Unmatched External Disturbances Research Articles

Sliding Mode Control for Markov Jump Singularly Perturbed Systems Under Piecewise Homogeneous Stochastic Communication Protocol.

This work involves the sliding mode control (SMC) issue for a class of Markov jump singularly perturbed systems (MJSPSs) under consideration of unmatched external disturbances and communication constraints. For the first time, the piecewise homogeneous Markov chain (MC) which depends on the system mode and the controller mode is applied to control the scheduling of stochastic communication protocol (SCP), so that the MCs in the system models, the controller and the SCP constitute a three-layer nonstationary Markov model (NMM). This model perfectly describes the different objects of the three MCs and reflects the mutual regulation among them. The critical issue is to devise an adaptive controller and a sliding surface (SS) simultaneously under SCP scheduling. By applying a standard singular sliding mode surface, an appropriate nonstationary SMC law is established to promise the accessibility of the SS and the stability of the closed-loop system (CLS), and meet the expected performance indicator. Further, using the mode-dependent Lyapunov function and piecewise homogeneous Markov model method, sufficient criteria are obtained. The specific expression of the control gain is obtained by matrix decoupling technology. Finally, a numerical simulation is furnished to testify the correctness of the conclusion.

Disturbance‐observer‐based adaptive finite‐time dynamic surface control for PMSM with time‐varying asymmetric output constraint

AbstractThis article presents a disturbance‐observer‐based adaptive finite‐time dynamic surface control scheme, capable of guaranteeing transient behavior for the PMSM with arbitrary asymmetric time‐varying output constraint and unmatched external disturbance. The major challenge of this paper is devising efficient strategies to tackle the nonsymmetric output restraints with arbitrary characteristics and unmatched external perturbation for the system under the finite‐time backstepping framework. Given this, a nonlinear transformation function is adopted to coordinate from the output‐constrained dynamic model to an uncontained one, and a finite‐time disturbance observer is introduced to evaluate the unmatched external perturbation. Then, a dynamic surface control approach having adaptive properties for PMSM is conceived by combing a neural network to evaluate the nonlinear functions and a first‐order filter to handle the “explosion of complexity.” Additionally, it is proved that the signals in the closed‐loop system can narrow down to a bounded region and the tracking error can merge in a limited time to tiny vicinity of zero by employing a fast finite‐time stability principle. Eventually, simulation cases and contrast results reveal the tracking performance and immunity to the disturbance of the devised controller.

DO-Based Adaptive Consensus Control for Multiple MUAVs With Dynamic Constraints

This article investigates the adaptive consensus control problem for a group of multirotor unmanned aerial vehicles (MUAVs) subject to dynamic state constraints and unmatched external disturbances. An adaptive inner–outer loop controller is devised based on the backstepping method, where the issue of “explosion of complexity” is solved via a first-order sliding-mode differentiator. By introducing a barrier function-based state transformation technique into the outer loop controller design, the dynamic constraints covering different types of time-varying state constraints can be addressed without reconfiguring the controller structure. Meanwhile, a neural-network-based disturbance observer is constructed to estimate the external disturbances. Consequently, the applicability and robustness of controller are improved, such that the position tracking control can be implemented in severe environments. Moreover, the inner loop controller is established by virtue of a distributed sliding-mode estimator so as the consensus control for attitude systems of multiple MUAVs can be realized rapidly. Finally, a simulation example is presented to demonstrate the validity and superiority of the proposed control strategy.

