictive control (FCS-MPC) of electric drives, has lagged behind advancements in engineering practice. To address this gap, this article introduces a unified control method that integrates disturbance estimation and control Lyapunov functions (CLFs) within the FCS-MPC framework. This approach is applied to perturbed electrical drive systems, with inverter-fed permanent magnet synchronous motor systems as a primary example. First, we propose a specific class of CLFs that enables separate design of disturbance estimation, later incorporating it as a constraint in the optimization problem. Theorems and lemmas are then provided to demonstrate that using the disturbance-estimation-based control Lyapunov function constraint in an FCS-MPC setting ensures a nonempty feasible control set, guaranteeing closed-loop stability by design. Experiments conducted on a test bench validate the practicability of the proposed method. A comprehensive performance evaluation is presented under various conditions.

In overhead cranes, the inclination angle of the payload must be limited within an acceptable range to ensure safety, and the trolley reaches a desired position simultaneously. However, the payload can be disturbed by strong winds, which poses a certain threat to the safety of overhead crane operation. In addition, when multiple overhead cranes communicate with each other via a shared network, the communication and computational resources available to each overhead crane become constrained. Taking into account the above factors, a novel event-triggered safety-critical model predictive control (ESMPC) algorithm is proposed for underactuated overhead crane systems to achieve satisfactory performance. In the proposed ESMPC algorithm, disturbances acting on the payload are estimated by a discrete-time disturbance observer. Then, the discrete-time predictive control barrier function is devised to guarantee operational safety. Subsequently, the prediction model is derived and the quadratic programming (QP) problem is formulated. The optimal control sequence can be obtained by solving the QP problem at each event-triggering instant. After that, the predicted control inputs are fully exploited and applied to the trolley one by one chronologically. Finally, the experimental results show that the payload swing angle can be limited within the safe range and the trolley can reach the desired position by using fewer communication and computing resources under the proposed ESMPC method.

Short-term time series forecasting is pivotal in various scientific and industrial fields. Recent advancements in deep learning-based technologies have significantly improved the efficiency and accuracy of short-term time series modeling. Despite advancements, current time short-term series forecasting methods typically emphasize modeling dependencies across time stamps but frequently overlook inter-variable dependencies, which is crucial for multivariate forecasting. We propose a multi patterns memory model discovering various dependency patterns for short-term multivariate time series forecasting to fill the gap. The proposed model is structured around two key components: the short-term memory block and the long-term memory block. These networks are distinctively characterized by their use of asymmetric convolution, each tailored to process the various spatial-temporal dependencies among data. Experimental results show that the proposed model demonstrates competitive performance over the other time series forecasting methods across five benchmark datasets, likely thanks to the asymmetric structure, which can effectively extract the underlying various spatial-temporal dependencies among data.

This article aims to derive an adaptive optimal speed regulator for permanent magnet synchronous motors (PMSMs) affected by both disturbances and actuator faults. Load torque is first modeled as a mismatched disturbance, where its estimation via a disturbance observer is drawn to construct an error system. Then, optimal speed regulation problem for PMSM is equivalently transformed into an optimal control problem for the error system. Given the presence of model variable couplings, an adaptive dynamic programming method is adopted to derive the optimal controller, where a critic neural network (NN) and an actor NN are used to approximate the cost function and the optimal controller, respectively. Notably, this article addresses the simultaneous occurrence of disturbances and actuator faults within the optimal control framework by designing separate treatments. Eventually, a composite controller, fulfilling optimality, robustness and safety constraints, is presented with rigorous proof via Lyapunov method. The proposed method is substantiated through both comparative numerical examples and experimental validation on a PMSM platform.

The stability of second-order non-smooth control system under denial-of-service (DoS) attack is studied in this paper. Non-smooth control method can be used to stabilize the system states to the equilibrium point in a finite time if there is no DoS attack. However, under DoS attack, the controller will maintain the latest received data, which may lead to local divergence of the system states. By designing a Lyapunov function, it is proven that under energy-constrained DoS attack, the states of closed-loop system can still converge to the equilibrium point in a finite time. The simulation results further validate the effectiveness of the theory.

Because of its excellent efficiency, compact dimen-sions, and accurate control features, Permanent Magnet Syn-chronous Motor (PMSM) are experiencing widespread applications across various industries. By accurately characterizing the dynamic behavior of PMSM systems through system identi-fication, engineers can ensure that PMSM motors reach their maximum potentials and meet the stringent requirements of modern industrial and technical systems while reducing energy consumption and maintenance costs. The traditional recursive least squares method is sensitive to noises, and unable to accu-rately identify parameters in complex environments. Pure data-driven models lack interpretability and require complex model architecture and computational costs. To this end, this work draws knowledge-informed neural ordinary differential equations (NODEs) for system identification, which embeds system prior knowledge into the NODEs for more efficient and accurate model learning. Comparative simulations show that this method not only obtains a higher-precision system model, but also significantly reduces the amount of training data and computation costs.

Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works have focused on NODEs in concise forms, while numerous physical systems taking straightforward forms in fact belong to their more complex quasi-classes, thus appealing to a class of general NODEs with high scalability and flexibility to model those systems. This however may result in intricate nonlinear properties. In this paper, we introduce ControlSynth Neural ODEs (CSODEs). We show that despite their highly nonlinear nature, convergence can be guaranteed via tractable linear inequalities. In the composition of CSODEs, we introduce an extra control term for learning the potential simultaneous capture of dynamics at different scales, which could be particularly useful for partial differential equation-formulated systems. Finally, we compare several representative NNs with CSODEs on important physical dynamics under the inductive biases of CSODEs, and illustrate that CSODEs have better learning and predictive abilities in these settings.

