Flatness-based adaptive sliding mode tracking control for a quadrotor with disturbances

In this paper, a flatness-based adaptive sliding mode control strategy is presented to solve the trajectory tracking problem of a quadrotor. According to the differential flatness theory, the typical under-actuated quadrotor dynamics is transformed into a fully-actuated one. Based on this model, backstepping sliding mode controllers are designed to solve the trajectory tracking problem. To improve the robustness to disturbances, extended state observers are applied as a feedforward compensation of disturbances. Moreover, considering the high-order dynamics and possible instability caused by large observer gains, the adaptive method is applied to compensate for the estimation error. The effectiveness of the proposed control scheme is verified in simulations.     

Spacecraft output feedback attitude control based on extended state observer and adaptive dynamic programming

This paper investigates spacecraft output feedback attitude control problem based on extended state observer (ESO) and adaptive dynamic programming (ADP) approach. For the plant described by the unit quaternion, an ESO is first presented in view of the property of the attitude motion, and the norm constraint on the unit quaternion can be satisfied theoretically. The practical convergence proof of the developed ESO is illustrated by change of coordinates. Then, the controller is designed with an involvement of two parts: the basic part and the supplementary part. For the basic part, a proportional-derivative control law is designed. For the supplementary part, an ADP method called action-dependent heuristic dynamic programming (ADHDP) is adopted, which provides a supplementary control action according to the differences between the actual and the desired system signals. Simulation studies validate the effectiveness of the proposed scheme.     

Real time implementation of indirect rotor flux oriented control of a five-phase induction motor with novel rotor resistance adaption using sliding mode observer

High performance multiphase motor drive requires precise knowledge of the state quantities and the machine parameters. Access to these state quantities is through measurement using sensors whose accuracy is paramount to achieve the performance level required by industrial applications. However, the problems of the parameters variations, inaccessibility to the measurement of some states, no-observability of the machine in some regions, the cost of the sensors and their lack of precision, make this very difficult task. To address these problems, it is necessary to resort to soft sensors through the design of observers and estimators. In multiphase induction motor drive, the observation problem arises especially for rotor flux that is not accessible for measurement. About the parameters variations, the rotor resistance and the stator resistance are the most critical parameters of the machine because their influence is crucial for the control and observation. The change in the resistances can be as large as 40–50% of the rated value, which may affect the control adversely. This paper develops a new structure of an adaptive sliding mode observer based on an online estimation of the rotor resistance value in order to avoid the effect of its variation in the rotor flux oriented control. The results show convergent (the errors in the transient and steady states are 5% and 1%, respectively) behavior of the drive using the proposed control scheme for large rotor resistance variation under loaded condition. The stability of the drive is proved using Lyapunov criteria. The simulation results are validated using real time implementation.     

Finite-time fractional-order adaptive intelligent backstepping sliding mode control of uncertain fractional-order chaotic systems

This paper precedes chaos control of fractional-order chaotic systems in presence of uncertainty and external disturbances. Based on some basic properties on fractional calculus and the stability theorems, we present a hybrid adaptive intelligent backstepping-sliding mode controller (FAIBSMC) for the finite-time control of such systems. The FAIBSMC is proposed based on the concept of active control technique. The asymptotic stability of the controller is shown based on Lyapunov theorem and the finite time reaching to the sliding surfaces is also proved. Illustrative and comparative examples and simulation results are given to confirm the effectiveness of the proposed procedure, which consent well with the analytical results.     

Super-twisting observer-based sliding mode control with fuzzy variable gains and its applications to fully-actuated hexarotors

In this paper, we consider the super-twisting observer-based sliding mode control algorithm with fuzzy variable gains (STOSMC) for the fully-actuated hexarotor. Our hexarotor has full actuation due to six titled propellers that allows to control position and orientation (attitude) simultaneously, and resolves the singularity problem of the rotational matrix by using the quaternion modeling framework. We show that the proposed STOSMC for the hexarotor guarantees finite-time convergence of the estimation error and asymptotic stability of the hexarotor. In simulations, we demonstrate the nonsingularity and fully-actuated control performance of the hexarotor by considering extreme position and attitude control scenarios. Moreover, the simulation results show that the hexarotor achieves the fast and precise tracking performance to the desired position and the desired attitude and the chattering phenomenon is reduced compared with the fixed-gains observer-based super-twisting sliding mode control due to the fuzzy mechanism.     