Programming-Based Optimal Learning Sliding Mode Control for Cooperative Dual Ship-Mounted Cranes Against Unmatched External Disturbances

When lifting and transporting large payloads in the marine environment, the dual ship-mounted crane system plays a very important role for cargos transportation, which exhibits strong load capacity and high flexibility. However, apart from the nonlinearity and underactuation characteristic, some unknown or uncertain unmatched wave disturbances may also cause positioning errors, which may induce various risks during the transportation process; besides, lots of existing methods ignore a part of the cooperative crane motions, and the control issue of dual ship-mounted crane system with five degrees of freedoms (5 DOF) is still open. In terms of the aforementioned problems, an adaptive dynamic programming (ADP)-based optimal learning sliding mode controller is proposed in this paper. Specifically, under the frame of adaptive dynamic programming, the Hamilton-Jacobi-Bellman (HJB) equation can be addressed. Then, based on the gradient attenuation algorithm, critic neural networks (NNs) are trained depending on the designed updating law and the approximate optimal learning controller can be obtained. Lyapunov techniques and Lasalle’s invariance principle are used to guarantee asymptotic stability of the dual ship-mounted cranes system. Finally, a series of simulation results are depicted to show the effectiveness of the proposed optimal learning sliding mode controller. Note to Practitioners—In this paper, the control problem of a 5 DOF dual ship-mounted cranes system with unmatched wave disturbance is studied. Due to the complex nonlinear characteristics of the dual ship-mounted cranes and the need to consider the cooperative lifting and wave disturbances, the operation of the dual ship-mounted cranes are very challenging. Moreover, it brings more difficulties to the design of this kind of controller due to its nonlinear underactuated property. Existing control methods for dual ship-mounted cranes are based on linearized or oversimplified crane models, or require accurate model. To solve these kinds of problems, this paper proposes a new control approach for dual ship-mounted cranes suffering from unmatched wave disturbances to achieve satisfactory performance. The stability analysis of the closed-loop systems equilibrium point is implemented by Lyapunov techniques, implying that the accurate positioning and fast payload swings suppression against unmatched wave disturbances are achieved concurrently. In the future studies, we will apply the proposed control method to industrial dual ship-mounted cranes systems to improve their working safety and efficiency.

Adaptive fuzzy-based composite anti-disturbance control for a class of switched nonlinear systems with unknown backlash-like hysteresis

For a class of switched nonlinear systems with unmatched external disturbances and unknown backlash-like hysteresis, an adaptive fuzzy-based control strategy is proposed to handle the anti-disturbance issue. The unmatched external disturbances come from a switched exosystem. Our aim is to achieve the output tracking performance and the disturbance attenuation by using the adaptive fuzzy-based composite anti-disturbance control technique. First, based on the fuzzy logics, we design a switching adaptive fuzzy disturbance observer to estimate unmatched external disturbances. Second, a composite switching adaptive anti-disturbance controller is constructed. By means of the backstepping technique, disturbance estimations are added in each virtual control to offset the unmatched disturbances, which results in the different coordinate transformations. At last, the availability of the proposed approach is illustrated by a mass-spring-damper system.

Continuous adaptive integral-type sliding mode control based on disturbance observer for PMSM drives

This paper concerns the speed regulation problem for permanent magnet synchronous motor (PMSM) drive system with matched and mismatched disturbance. A novel single-loop speed and current control strategy with continuous integral-type terminal sliding mode control (ITSMC) and disturbance observer (DOB) is proposed. Firstly, the nonlinear motor model including the lumped disturbance is constructed. Then, by introducing a virtual control, a continuous integral-type sliding mode controller, which has the non-cascade structure, is developed based on terminal sliding mode surface, and it has the globally asymptotic stability based on Lyapunov criterion. However, when the drive system has large disturbance, especially for unmatched external disturbance, the performance of the whole system will be influenced. To further improve the anti-disturbance performance, a disturbance observer is introduced to estimate both the matched and mismatched disturbance in the system, and it is used for the feed-forward compensation, and the stability of the system is proved. Finally, the novel scheme is tested on a surface-mounted PMSM by experiment, and the comparative results in different operation conditions verify that the proposed method has the fast transient response and the strong robustness for the disturbance.