This paper investigates distributed formation control of multi-mobile robot systems with collision avoidance. A novel guidance module based formation control scheme is established, which consists of two main parts. In the first part, on the communication network of the multi-mobile robot system, a distributed guidance module is constructed from some predesigned virtual dynamics scattered in the robots’ feedback loops. By using some proper distributed formation control methods and distributed observer techniques, some formation references are generated by the guidance module. In the second part, by taking these references as the tracking references, some tracking controllers are designed and assigned to the robots such that the robots’ positions track their respective references asymptotically. A “two-layer constraint mechanism” is presented in the above controller design to limit both the formation references and the robots’ tracking errors such that robots’ collision avoidance is guaranteed. In this way, the multi-mobile robot system completes the desired collision-free formation control task. Compared with existing results, the method proposed in this paper has a better plug-and-play function and wider application scope, especially when the practical robots have tight encapsulations such that their pre-equipped tracking controllers cannot be arbitrarily redesigned. Moreover, under the proposed scheme, the asymptotic formation convergence is achieved by the robots without extra limitations on robots’ initial states and the utilization of global information. Some simulations and an experiment are given to validate the effects of the proposed methods. Note to Practitioners—This paper is motivated by controller encapsulation characteristics of practical mobile robot products. To complete various formation tasks, most of the related existing formation control methods require robots’ controllers to be continually updated and redesigned. However, this purpose is sometimes unachievable because actual mature robot products may have tight controller packages for trade secrets and intellectual property, or engineers want to retain robots’ well-adjusted default performances. To overcome this practical limitation, this paper provides a novel “guidance module based formation control scheme”. Under this scheme, engineers only need to put most efforts on a guidance module design to generate desired real-time desired tracking references for robots. A new “two-layer constraint mechanism” is proposed and applied here to guarantee collision avoidance among the robots when using the proposed scheme. With this scheme, engineers can establish required formation control strategies without robots’ pre-equipped controllers changed and the original control performances abandoned, as long as the robots have some basic capability of tracking given trajectories. Theoretical analysis and experiments on this scheme are all shown. In future research, based on the proposed scheme, we will continue to develop application-oriented formation control methods to improve the anti-disturbance performance and robustness of the multi-mobile robot systems.

In this paper, the output voltage tracking control of DC-DC boost converters is studied. To meet the increasing safety requirements and enhance the control system robustness, overcurrent protection and disturbance rejection are investigated simultaneously. A simple and effective control scheme is proposed to achieve all these three goals, which includes two parts. In the first part, a disturbance observer is constructed to estimate multiple disturbances (including the input voltage fluctuations and the load variations). In the second part, a composite current-constrained controller is proposed by embedding the disturbance estimates and the nonlinear penalty term into the passivity-based control law. Under the novel control scheme, rapid tracking performance and safe overcurrent protection are obtained, even in the presence of multiple disturbances. Rigorous stability analysis is conducted to demonstrate the accomplishment of the output voltage tracking task and the strict guarantee of the current constraint. Simulations and experiments are performed to verify the effectiveness of the proposed control scheme.

Considering the multi-frequency-band uncertainties with distinctive forms and perturbed coefficients faced by flexible gimbal servo systems (GSSs) in control moment gyros (CMGs), a robust high-accuracy speed-regulation controller is proposed in this paper. Firstly, to obtain a more precise uncertainties compensation, a generalized model of flexible GSS with refined classification and description upon various types of uncertainties is accomplished. Then a comprehensive disturbance observer is designed based on this generalized model to accurately estimate compound disturbances in multi-frequency-band simultaneously, and a novel quantitative robustness analysis and method against the frequency deviations of faced periodic disturbance is further conducted. Due to the nominal recovery performance guaranteed by this estimation-based feedforward framework, a resonance cancellation-based composite controller is designed for the speed vibration suppression during the transient processes even in the presence of flexibility coefficients perturbation. Rigorous robust stability analysis for the closed-loop system is established. Experimental results with various uncertainties are provided to fully validate the effectiveness of the proposed scheme.

This article investigates the event-triggered model predictive control (MPC) problem for a class of networked nonlinear uncertain systems subject to time-varying disturbances. Different from the traditional MPC, the proposed periodic event-triggered MPC (PETMPC) method does not generate new control sequence unless a predesigned periodic event-triggering mechanism (PETM) is violated. First, a generalized proportional-integral observer (GPIO) is developed to estimate the unknown state and disturbance information by using the sampled-data output of controlled system. Then, the disturbance predictions for future finite steps are obtained based on forward Euler method. After that, with the help of prediction model, the optimal control sequence, including the future finite step predicted control inputs, is generated and dexterously exploited during the interevent interval by storing it in a buffer installed between the control sequence generator and actuator, thereby leading to the further reduction of signal transmission number and the frequency of control sequence computations. Through a rigorous stability analysis, it can be proved that the closed-loop hybrid control system is globally bounded stable under the nominal PETMPC law. Finally, numerical simulations are conducted to substantiate the feasibility and superiority of the proposed PETMPC method.

