This study proposes a fractional-order (FO) improved fast terminal sliding mode controller for permanent-magnet synchronous motor speed regulation system. By designing an FO proportional–integral controller for current loops, an FO model between reference q-axis current and speed output is proposed. By introducing an FO terminal sliding mode surface, a novel FO terminal sliding mode controller is designed for speed loop to improve the speed tracking performance. The proposed FO controller can make speed reach reference value in finite time. Moreover, it is proved that the control time of the FO sliding mode controller is shorter than integer-order (IO) sliding mode controller. To further enhance the convergence speed, the fast terminal sliding mode control method is used. Meanwhile, FO disturbance observer is utilised to enhance the disturbance-rejection ability. The control law of the proposed controller is designed according to Lyapunov stability theorem. Finally, Simulation and experimental results demonstrate the effectiveness, high control performance and high disturbance-rejection ability of the proposed composite FO controller in comparison with IO controller.

This study investigates the problem of distributed receding horizon control (DRHC) for constrained networked systems with polytopic uncertainty description, subject to time delays. Considering the limited communication capacity of the network and computational complexity, the approach of this study is based on a synchronous and non-iterative structure. Thus, for each subsystem, assumed predictive state evolutions of the neighbours are used. To restrict the assumed evolutions not deviating much from the true ones, the compatibility condition is derived concerning global stability. Time delays are handled by introducing an augmented polytopic uncertainty description, and the local optimisation problem is properly formulated by means of the robust receding horizon control technique. Applying the DRHC approach of this study, the recursive feasibility of the optimisation problem and exponential stability of the global system are guaranteed. An example is provided to illustrate the effectiveness of the proposed approach.

The uncertainty and disturbance estimator (UDE)-based robust control approach is widely investigated and applied due to its excellent performance and simple implementation. However, its stabilisability of unstable systems has not been documented. In this study, the sufficient and necessary stabilisability conditions of the UDE-based robust control are investigated. According to the stabilisability conditions, a systematical design method is presented for the reference model based on the controllable canonical transformation and pole placement. This is then applied to a magnetic levitation system (MagLev) subject to model uncertainties and external disturbance as an example. Simulation results are presented to illustrate the effectiveness of the proposed control approach with respect to matched uncertainties.

This study addresses robust QSR-dissipativity and feedback dissipation of a class of fractional-order (FO) uncertain linear systems. Both the state and controlled output matrices are with time-varying norm-bounded parameter uncertainties. Firstly, some new notions of QSR-dissipativity and passivity for FO systems are introduced, the relationship between QSR-dissipativity and asymptotic stability and input–output stability are discussed, respectively. Then, a sufficient condition in the form of linear matrix inequality (LMI) is proposed to ensure that such system is robustly QSR-dissipative. According to this condition, a state feedback controller is proposed when the full states can be measured. Secondly, by employing LMI techniques and matrices singular value decomposition, sufficient conditions for the existence and a robust dissipation synthesis method are derived, respectively. Thirdly, a design method of dynamic output feedback controller is developed in order to guarantee that the closed-loop system is dissipative. Finally, some numerical examples are provided to show the application of the proposed methods.

In this study, a new adaptive controller is introduced for the induction motors (IMs) based on immersion and invariance (I&I) technique. The dynamics of the IM system are perturbed by some disturbances such as time-varying rotor resistance and load torque. Accordingly, an adaptive controller is designed and the uncertain parameters are online estimated. The adaptation laws are obtained from the stability analysis based on I&I method. The simulation results verified the effectiveness of the proposed control method. It is revealed that the outputs of the IM could track the desired signals in the presence of the mentioned disturbances. Also, the results are compared with the conventional control methods and it is concluded that the proposed control approach resulted in better performance.