Composite adaptive dynamic programming for missile interception systems with multiple constraints and less sensor requirement

The adaptive integrated guidance and control issue of missiles with less sensor requirement is investigated in the optimal stabilization problem of an uncertain nonlinear system subjected to state and input constraints. The nonlinear system with partially unmeasurable states is transformed into the non-strict feedback form, firstly. Then, an adaptive observer is designed to approximate the full states, where a disturbance estimator is incorporated to suppress the unmatched external disturbances. Next, by employing a Barrier Lyapunov Function (BLF) and an auxiliary system to tackle the multiple constraints, an adaptive feedforward controller is raised to reduce the stabilization issue of the nonlinear system in non-strict feedback form to the equivalent control problem of an affine nonlinear system. Subsequently, an optimal controller is derived by utilizing adaptive dynamic programming (ADP) theory. The system stability is rigorously proved by using Lyapunov theory. Finally, simulations are performed to validate the effectiveness of the proposed control strategy.

Adaptive Fuzzy Output Feedback Fault-Tolerant Compensation for Uncertain Nonlinear Systems With Infinite Number of Time-Varying Actuator Failures and Full-State Constraints.

This paper focuses on the observer-based fuzzy adaptive fault-tolerant tracking control problem for uncertain nonlinear systems subject to unmeasured states and unmatched external disturbances. By designing a high gain state observer and a disturbance observer, unmeasured states and unmatched external disturbances are estimated and robust tracking performance is improved. Moreover, the barrier-type functions are introduced to the backstepping design procedure to address the problem that all states do not violate their constraint bounds. Finally, a novel fault-tolerant control scheme for output feedback is proposed by combining with the projection technique. By designing appropriate Lyapunov functions, it is concluded that all signals of the plant are bounded and the desired tracking error can be regulated to a small neighborhood around the origin. The simulation results show the effectiveness of the designed control scheme.

Robustness Improvement of Computationally Efficient Cooperative Fuzzy Model Predictive-Integral Sliding Mode Control of Nonlinear Systems

This paper introduces a systematic and comprehensive method to design a constrained fuzzy model predictive control (MPC) cooperated with integral sliding mode control (ISMC) based on the Takagi-Sugeno (T-S) fuzzy model for uncertain continuous-time nonlinear systems subject to external disturbances. The proposed controller benefits from the robustness, optimality, and practical constraints considerations. The robustness against the uncertainties and matched external disturbances is achieved by the proposed ISMC without iterative calculation for obtaining the robust invariant set. The MPC schemes are designed separately based on the both quadratic and non-quadratic Lyapunov functions. By the proposed MPC, the states of the system reach the desired values in the optimal, constrained, and robust manner against the unmatched external disturbances. New linear matrix inequalities (LMIs) conditions are proposed to design both the proposed MPC schemes. Also, the practical constraints on the control signals are guaranteed in the design procedure based on the invariant ellipsoid set. To evaluate the effectiveness of the suggested strategy, some simulation and experimental tests were run.

On $H_\infty$ Sliding Mode Control Under Stochastic Communication Protocol

This paper is concerned with the sliding mode control (SMC) problem for a class of uncertain discrete-time systems subject to unmatched external disturbances and communication constraints. In order to reduce the bandwidth usage between the controller and the actuators, the stochastic communication protocol (SCP) is utilized to determine which actuator should be given the access to the network at a certain instant. A key issue of the addressed problem is to design both the sliding surface and the sliding mode controller under the SCP scheduling. An updating rule on actuator input is first introduced and then a token-dependent SMC law is designed. Sufficient conditions are established for the resultant SMC systems such that not only the reachability with a sliding domain around the specified sliding surface is ensured, but also the stochastic stability with a prescribed $H_\infty$ performance level is guaranteed. Based on these conditions, a set of coupled matrix inequalities is given to acquire the token-dependent parameter matrices in the proposed SMC law. Finally, a numerical example is presented to illustrate the effectiveness of the proposed $H_\infty$ SMC scheme under the SCP scheduling.