This article addresses the tracking control problem of nonlinear pure-feedback systems, where the control coefficients and the dynamics of the references are unknown. Fuzzy-logic systems (FLSs) are used to approximate the unknown control coefficients and at the same time the adaptive projection law is designed to allow each fuzzy approximation to cross zero, which yields that the proposed method avoids the assumption of using Nussbaum function, that is, the unknown control coefficients never cross zeros. Another adaptive law is designed to estimate the unknown reference and then it is intergraded into the saturated tracking control law to achieve the uniformly ultimately bounded (UUB) performance of the resulting closed-loop system. Simulations show the feasibility and effectiveness of the proposed scheme.

This article investigates the robust control problem for speed regulation of networked permanent magnet synchronous motor subject to the limited communication bandwidth. To handle this, a new sampled-data disturbance rejection control method is developed via a well-designed discrete-time dynamic event-triggered mechanism (DETM). First, a predictor-based generalized proportional integral observer is introduced to estimate the lumped disturbances, when only the sampled-data output is available. Then, a composite proportional feedback controller is formed by fully utilizing disturbance estimation. The composite controller updates only when the designed discrete-time DETM is violated, resulting in remarkable communication and computation resource savings while maintaining the desirable disturbance rejection ability. The designed DETM can be applied to digital computers easily due to the discrete-time detection. Simulations and experiments are carried out to validate the feasibility and effectiveness of the proposed control scheme.

Inspired by the concept of recently proposed dual control for exploration and exploitation, this article presents a multistep dual control for exploration and exploitation with guaranteed convergence in search for autonomous sources. To deal with an unknown source position and environment, the proposed dual control algorithm faces significant challenges in demonstrating its recursive feasibility and convergence. With the help of the properties of Bayesian estimators, we redesign a multistep dual control for exploitation and exploration algorithm with necessary terminal ingredients and show that the recursive feasibility and the convergence of the modified dual control algorithm are guaranteed. Two simulation scenarios are conducted, which demonstrate that the proposed algorithm outperforms the stochastic model-predictive control approach and the informative path planning approach in terms of searching successful rates and efficiency.

The partial discharge (PD) detection is of critical importance in the stability and continuity of power distribution operations. Although several feature engineering methods have been developed to refine and improve PD detection accuracy, they can be suboptimal due to several major issues: 1) failure in identifying fault-related pulses; 2) the lack of inner-phase temporal representation; and 3) multiscale feature integration. The aim of this article is to develop a learning-based multiscale feature engineering (LMFE) framework for PD detection of each signal in a three-phase power system, while addressing the above issues. The three-phase measurements are first preprocessed to identify the pulses together with the surrounded waveforms. Next, our feature engineering is conducted to extract the global-scale features, i.e., phase-level and measurement-level aggregations of the pulse-level information, and the local-scale features focusing on waveforms and their inner-phase temporal information. A recurrent neural network (RNN) model is trained, and intermediate features are extracted from this trained RNN model. Furthermore, these multiscale features are merged and fed into a classifier to distinguish the different patterns between faulty and nonfaulty signals. Finally, our LMFE is evaluated by analyzing the VSB ENET dataset, which shows that LMFE outperforms existing approaches and provides the state-of-the-art solution in PD detection.

In this paper, a robust predictive generalized proportional-integral observer (PGPIO)-based control is investigated for transmission control protocol (TCP)/active queue management (AQM) networks. In the design of the congestion control scheme, the round-trip time (RTT) is considered as the input time-delay, while the non-response flows (e.g., user datagram protocol flows) are regarded as external disturbances. A novel PGPIO is proposed to provide future information about the disturbance as well as the system dynamics in the presence of time-delay. Based on the predictions, a robust composite controller is constructed as the AQM algorithm to avoid congestion. The performance is demonstrated through rigorous mathematical analysis. Finally, some simulation results are presented to verify the feasibility and effectiveness of the proposed method.

In this paper, the output feedback based periodic event-triggered control problem is considered for a class of nonminimum-phase nonlinear systems via dynamic event-triggering mechanism. When only the sampled-data output is known, a new periodic event-triggered control method is proposed via output feedback and the control input updates based on a discrete-time dynamic event-triggering condition. Despite the unstable zero dynamics, the proposed control method can asymptotically stabilize the hybrid control systems by closing the loop only when it is necessary. In contrast to the continuous-time static one, the proposed dynamic triggering condition has several advantages including the easier digital implementation and the larger average inter-event time interval. The delicate analysis gives the explicit expression of the maximum allowable sampling period, and the global asymptotic stability can be achieved for the hybrid control systems. Finally, the effectiveness of the proposed periodic event-triggered control method is verified by a numerical simulation.

This article considers the problem of periodic event-triggered control design for dual-rate networked control systems subject to nonvanishing disturbance. The plant considered in this article is a kind of dual-rate networked control system, where the sensor samples the measurement output at a slow rate and the actuator updates the control input at a fast rate. Despite the slow-rate sampling of the sensor, a new output predictor-based observer is proposed to accurately estimate system state and disturbance in the intersample time interval, and an active anti-disturbance controller that updates at a fast rate is accordingly proposed, such that the desirable control performance and disturbance rejection performance can be achieved. At each fast-rate updating time instant, we use the prediction technique to generate a data packet, including the computed current control input and the predicted values of the control inputs for the future finite steps, and design a new periodic event-triggered mechanism to determine whether to transmit the data packet via a communication network or not. The proposed control method is easily implemented in digital platform since it has a discrete-time form. To verify the effectiveness of the proposed control method, we finally present the simulation results of a practical speed control system.