Adaptive fractional order sliding mode controller with neural estimator

In this study, an adaptive fractional order sliding mode controller with a neural estimator is proposed for a class of systems with nonlinear disturbances. Compared with traditional sliding mode controller, the new proposed fractional order sliding mode controller contains a fractional order term in the sliding surface. The fractional order sliding surface is used in adaptive laws which are derived in the framework of Lyapunov stability theory. The bound of the disturbances is estimated by a radial basis function neural network to relax the requirement of disturbance bound. To investigate the effectiveness of the proposed adaptive neural fractional order sliding mode controller, the methodology is applied to a Z-axis Micro-Electro-Mechanical System (MEMS) gyroscope to control the vibrating dynamics of the proof mass. Simulation results demonstrate that the proposed control system can improve tracking performance as well as parameter identification performance.     

Finite-time sliding mode control of Markovian jump systems subject to actuator nonlinearities and its application to wheeled mobile manipulator

This work is concerned with the finite-time sliding mode control for a class of Markovian jump systems subject to actuator nonlinearities, where the elements in the transition rate matrix are uncertain or even completely unknown. A suitable sliding mode controller is designed such that the finite-time stochastic boundedness of state trajectories is attained during a given finite-time interval, in which two different robust terms are introduced for the known and unknown modes to deal with the effect of uncertain transition rates. Moreover, the connections among sliding functions under Markovian jumping for SMC systems are analyzed. Finally, some simulation results with a wheeled mobile manipulator are provided.     

Observer based sliding mode controller for vehicles with roll dynamics

In this work, considering the roll dynamics and actuator dynamics, an observer-based control scheme for a vehicle is proposed. The proposal considers a nonlinear higher order sliding mode observer to estimate unmeasurable lateral velocity, roll angle and roll velocity. Using the observer information, a controller based on block control with sliding mode technique is designed for the reference trajectory tracking of the lateral and yaw velocities of the vehicle. The stability of the complete closed-loop system including zero dynamics is analyzed. The effectiveness of the proposed scheme is demonstrated through CarSim simulations.     

Adaptive fuzzy sliding mode command-filtered backstepping control for islanded PV microgrid with energy storage system

This study focuses on the control of islanded photovoltaic (PV) microgrid and design of a controller for PV system. Because the system operates in islanded mode, the reference voltage and frequency of AC bus are provided by the energy storage system. We mainly designed the controller for PV system in this study, and the control objective is to control the DC bus voltage and output current of PV system. First, a mathematical model of the PV system was set up. In the design of PV system controller, command-filtered backstepping control method was used to construct the virtual controller, and the final controller was designed by using sliding mode control. Considering the uncertainty of circuit parameters in the mathematical model and the unmodeled part of PV system, we have integrated adaptive control in the controller to achieve the on-line identification of component parameters of PV system. Moreover, fuzzy control was used to approximate the unmodeled part of the system. In addition, the projection operator guarantees the boundedness of adaptive estimation. Finally, the control effect of designed controller was verified by MATLAB/Simulink software. By comparing with the control results of proportion-integral (PI) and other controllers, the advanced design of controller was verified.     

Robust stabilization of uncertain 2-D discrete-time delayed systems using sliding mode control

This paper aims to solve the problem of sliding mode control for an uncertain two-dimensional (2-D) systems with states having time-varying delays. The uncertainties in the system dynamics are constituted of mismatched uncertain parameters and the unknown nonlinear bounded function. The proposed problem utilizes the model transformation approach. By segregating the proper Lyapunov–Krasovskii functional in concert with the improved version of Wirtinger-based summation inequality, sufficient solvability conditions for the existence of linear switching surfaces have been put forward, which ensure the asymptotical stability of the reduced-order equivalent sliding mode dynamics. Then, we solve the controller synthesis problem by extending the recently proposed reaching law to 2-D systems, whose proportional part is appropriately scaled by the factor that does not depend on some constant terms but rather on current switching surface’s value, which in turn ensures the faster convergence and better robustness against uncertainties. Finally, the proposed results have been validated through an implementation to a suitable physical system.     