Anti-disturbance dynamic surface control scheme for a class of uncertain nonlinear systems with asymmetric dead-zone nonlinearity

This study proposes anti-disturbance dynamic surface control scheme for nonlinear strict-feedback systems subjected simultaneously to unknown asymmetric dead-zone nonlinearity, unmatched external disturbance and uncertain nonlinear dynamics. Radial basis function-neural network (RBF-NN) is invoked to approximate the uncertain dynamics of the system, and the dead-zone nonlinearity is represented as a time-varying system with a bounded disturbance. The nonlinear disturbance observer (NDO) is proposed to estimate the unmatched external disturbance which further will be used to compensate the effect of the disturbance. Then, by integrating RBF-NN, NDO and dynamic surface control (DSC) approaches, the proposed anti-disturbance control scheme is designed. Stability analysis of the closed-loop system shows that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error can be made arbitrarily small by proper selection of the design parameters. In comparison with the existing methods, the proposed scheme deals with the unmatched external disturbance, uncertain dynamics and unknown asymmetric dead-zone nonlinearity, simultaneously; it avoids the "explosion of complexity" problem and develops the simple control law without singularity concern. Furthermore, some imposed assumptions to the dead-zone input and disturbances are relaxed. Simulation and comparison results verify the effectiveness of the proposed approach.

Hypersonic Missile Adaptive Sliding Mode Control Using Finite- and Fixed-Time Observers

Finite- and fixed-settling time differentiators utilizing a nonrecursive higher order sliding mode (HOSM) observer are studied. Fixed convergence time estimation is achieved independent of initial conditions of the differentiation errors. The corresponding convergence/settling times are estimated. The finite- and fixed-time HOSM differentiators’ performance is compared against the Levant recursive one via a hypersonic missile control simulation case study during the missile's terminal phase of flight. A continuous adaptive HOSM control is utilized. The double-layer adaptive algorithm is based on an equivalent control concept and does not allow overestimation of the control gains that mitigates control chattering. The robustness and high-accuracy output tracking in the presence of matched and unmatched external disturbances and missile model uncertainties is demonstrated for both the differentiators and the controller.

Decentralised disturbance-observer-based adaptive tracking in the presence of unmatched nonlinear time-delayed interactions and disturbances

ABSTRACTThis paper proposes an approximation-based nonlinear disturbance observer (NDO) approach for decentralised adaptive tracking of uncertain interconnected pure-feedback nonlinear systems with unmatched time-delayed nonlinear interactions and external disturbances. Compared with the existing approximation-based NDO approach for uncertain interconnected nonlinear systems where the centralised design framework was proposed, the main contribution of this paper is to develop a decentralised and memoryless NDO-based adaptive control scheme in the presence of unknown time-varying delayed interactions and disturbances unmatched in the control inputs. The recursive design methodology is derived to construct the decentralised NDO and controller where the function approximators used in the decentralised NDO are employed to design the decentralised adaptive controller. From the Lyapunov stability theorem using Lyapunov--Krasovskii functionals, it is shown that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors converge to an adjustable neighbourhood of the origin.

Memoryless disturbance-observer-based adaptive tracking of uncertain pure-feedback nonlinear time-delay systems with unmatched disturbances

This paper presents a delay-independent nonlinear disturbance observer (NDO) design methodology for adaptive tracking of uncertain pure-feedback nonlinear systems in the presence of unknown time delays and unmatched external disturbances. Compared with all existing NDO-based control results for uncertain lower-triangular nonlinear systems where unknown time delays have been not considered, the main contribution of this paper is to develop a delay-independent design strategy to construct an NDO-based adaptive tracking scheme in the presence of unknown time-delayed nonlinearities and non-affine nonlinearities unmatched in the control input. The proposed delay-independent scheme is constructed by employing the appropriate Lyapunov-Krasovskii functionals and the same function approximators for the NDO and the controller. It is shown that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin.