In this article, we studied the parameters identification problem for the single sinusoidal signal based on the finite-time observer technique. After representing the sinusoidal signal with known frequency as a second-order time-invariant system, a finite-time observer-based estimation strategy is designed based on the homogeneous system theory to obtain unknown amplitude and phase angle. When the signal frequency is unknown, the original signal will be constructed into a third-order nonlinear system, which is challenging to design the corresponding state estimator. Based on the Lyapunov analysis method and adding a power integrator technique, a finite-time estimation scheme is developed and analyzed strictly. Finally, for a single-phase grid signal, some experimental results are provided to illustrate the efficacy of the proposed method.

This article investigates the finite-time distributed approximate optimization problem of higher order multiagent systems, where the local cost functions are considered to be quadratic functions. This problem is solved via penalty-function-based method. First, by the penalty-function method, a global approximate cost function is constructed. Second, nonlinear distributed optimization algorithms are proposed for higher order multiagent systems by the tool of adding a power integrator technique. In the optimization algorithms design, the gradients of the approximate cost function are utilized. Under the proposed optimization algorithms, the agents approach the approximate optimal solution in finite time. Although there exist errors (they may be called approximation errors) between the approximate minimizers and the global accurate minimizer, the approximation errors can be regulated by penalty parameter and the relationship between the bound of the approximation errors and the penalty parameter is given explicitly. Furthermore, the proposed distributed approximate optimization algorithms are applied to the optimal rendezvous problem of wheeled multimobile robots, making the mobile robots achieve approximate optimization rendezvous in finite time. The effectiveness of the proposed distributed optimization algorithms and their applications to optimal rendezvous problem are validated by simulations.

In this article, the distributed finite-time optimization problem is investigated for second-order multiagent systems with disturbances. To solve this problem, a feedforward-feedback composite control framework is established, which contains two main stages. In the first stage, for disturbed second-order individual systems with generally strongly convex cost functions, a composite finite-time optimization control scheme is proposed based on the combination of adding a power integrator and the finite-time disturbance observer techniques and the use of the cost functions' gradients and Hessian matrices. In the second stage, based on the result of the first stage, a distributed composite finite-time optimization control framework is built for disturbed second-order multiagent systems with quadratic-like local cost functions. This framework involves a kind of finite-time consensus algorithm, some novel distributed finite-time estimators designed for each agent to estimate the velocity, the gradient and Hessian matrix for the local cost function of any other agent, and some optimization terms in the form of the optimization controllers proposed in the first stage and based on the estimates from the distributed estimators. The finite-time convergence of the closed-loop systems is rigorously proved. The simulation results illustrate the effectiveness of the proposed control framework.

This paper develops a new estimate-based dynamic event-triggered output feedback controller for networked control systems subject to nonlinear uncertainties. Specifically, based on the sampled-data, a discrete-time output feedback controller and a discrete-time dynamic event-triggering condition are proposed by the virtue of feedback domination technique. The proposed event-triggered control method is easy to implement in digital computers due to the form of discrete time. Under the proposed dynamic event-triggered control method, the selection regions of the sampling period and the scaling gain are explicitly given to guarantee the global practical/asymptotic stability of the closed-loop system. Finally, two examples are employed to verify the efficiency of the proposed dynamic event-triggered control approach.

This article is concerned with the problem of global finite-time output stabilization for a class of second-order nonlinear systems with both uncertain nonlinear dynamics and unknown external disturbance. Specifically, at the first step, without considering the external disturbance, a global finite-time state feedback controller is proposed to dominate uncertain nonlinear dynamics of the second-order system. To address the more challenging case where only the system output is available, a novel design idea of the nonseparation principle is employed. By treating the unknown external disturbance as a generalized state, a finite-time convergent extended state observer is constructed to estimate the unmeasured state and the unknown external disturbance. Based on this observer, an output-based composite controller with finite-time convergence is developed. The global uniform finite-time stability of the overall closed-loop system is proven based on the Lyapunov method. Simulation results of the inverted pendulum system demonstrate the superiority of the proposed control method in terms of both convergence performance and disturbance rejection performance.

This paper proposes a new output-based dynamic event-triggered mechanism (ETM) for disturbance rejection control of a class of networked nonlinear uncertain systems subject to additive time-varying disturbance. In the proposed control method, a new robust output feedback controller is first designed based on a generalized proportional-integral observer to attenuate/compensate the undesirable influence of nonlinear uncertainties and disturbances. Different from the static ETM, two new dynamic variables are defined, and thereafter, two kinds of different discrete-time dynamic ETMs are developed only using the sampled-data output signal, such that a better tradeoff between the communication properties and the control properties can be obtained. It is shown that under the proposed control methods, the global bounded stability of the closed-loop hybrid system can be guaranteed by choosing some appropriate parameters. Finally, the numerical simulations of a single link robot arm are conducted to demonstrate the feasibility and efficacy of the proposed control approach.