Finite-time stabilization of nonlinear time delay systems using LQR based sliding mode control

In this paper, we discussed the robust finite-time stability of conic type nonlinear systems with time varying delays. Some novel conditions are derived to design a linear quadratic regulator (LQR) based sliding mode control (SMC) by proposing an integral switching surface. The sufficient conditions are derived for the considered nonlinear system using Lyapunov–Krasovskii stability theory and linear matrix inequality (LMI) approach. The proposed conditions can be solved using some standard numerical packages. Finally, a practical example is provided to validate the advantages and effectiveness of the proposed results.     

Security control for Markov jump system with adversarial attacks and unknown transition rates via adaptive sliding mode technique

This paper is concerned with the security control problem for a class of Markov jump systems subject to false data injection attack and incomplete transition rates. An on-line estimation strategy is provided for the time-variant and unknown cyber-attack modes. And then, an adaptive sliding mode controller is synthesized with different robust terms for different modes to guarantee the reachability of the specified sliding surface. Moreover, the sufficient conditions for the stability of the closed-loop systems are derived. Finally, it is shown from simulation results that the effect of both false data injection attack and incomplete TRs can be effectively attenuated by the present adaptive SMC method.     

Event-triggered fault estimation and sliding mode fault-tolerant control for a class of nonlinear networked control systems

This paper is concerned with integrated event-triggered fault estimation (FE) and sliding mode fault-tolerant control (FTC) for a class of discrete-time Lipschtiz nonlinear networked control systems (NCSs) subject to actuator fault and disturbance. First, an event-triggered fault/state observer is designed to estimate the system state and actuator fault simultaneously. And then, a discrete-time sliding surface is constructed in state-estimation space. By the use of a reformulated Lipschitz property and delay system analysis method, the sliding mode dynamics and state/fault error dynamics are converted into a unified linear parameter varying (LPV) networked system model by taking into account the event-triggered scheme, actuator fault, external disturbance and network-induced delay. Based on this model and with the aid of Lyapunov–Krasovskii functional method, a delay-dependent sufficient condition is derived to guarantee the stability of the resulting closed-loop system with prescribed H_∞ performance. Furthermore, an observed-based sliding mode FTC law is synthesized to make sure the reachability of the sliding surface. Finally, simulation results are conducted to verify the effectiveness of the proposed method.     

Optimized sliding mode current controller for power converters with non-minimum phase nature

This paper proposes a unified method to design an optimized type of the hysteresis modulation-based sliding mode current controller for non-minimum phase power converters in continuous conduction mode. The traditional sliding mode controlled converters have a slow transient voltage response at heavy loads, a large overshoot at light loads and during abrupt output resistance variations. To solve these problems, an optimized feedback control scheme is used according to the output resistance to adjust the coefficients of the controller. The basic idea of this controller is to suggest a new way for reduction of the sensitivity function amplitude of the closed loop system. The presented approach is developed for three basic DC/DC converters; i.e. boost, buck-boost and quadratic boost converters. Generally, the certain advantages of the suggested control approach are: (i) a fast transient response can be achieved in heavy load conditions, (ii) the voltage overshoot can be effectively reduced during load variations; (iii) the transient voltage overshoot can be eliminated in light load conditions; (iv) the closed loop control sensitivity can be reduced and therefore, the performance specification of a control system can be improved compared with the conventional sliding mode current control. To show the reliability of the suggested control scheme, simulations and experimental results for the derived systems are developed. Several conditions are performed to confirm the effectiveness of the proposed controller.     

Sparsely distributed sliding mode control for interconnected systems

This paper proposes a framework for the design of sparsely distributed output feedback discrete-time sliding mode control (ODSMC) for interconnected systems. The major target here is to develop an observer based discrete-time sliding mode controller employing a sparsely distributed control network structure in which local controllers exploit some other sub-systems’ information as well as its own local information. As the local controllers/observers have access to some other sub-systems’ states, the control performance will be improved and the applicability region will be widened compared to the decentralised structure. As the first step, a stability condition is derived for the overall closed-loop system obtained from applying ODSMC to the underlying interconnected system, by assuming a priori known structure for the control/observer network. The developed LMI based controller design scheme provides the possibility to employ different information patterns such as fully distributed, sparsely distributed and decentralised patterns. In the second step, we propose a methodology to identify a sparse control/observer network structure with the least possible number of communication links that satisfies the stability condition given in the first step. The boundedness of the obtained overall closed-loop system is analysed and a bound is derived for the augmented system state which includes the closed-loop system state and the switching function.     