In this study, the power sharing problem of ac microgrids with massive penetration of photovoltaic generators (PVG) is addressed. A robust distributed cooperative control strategy is proposed to control multiple PVGs in ac microgrids under a complex environment (e.g. subject to transmission time delays and noise disturbances). The existing distributed control strategies have been commonly designed assuming ideal communication among PVGs. However, due to inherent communication delays and environmental noises, the real-life practical channels are affected by time delay and additive noise leading each PVG to receive measurements of the states of its neighbours. Thus, the proposed distributed cooperative control strategy will achieve the accurate power sharing property among PVGs through a sparse communication network subject to time delays and noise disturbances. The theoretical concepts and necessary conditions for stability and robust performance of the proposed distributed cooperative control strategy are outlined by the Lyapunov functional method and stochastic differential equation theory. Furthermore, the proposed control strategy is fully implemented and thus satisfies the plug-and-play feature of the future smart grid. Simulation results on an islanded microgrid test system are provided to reveal the effectiveness of the proposed control method to provide accurate proportional power sharing in the MATLAB/SimPowerSystems Toolbox.

A robust control approach for three-phase two-level grid-connected power converters using an adaptive super-twisting algorithm (ASTA) is studied. A cascaded structure of the proposed control method is employed, which consists of two control loops, the dc-link capacitor voltage regulation loop (outer loop) and the grid phase current tracking loop (inner loop). In the outer control loop, a proportional controller using technique is considered, which is designed to regulate the dc-link capacitor voltage to some desired value. An extended state observer used to asymptotically estimate the external disturbance is integrated into the outer control loop. For the inner control loop, two ASTA-based controllers are implemented that force the grid phase currents to their desired values in finite time. Lyapunov analysis is provided to show the finite time convergence of the closed-loop system. With the help of ASTA, a priori knowledge of the upper bounds of the derivative of the disturbances is not required. Illustrative simulation results in comparison with the linear proportional–integral control method are provided to demonstrate the effectiveness and robustness of the proposed ASTA, in the presence of load variation and parametric uncertainty.

This article is devoted to the problem of model predictive control (MPC) design for discrete-time and continuous-time positive systems with state and input constraints. The proposed controllers are so designed that the closed-loop constrained systems are positive and stable, meanwhile, linear infinite horizon cost functions through their upper bounds are minimised. In the discrete-time case, the performance of the control system compared to existing studies is remarkably improved. Moreover, in the continuous-time case, the proposed MPC is such that can be directly applied to the continuous-time positive system without discretisation. The merit of this method is that the sampling interval has nothing to do with the stability of the system, just a shorter sampling period results in better optimality and performance. In addition, by defining a slack variable and accounting it in the minimisation problems, a fast rate of convergence will be obtained. In order to solve the optimisation problem of MPC, linear programming (LP) is used which needs to be solved at each iteration. All conditions are derived in the form of LP. Finally, to demonstrate the effectiveness of the proposed method, comparisons with the existing studies are presented through practical and numerical examples.

This study proposes a sliding mode fault-tolerant control (FTC) scheme for the medium-scale unmanned autonomous helicopter with rotor flapping dynamics in the presence of wind gusts and actuator faults using extended state observer technique. The radial basis function neural networks are employed to tackle the unknown non-linear interaction functions and adaptive neural network extended state observers are constructed to estimate the unknown wind gusts. Meanwhile, the adaptive fault observers are developed to estimate the fault parameters in position, attitude and flapping motion subsystems. With the aim of obtaining satisfactory trajectory tracking performance, a robust adaptive sliding mode FTC scheme is presented based on the backstepping sliding mode control technique and the closed-loop system stability is rigorously proved via Lyapunov analysis. Simulation results are carried out to validate the effectiveness of the proposed control method.

This paper presents the development of a new double integral inequality (II) with the motivation of yielding quadratic approximation. It is well known that approximating integral quadratic terms with quadratic terms involves a certain degree of conservatism. In this paper, a sufficient gap has been identified in the approximation of two recent IIs reported in the literature, thereby leading to the new double II. The developed inequality has been applied to access the stability of a linear retarded system to estimate a maximum delay upper-bound. Furthermore, a mathematical relationship of the new double II with existing inequalities is discussed to show that the developed inequality is more general, effective and bears less computational burden. Four numerical examples are given to validate the authors' claim with regard to the effective estimate of delay bound results for a linear retarded system.