DC-DC converter systems have drawn extensive research attentions and shown upward tendencies for industrial and military applications. In this article, a novel digital fast terminal sliding mode control (FTSMC) approach is investigated for dc-dc buck converters with mismatched disturbances. Specifically, the approximated discrete-time model of the converters with multiple disturbances is first obtained and analyzed based on the Euler's discretization method. Then, by adopting the delayed estimation technique, it is easy to obtain the accurate estimations of the lumped disturbances. Integrating disturbance compensations into the modified digital fast terminal sliding mode surface, the proposed controller is finally constructed on the basis of equivalent control method and the performance analysis is presented. Both simulation and experimental comparisons are made for the proposed digital FTSMC approach and the existing discretized linear sliding mode controllers to validate the effectiveness and feasibility of the presented controller. The proposed FTSMC approach is characterized by higher voltage tracking accuracy and better dynamic properties in different operating conditions.

As a virtual sensor, disturbance observer provides an alternative approach to reconstruct lumped disturbances (including external disturbances and system uncertainties) based upon system states/outputs measured by physical sensors. Not surprisingly, measurement errors bring adverse effects on the control performance and even the stability of the closed-loop system. Toward this end, this paper investigates the problem of disturbance observer-based control for a class of disturbed uncertain nonlinear systems in the presence of unknown output measurement errors. Instead of inheriting from the estimation-error-driven structure of Luenberger-type observer, the proposed disturbance observer only explicitly uses the control input. It has been proved that the proposed method endows the closed-loop system with strong robustness against output measurement errors and system uncertainties. With rigorous analysis under the semiglobal stability criterion, the guideline of gain choice based upon the proposed structure is provided. To better demonstrate feature and validity of the proposed method, numerical simulation and comparative experiments of a helicopter model are implemented.

In this article, the distributed optimization problem is studied for second-order multiagent systems with both mismatched and matched disturbances. For this problem, a distributed active antidisturbance control framework is established, which consists of both disturbance estimation/compensation and distributed feedforward-feedback composite control design. In the first stage, some disturbance estimators are utilized to estimate various types of matched/mismatched disturbances for each agent. In the second stage, for each agent, based on the disturbance estimates, the information exchanges between the neighboring agents, and the gradient of the local cost function only accessible to itself, a kind of distributed composite controllers are proposed. Under these controllers, all the agents' outputs asymptotically reach consensus to the minimizer of the global cost function, which is the sum of all the local cost functions. The closed-loop system convergence is proven based on a new Lyapunov function, convex analysis, and an input-to-state stability criterion. Simulations demonstrate the effectiveness of the proposed control scheme.

This paper investigates a novel nonrecursive tracking control law design for a class of nonlinear systems via dynamic output feedback. As the main contribution of this paper, a global nonrecursive tracking design procedure is first proposed to render a simple construction of a realizable output feedback control law, whose gain selections follow the conventional pole placement approach while the stability margin can be guaranteed via a sufficiently large scaling gain. By introducing a Lyapunov function which neglects the virtual controllers in essence, rigorous analysis is presented to ensure the global stability. In addition, finite-time and asymptotical tracking results can now be achieved within the same design framework whereas the tunable homogeneous degree plays as a key role. As another contribution, by proposing a saturated dynamic compensator, a less ambitious but practical control objective, namely semiglobal stability is achieved of the closed-loop system to relax the requirement of the restrictive growth conditions for global control design. Taking consideration of the case when system is subject to mismatched disturbances, a unified design and stability analysis framework shows that the practical tracking result can also be realized. A numerical example is provided to illustrate the effectiveness of the nonrecursive design and the simplicity of the proposed tracking control algorithm.

The wide utilization of power electronic converters causes the constant power load stability issue in DC microgrids. This paper proposes an offset-free model predictive controller for a DC/DC boost converter feeding constant power loads. First, a baseline nonlinear model predictive controller is designed by solving a receding horizon optimization problem explicitly. Then a higher-order sliding mode observer is utilized to estimate the unknown load variation and system uncertainties. Finally an offset-free controller is integrated by the baseline controller and observer. The proposed controller achieves optimized transient dynamics and accurate tracking with large signal stability. Simulation results are presented to verify the proposed approach.

This paper develops a methodology on sampled-data-based event-triggered active disturbance rejection control (ET-ADRC) for disturbed systems in networked environment when only using measurable outputs. By using disturbance/uncertainty estimation and attenuation technique, an event-based sampled-data composite controller is proposed together with a discrete-time extended state observer. Under the presented new framework, the newest state and disturbance estimates as well as the control signals are not transmitted via the common sensor-controller network, but instead communicated and calculated until a discrete-time event-triggering condition is violated. Compared with the periodic updates in the traditional time-triggered active disturbance rejection control, the proposed ET-ADRC scheme can remarkably reduce the communication frequency while maintaining a satisfactory closed-loop system performance. The proposed discrete-time control scheme provides the engineers with a manner of direct and easier implementation via networked digital computers. It is shown that the bounded stability of the closed-loop system can be guaranteed. Finally, an application design example of a dc-dc buck converter with experimental results is conducted to illustrate the efficiency of the proposed control scheme.