Robust global second-order sliding mode control with adaptive parameter-tuning law for perturbed dynamical systems

This paper offers an adaptive global second-order sliding surface for perturbed dynamical systems with matched and unmatched external disturbances. Based on the composite nonlinear feedback theory, a nonlinear function Ψ( x1) is employed in the switching surface to adjust the damping ratio of the controlled system. Initially, using a constant gain matrix, a small value of the damping ratio is achieved presenting a fast performance. As the system state converges to the origin, the damping ratio of the closed-loop system is increased that yields fast settling time and a low overshoot. A novel smooth and chattering-free controller is proposed to fulfill the removal of the reaching mode and the existence of the sliding behavior around the surface from the beginning. The adaptive gain tuning controller reduces the required information for the upper bound of disturbances. Moreover, the selection of the constant parameters μ1 and τ1 for the control law is turned into a cost function and solved by a particle swarm optimization method. Several criteria are derived to assure the robust stability of the uncertain dynamical system. Some simulations are offered to demonstrate the effectiveness of the planned technique.

Approximation-based disturbance observer approach for adaptive tracking of uncertain pure-feedback nonlinear systems with unmatched disturbances

ABSTRACTThis paper presents an approximation-based nonlinear disturbance observer (NDO) methodology for adaptive tracking of uncertain pure-feedback nonlinear systems with unmatched external disturbances. Compared with existing control results using NDO for nonlinear systems in lower-triangular form, the major contribution of this study is to develop an NDO-based control framework in the presence of non-affine nonlinearities and disturbances unmatched in the control input. An approximation-based NDO scheme is designed to attenuate the effect of compounded disturbance terms consisting of external disturbances, approximation errors and control coefficient nonlinearities. The function approximation technique using neural networks is employed to estimate the unknown nonlinearities derived from the recursive design procedure. Based on the designed NDO scheme, an adaptive dynamic surface control system is constructed to ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a neighbourhood of the origin. Simulation examples including a mechanical system are provided to show the effectiveness of the proposed theoretical result.

Integral Sliding Manifold Design for Linear Systems With Additive Unmatched Disturbances

This note offers an integral sliding manifold design method for linear systems that minimizes the impact of unmatched constant external disturbances. System sensitivity upon an unmatched disturbance vector is assessed by the steady-state dependent criterion function. The derived procedure easily finds a unique integral sliding manifold that minimizes a quadratic optimization criterion. Applicability of this method in case of slowly-varying disturbances is supported by determining disturbance frequency limit that guarantees satisfactory performance. The proposed approach has been demonstrated on a numerical example and verified by simulations.

Continuous higher order sliding mode control with adaptation of air breathing hypersonic missile

SummaryHypersonic missile control in the terminal phase is addressed using continuous adaptive higher order sliding mode (AHOSM) control with adaptation. The AHOSM self‐tuning controller is proposed and studied. The double‐layer adaptive algorithm is based on equivalent control concepts and ensures non‐overestimation of the control gain to help mitigating control chattering. The proposed continuous AHOSM control is validated via simulations of a hypersonic missile in the terminal phase. The robustness and high‐accuracy output tracking in the presence of matched and unmatched external disturbances and missile model uncertainties is demonstrated. Copyright © 2016 John Wiley & Sons, Ltd.

Robust control of electromagnetic suspension based on vortex algorithms

We design vortex control algorithms for an electromagnetic suspension in the keeper position tracking problem. The main feature of these vortex algorithms concerns the invariance property with respect to unmatched external disturbances of a wide class. It is shown that the suggested algorithms guarantee the closed-loop stability under uncertain parameters of the electromagnetic suspension (mass, electrical circuit parameters, etc.). Simulation results demonstrate the efficiency of the designed algorithms.

Global Finite-Time Stabilization for Nonholonomic Mobile Robots Based on Visual Servoing

In this paper, the global finite-time stabilization problem is considered for nonholonomic mobile robots based on visual servoing with uncalibrated visual parameters, control direction and unmatched external disturbances. Firstly, the simple dynamic chained-form systems is obtained by using a state and input transformation of the kinematic robot systems. Secondly, a new discontinuous switching controller is presented in the presence of uncertainties and disturbances, it is rigorously proved that the corresponding closed-loop system can be stabilized to the origin equilibrium point in a finite time. Finally, the simulation results show the effectiveness of the proposed control design approach.