Novel integral sliding mode control for small-scale unmanned helicopters

Integral sliding mode (ISM) control which consists of a nominal control and a sliding-mode motion control, provides a nice framework for high tracking performance and good disturbance reduction. Our work develops ISM to attenuate the adverse effect of mismatched perturbations. By properly choosing sliding-manifold surface, the elimination of disturbances on control outputs enables to be achieved. Additionally, the chattering of sliding-mode control part is attenuated based on second-order sliding mode idea. Then, the proposed novel ISM control scheme is applied to address trajectory tracking problem for helicopters under perturbations. Approximated input-output linearization is implemented, such that the obtained linearized model is suitable for applying the proposed ism control. The stability of the closed-loop system for helicopter and its convergence to zeros of tracking errors are demonstrated by Lyapunov theory analysis. Several comparison simulations illustrate the effectiveness and superiority of the proposed methods.     

Robust sensorless observer-based adaptive sliding modes control of synchronous motors

Using a nonlinear complete order model of a synchronous motor, a robust second order sliding mode observer based control scheme is proposed. For that, a generalized super-twisting 3rd order observer is proposed for nonlinear systems. Based on the proposed observer scheme, a robust rotor flux observer is designed, then, a stator current observer is proposed using a classical super-twisting algorithm for extracting information of the rotor speed by means of the equivalent control method. The control design for the output tracking of a desired reference signal for the rotor speed is carried out with a classical super-twisting sliding mode algorithm and adaptive backstepping techniques. Due to the number of inputs, the flux in the excitation winding, and the direct component of the stator currents are also regulated. Numeric simulations predict a good performance of the closed-loop synchronous motor with parameter variations.     

Analysis and experimental investigation into a finite time current observer based adaptive backstepping control of buck converters

In this paper, the issue of output voltage regulation in buck type dc-dc converters is addressed using a current sensorless control technique. The proposed strategy integrates a finite time current observer with an adaptive backstepping control scheme to yield a cost-effective and robust control mechanism. The overall controller stability in the sense of Lyapunov is proved. Applicability of the proposed control is verified experimentally on a buck converter in the laboratory. The control scheme is implemented on dSPACE DS1103 platform based on DSP TM320F240 processor. To examine the efficacy of the proposed method, the buck converter is subjected to a wide change in input voltage, load resistance and reference voltage. For comparison purpose, a conventional adaptive backstepping control scheme is evaluated under identical conditions of experimental study to examine the merit of the proposed control. The results obtained reveal that the proposed control is prompt in rejecting perturbations and achieves a smooth, reliable and satisfactory output voltage regulation with faithful and time bound estimation of inductor current. Thereby, this investigation demonstrates the validity of the proposed control in maintaining a stringent output voltage regulation in buck converters.     

A new singular system approach to output feedback sliding mode control for fractional order nonlinear systems

This paper studies the problem of output feedback sliding mode control (OFSMC) for fractional order nonlinear systems. A necessary and sufficient condition for the existence of a sliding surface is obtained by a new singular system approach and a linear matrix equality (LMI), which reduces the conservativeness of the system. Then an OFSMC law is designed based on a fractional order Lyapunov method, which ensures that the resulting fractional closed-loop system is asymptotically stable and the states of the fractional closed-loop system converge to the sliding surface in finite time. A fractional electrical circuit is discussed to illustrate the effectiveness of the proposed approach.     

Observer-based adaptive fuzzy control of a class of MIMO non-strict feedback nonlinear systems

This paper investigates the adaptive fuzzy control design problem of multi-input and multi-output (MIMO) non-strict feedback nonlinear systems. The considered control systems contain unknown control directions and dead zones. Fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and the state observers are designed to estimate immeasurable states. By constructing a dead zone compensator and introducing a Nussbaum gain function into the backstepping technique, an adaptive fuzzy output feedback control method is developed. The proposed adaptive fuzzy controller is proved to guarantee the semi-globally uniformly ultimately bounded (SGUUB) of the closed-loop system, and can solve the control design problems of unmeasured states, unknown control directions and dead zones. The simulation results are given to demonstrate the effectiveness of the proposed control method.