Under the noncascade structure, a permanent-magnet synchronous motor (PMSM) regulates the speed and current in one loop. On the one hand, fast dynamic performance requires large transient current to provide a high torque. On the other hand, unlike a cascade control, the q-axis current is no longer governed by a reference current signal. In such a system, the nominal controllers cannot guarantee that the q-axis current is within the required range. But an excessively large transient current may threaten the circuit safety. To solve the overcurrent protection problem, the ordinary solution is to choose conservative control parameters, but the dynamic performance inevitably suffers a certain degree of loss. In order to improve this drawback, a simple and effective control scheme is introduced with a current-constrained technique. By constructing a special nonlinear gain, the punishment mechanism for the q-axis current is established in the control action directly. The proposed control approach does not impose limitations on the initial state. Moreover, it has good robustness to load torque uncertainty and undergoes rigorous theoretical analysis. Besides, the proposed current-constrained controller has a very concise structure. It yields a higher reliability of the PMSM control system. Comparative simulation and experimental results between the classic PID and the current-constrained controller on the PMSM servo system verify the feasibility of the presented control scheme.

This paper studies the finite-time output consensus problem of higher-order multiagent systems subject to both mismatched disturbances and unknown state elements, where the disturbances are allowed to be fast time-varying. To solve this problem, an active anti-disturbance control approach is developed based on the disturbance estimation/compensation and the baseline feedback consensus protocols. First, to estimate the matched/mismatched disturbances and the agents unknown state elements, a finite-time generalized state observer is constructed for each agent. Second, by integrating the distributed adding a power integrator feedback control method and the estimates of the matched/mismatched disturbances and the agents unknown state elements together, composite consensus protocols are developed for both leaderless and leader-follower cases. In both cases, the proposed protocols guarantee that the agents outputs reach consensus in finite time. Simulations show the effectiveness of the proposed consensus algorithms.

This paper proposes a block backstepping trajectories tracking control scheme for a class of unmanned helicopters. The control objective is to make the position and yaw angle trajectories of the helicopter track the desired position and yaw angle trajectories. In order to design the controller, the helicopter system is divided into three subsystems at first. Then based on the block backstepping technique, four control inputs which constitute the helicopter controller are designed step by step in three subsystems. The asymptotic stability of the closed-loop helicopter trajectories tracking error system is verified based on Lyapunov stability analysis. Finally, numerical simulations demonstrate the effectiveness of the proposed block backstepping control scheme.

This paper investigates the angular velocity trajectory tracking problem for a DC permanent magnet motor with a DC-DC buck power converter based smooth starter. In practice, the composite control system is inevitably effected by unknown, exogenous, time-varying load torque disturbances. To this end, this paper specifically puts forward a disturbance rejection control approach. Under the proposed method, a novel disturbance observer is constructed to estimate the differences between actual states and the steady-state values of states and control. Therefore, an output feedback composite controller is designed. A key idea in the proposed control strategy is that the unmatched disturbances are transformed into matched ones ingeniously. The proposed control method is tested through simulation studies, where the results obtained validate the superiority of the proposed method.

This paper is devoted to solving the output consensus problem of leader-follower higher-order nonlinear multiagent systems subject to mismatched disturbances. The disturbances are allowed to be in higher-order forms. First, by constructing a generalized proportional-integral observer for each follower, estimates of the disturbances and their derivatives are obtained. At the same time, a distributed observer is also developed for the followers to estimate the leader state information. Second, based on the estimates of the disturbances and the leader state, together with the backstepping technique, a feedforward-feedback composite consensus control scheme is proposed. The designed distributed protocols guarantee asymptotic output consensus for the agents. Simulation results validate the effectiveness of the proposed composite control scheme.

During the past few years, finite control set predictive current control (PCC) method has attracted more and more attention in research and industry applications. However, PCC method could be improved by considering two points. First, the current reference used in the cost function of PCC control scheme is usually produced by a proportional and integration speed controller. Confront with load torque and time-varying system parameters, it is a better solution to design a disturbance estimation based feed-forward compensated controller. In this way, the current reference could be generated faster and more accurate. Second, the PCC method is model-based method which means the accuracy of the model parameters are essential. In real system, time-varying parameters existed almost always. This paper investigates a generalized proportional integral observer based PCC approach for dealing with load torque disturbance, time-varying parameter uncertainties. The effectiveness of the proposed method has also been confirmed by simulation and a lab-constructed experimental prototype.

One weakness of the model predictive control method is that the predicted states/outputs are constructed by an exact nominal model. Its accuracy varies if uncertainties exist, which will ultimately deteriorate the closed-loop control performances. To this end, we propose a generalized dynamic predictive control method for a class of lower-triangular systems subjected to nonparametric uncertainties. Instead of relying on the inherent robustness property of the standard predictive controller or on-/off-line parameter identification, a dual-layer adaptive law is designed to estimate the lumped effect of system uncertainties. As another main contribution, under a less ambitious but more practical control objective, namely semi-global stability, various nonlinearity growth constraints utilized in the existing related methods could be essentially relaxed. Numerical simulation and illustrative experimental tests of a series elastic actuator system are provided to demonstrate both simplicity and effectiveness of the proposed method.

This paper mainly studies the angle tracking problem in electronic throttle system with unknown time-varying disturbances. Firstly, generalized proportional integral observer (GPIO) is used to estimate the time-varying disturbances including model uncertainties, friction torque and spring initial torque. Secondly, a composite controller combining disturbance estimation and backstepping control method is designed, which is called the BSC+GPIO method. This control method is convenient to implement and the disturbance rejection capability is enhanced by feedforward compensating the estimated value of system disturbances. The simulation results show the effectiveness of the proposed method.