The problem of numerical instability of the classical Kalman filter (KF) still remains one of the most important topics in engineering literature. For improving its robustness with respect to roundoff errors, the singular value decomposition (SVD) methodology has been proposed for implementing the underlying classical KF Riccati recursion. In this study, SVD-based filtering is derived for an alternative KF mechanisation that is based on the so-called Chandrasekhar recursion and yields a family of fast KF implementations. The new methodology involves hyperbolic SVD (HSVD) factorisation rather than usual SVD utilised in the Riccati-based filtering. The results of numerical study indicate that the HSVD-based filtering strategy outperforms the conventional Chandrasekhar-based KF while solving ill-conditioned state estimation problem. Together with the existed Cholesky-based algorithms, they are the preferred implementations when solving applications with high reliability requirements within the class of fast Chandrasekhar-based KF implementations.

In this study, an event-triggered fuzzy controller is designed to stabilise a class of non-linear systems expressed as a Takagi–Sugeno (T–S) fuzzy model with mismatched membership functions. At first, an event-triggered fuzzy controller has been designed in terms of induced time delay. Secondly, the event-triggered fuzzy system is presented as a time-delay model with the asynchronous premise variables. Then, by introducing a time-dependent Lyapunov–Krasovskii functional and based on the fuzzy based control approach, linear matrix inequality-based stability conditions are established to guarantee the asymptotic stability of the proposed T–S fuzzy model. The derived conditions utilise the information on the membership functions of both fuzzy system and fuzzy controller. Finally, the proposed theoretical results are applied to stabilise the variable speed wind turbine system while saving the limited network resources. Further, through the truck–trailer example, the merits and the design procedure of the proposed technique have been demonstrated.

This studies the stability under events for a class of hybrid dynamical systems (HDSs). The HDS is modelled via continuous and discrete time (CDT) variables. It is allowed that an HDS has time-varying, unstable, non-linear, different dwell time, and infinite number of subsystems. The stability under events reflects the effects of switching and impulse type events in HDS. By defining the length of CDT variable and extending the notion of hybrid-event-time in the literature, the concepts on global uniform asymptotic stability (GUAS) and event-GUAS are reasonably defined. By employing multiple Lyapunov-like functions, criteria on GUAS and event-GUAS are established. Moreover, by extending average dwell time (ADT) to hybrid ADT, the relations between GUAS and event-GUAS are derived. And the criteria on global uniform exponential stability under events (event-GUES) are obtained. A method via maximal admissible probabilities of unstable subsystems is proposed to test the conditions of event-GUES. As two special cases, the traditional stability criteria of only continuous or discrete variables are also derived. Finally, three examples are provided to verify the main results.

Intermittent fault is a special kind of fault form, which often occurs in industry processes but has been less studied. This study focuses on the distributed fault-tolerant model predictive control (DFTMPC) problem for an intermittent fault in actuators or sensors. A novel state observer and DFTMPC controller integral framework are presented. The proposed distributed system state observer can both deal with the unknown inputs and compensate for the interconnected variables' estimation errors, achieving a more accurate estimation. A fault mode-switched model is constructed to describe the system with multi-intermittent faults in a hidden way. This allows us to design a distributed fault-tolerant controller without reconfiguration. For the proposed distributed model predictive controller, asymptotically stable conditions are given, meanwhile, the whole algorithm for multi-intermittent fault-tolerant control is concluded. A numerical example is simulated to verify the proposed method.

The distributed estimation problem for wireless sensor networks with limited communication/sensing ranges and observability is studied. A novel sensor measuring activation scheme based on a fully distributed event-triggered strategy is proposed to make each node achieve a better trade-off between estimation error and energy saving. The strategy depends on both the predicted synthetic performance index and the predicted position of the target. A distributed Kalman filtering algorithm based on the minimum trace fusion principle is proposed. It is proved that comparing with the time-triggered strategy, the proposed event-triggered measuring strategy has better performance. Although the event-triggered measuring topology is time-varying and each sensor is not observable, it is proved that as long as there exists at least one collaboratively observable sensor in the available distance-based sensing network at each time instant, the estimation errors are bounded in mean square sense. Simulation examples are given to illustrate the validity of the algorithm.

In this study, quasi-composite rotating formation control for second-order multi-agent systems over undirected communication topology is considered. To solve this problem, a novel distributed control protocol based on the local information is proposed. Next, the origin closed-loop system is changed into an equivalent one by taking a proper coordinate transformation. Under some mild conditions, it is proved that the quasi-composite rotating formation can be reached by analysing the matrix eigenvalues of the closed-loop system. Finally, the simulation results are provided to demonstrate the effectiveness of the theoretical results.