Current control of IPMSM servo system is investigated in this paper. Under the field-weakening control framework, nonlinear couplings of the voltage equations are very strong. The current control performance may not be well until such nonlinear couplings are well dealed. In this case, a DOB-based model predictive control is proposed to improve the current control performance under field-weakening control framework. The proposed control method consists of a forecasted model based on disturbance observer, feedback correction for model mismatch rejection, and receding optimization for an optimized control input. Numerical simulations demonstrate that proposed method achieves nonlinear coupling attenuation ability and well promising field-weakening control performance.

This paper proposes a new continuous terminal sliding mode guidance law for three-dimensional missile guidance system under maneuvering target with consideration of second-order autopilot dynamics. The proposed guidance law not only guarantees the azimuth rate and elevation rate of guidance system converge to zero in finite time but also ensures the continuity of control action. Simulations of a practical interception process under complex maneuvering target are carried and the simulation results demonstrate the effectiveness of the proposed guidance method.

Finite-control-set-based predictive torque control (PTC) method has received more and more attention in recent years due to its fast torque response. However, it also has two drawbacks that could be improved. First, the torque reference in the cost function of the existing PTC method is generated by the proportional-integral speed controller, so torque reference's generation rate is not fast and its accuracy is low especially when the load torque is given suddenly and inertia value is varying. In addition, the variable prediction of the traditional PTC method depends on the system model, which also has the problem of parameter uncertainties. This paper investigates a disturbance observer (DOB)-based PTC approach for induction motor systems subject to load torque disturbances, parameter uncertainties, and time delays. Not only does the speed loop adopt a DOB-based feed-forward compensation method for improving the system disturbance rejection ability and robustness, but the flux, current, and torque predictions are also improved by using this technique. The simulation and experimental results verified the effectiveness of the proposed method.

In this paper, the output voltage trajectory tracking for the conventional DC-DC boost power converter in the presence of circuit parameter perturbations is investigated. Based on the property of incremental passivity, a simple feedback controller is designed. Meanwhile, to obtain a better disturbance rejection property, we employ two nonlinear disturbance observers (NDOBs) to attenuate the uncertainties in the output voltage and inductor current channels, respectively. Moreover, global trajectory tracking performance of the system under disturbances is ensured. Finally, simulation and experiment studies are offered to confirm the feasibility and efficiency of the presented approach. The related results reveal the proposed controller delivers a nice antidisturbance performance as well as a superior nominal tracking ability.

An adaptive control scheme based on disturbance observer is proposed in this paper for the bank-to-turn missile autopilot design. In the past, the disturbance observer has been introduced for bank-to-turn missile system to improve system performance in the presence of severe disturbances. However, the disturbance rejection performance is not quite satisfying when considering the fluctuation of the aerodynamic parameters. Therefore, a kind of time-varying disturbance observer is proposed in this paper to enhance the robustness against variations of aerodynamic parameters. The main innovation is that the nominal model of the BTT missile in the disturbance observer is updated over time along with the aerodynamic parameters. And simulation comparisons in the last part show the effectiveness of the proposed adaptive control method.

In this paper, we propose an event-driven output feedback control strategy for a class of nonlinear systems subject to disturbances. Different from the time-driven control, the event-driven control can be regarded as a more reactive approach where the control actions are taken only when an event is triggered, thus the event-driven control has a better balance between the control performance and other system aspects (such as processor load, communication load, and system cost price). Based on the extended state observer (ESO), we propose a composite event-driven controller, which is asynchronously updated only when an intolerable effect on the closed-loop performance is produced. It is proved that the closed-loop system is globally uniformly bounded, and has a good robustness against disturbances. Meanwhile, the closed-loop system considered in this paper is a hybrid system, thus we need to consider the problem of Zeno behavior, which is a phenomenon unique to hybrid systems, and describes the situation where a hybrid system undergoes an unbounded number of discrete transitions in a finite and bounded length of time. Fortunately, it is proved that the system under the event-driven controller can avoids the Zeno behavior of the sampling, and has the significantly reduced sampling frequency compared with the time-driven controller. Finally, a simulation of DC-DC buck converter is conducted to demonstrate the efficiency of the new scheme.

In complex industrial situations, modern permanent magnet synchronous motor (PMSM) servo drive system always face different kinds of disturbances, especially constant or slowly-varying disturbances (load disturbances) and periodic disturbances (torque ripples). Conventional disturbance rejection techniques, e.g., the extended state observer based control (ES-OBC) and the disturbance observer based control (DOBC), can only reject asymptotically single kind of disturbances (constant or slowly-varying disturbances). To this end, it is essential to extend the conventional disturbance rejection approach for multiple disturbances. Inspired by the internal model principle (IMP), appropriately embedding the model of disturbances into the design of disturbance observer, a composite disturbance observer based control is proposed for PMSM with multiple disturbances. The proposed disturbance observer (named as IMESO), consisting of the internal model principle (IMP) and the extended state observer (ESO), can reject multiple disturbances asymptotically. Thus, a composite control law consisting of proportional feedback and disturbance feedforward compensation is developed to control the speed loop. The proposed method is effective to reject the intricate multiple external disturbances and unmodeled dynamics. Simulations and experiments both verify the effectiveness of the proposed method.

Model-based predictive direct control methods are advanced control strategies in the field of power electronics. To control an induction machine (IM), the predictive torque control (PTC) method evaluates the electromagnetic torque and stator flux in the cost function. The switching vector selected for the use in the insulated gate bipolar transistors (IGBTs) minimizes the error between references and the predicted values. The system constraints can be easily included. The predictive current control (PCC) strategy assesses the stator current in the cost function. The weighting factor is not necessary. Both the PTC and PCC methods are very useful direct control methods that do not require the use of a modulator. In this paper, the PTC and PCC methods are carried out experimentally for an IM on the same test bench. The behaviors and the robustness in steady state and the performances in transient state are evaluated.

Considering the existence of disturbance in the induction machine (IM) drive system, this paper develops a composite control scheme based on linear extended state observer (LESO) and continuous finite time control (FTC) to improve the disturbance rejection property of system. First, a LESO is introduced to estimate the disturbances of system. The estimated value is used in the feed-forward compensation design. Second, a continuous finite-time feedback control technique is applied in the feedback design. Then the stability of the controller is analyzed. Simulation and experimental comparisons with two other control methods, traditional Proportional Integral (PI) and Proportional feedback plus feedforward compensation based on LESO(P+LESO), are provided to verify the effectiveness of the proposed method.

This paper presents the finite-time control problem for permanent magnet synchronous motor (PMSM) speed servo system using different kinds of finite-time control methods. Integral terminal sliding mode controller and continuous finite-time controller are designed respectively for the speed loop and d-axis current loop. The proof of finite-time stability for PMSM speed servo system is also given. Compared with the corresponding control method of asymptotical stability, the controller based on the finite-time control can make the output of system track the desired speed reference signal in finite time and obtain a better dynamic response and anti-disturbance performance. Meanwhile, considering the large chattering phenomenon caused by high switching gains, a composite integral terminal sliding mode control method based on disturbance observer is proposed to reduce chattering. Through feed-forward compensation based on disturbance estimation, the composite integral terminal sliding mode controller may take a smaller value for the switching gain without sacrificing disturbance rejection performance. TMS320F2808 DSP experimental results are provided to show the superiority of the proposed methods.

In this paper, the distributed finite-time containment control problem for double-integrator multiagent systems with multiple leaders and external disturbances is discussed. In the presence of multiple dynamic leaders, by utilizing the homogeneous control technique, a distributed finite-time observer is developed for the followers to estimate the weighted average of the leaders' velocities at first. Then, based on the estimates and the generalized adding a power integrator approach, distributed finite-time containment control algorithms are designed to guarantee that the states of the followers converge to the dynamic convex hull spanned by those of the leaders in finite time. Moreover, as a special case of multiple dynamic leaders with zero velocities, the proposed containment control algorithms also work for the case of multiple stationary leaders without using the distributed observer. Simulations demonstrate the effectiveness of the proposed control algorithms.

A new continuous dynamic sliding-mode control (CDSMC) method is proposed for high-order mismatched disturbance attenuation in motion control systems using a high-order sliding-mode differentiator. First, a new dynamic sliding surface is developed by incorporating the information of the estimates of disturbances and their high-order derivatives. A CDSMC law is then designed for a general motion control system with both high-order matched and mismatched disturbances, which can attenuate the effects of disturbances from the system output. The proposed control method is finally applied for the airgap control of a MAGnetic LEViation (MAGLEV) suspension vehicle. Simulation results show that the proposed method exhibits promising control performance in the presence of high-order matched and mismatched disturbances.

This paper investigates the speed regulation problem of permanent magnet synchronous motor servo system based on terminal sliding mode control method. By introducing a non-singular terminal sliding mode manifold, a novel terminal sliding mode controller is designed for the speed loop. This controller can make the states not only reach the manifold in finite time, but also converge to the equilibrium point in finite time. Thus, the controller could make the motor speed reach the reference value in finite time, obtaining a faster convergence and a better tracking precision. Meanwhile, considering the large chattering phenomenon caused by high switching gains, a composite terminal sliding mode control method based on disturbance observer is proposed to reduce chattering. Through disturbance estimation for feed-forward compensation, the composite terminal sliding mode controller may take a smaller value for the switching gain without sacrificing disturbance rejection performance. Matlab simulation and TMS320F2808 DSP experimental results are provided to show the superiority of the proposed methods.

In this paper, the speed regulation problem for permanent magnet synchronous motor (PMSM) system under vector control framework is studied. First, a speed regulation scheme based on standard internal model control (IMC) method is designed. For the speed loop, a standard internal model controller is first designed based on a first-order model of PMSM by analyzing the relationship between reference quadrature axis current and speed. For the two current loops, PI algorithms are employed respectively. Second, considering the disadvantages that the standard IMC method is sensitive to control input saturation and may lead to poor speed tracking and load disturbance rejection performances, a modified IMC scheme is developed based on a two-port IMC method, where a feedback control term is added to form a composite control structure. Third, considering the case of large variations of load inertia, two adaptive IMC schemes with two different adaptive laws are proposed. A method based on disturbance observer is adopted to identify the inertia of PMSM and its load. Then a linear adaptive law is developed by analyzing the relationship between the internal model and identified inertia. Considering the control input saturation in practical applications, a fuzzy adaptive law based IMC scheme is developed based on apriori experimental tests and experiences, where a fuzzy inferencer based supervisor is designed to automatically tune the parameter of speed controller according to the identified inertia. The effectiveness of the proposed methods have been verified by Matlab simulation and TMS320F2808 DSP experimental results.