Unmatched Disturbances Research Articles

Adaptive super twisting extended state observer based sliding mode control for diesel engine air path subject to matched and unmatched disturbance

This paper develops an Adaptive super twisting extended state observer (Asteso) based sliding mode control for diesel engine air path, system subject to matched and unmatched disturbances. The main advantage of the proposed Asteso observer is its capability to estimate simultaneously the matched and the unmatched disturbances affecting the Turbocharged diesel engine (Tde) air path without knowing precisely their bounds. The disturbances estimations provided by the Asteso are incorporated in a composite controller which has two main advantages in terms of alleviating the chattering problem and maintaining the nominal performance of the system in the absence of disturbances. Simulations results of the proposed controller on a recently validated experimental air path diesel engine model, show the efficiency of the approach in terms of tracking performance and robustness facing model parametric uncertainties and Tde air path actuators faults.

Enhanced Finite Spectrum Assignment with disturbance compensation for LTI systems with input delay

This paper presents a Finite Spectrum Assignment (FSA) with a generalized feedforward control for Linear Time-Invariant (LTI) systems with input delay and bounded unmeasured disturbances. A novel two-layer feedforward strategy is proposed in order to deal with matched and unmatched disturbances. The proposed control law is based on a filtered disturbance estimator and a generalized feedforward compensation which can be applied to any Artstein based predictor. An optimization design procedure is presented to improve disturbance attenuation properties in the presence of band-limited disturbances. The conditions to achieve disturbance rejection are also shown to deal with deterministic disturbance models. Furthermore, the proposed solution can be used to define either continuous-time or discrete-time control algorithms. Two case studies are presented to illustrate the benefits of the new approach.

Robust feedback‐linearisation control of a boost converter feeding a grid‐tied inverter for PV applications

In this study, the feedback-linearisation (FBL) technique is employed to design a dc-dc boost voltage regulator feeding a grid-tied inverter for photovoltaic (PV) systems. The key feature of the proposed approach is that only a voltage control loop is used to generate the driving signal for the converter and no current control loop is required. Thereby, unlike the cascaded structure, the bandwidth of the voltage control loop can be specified only by the switching frequency as there is no need for an intermediate inner-loop. The major concern of this control scheme is its limited ability to eliminate completely the steady-state error under model uncertainty and unknown disturbance such as the PV current, which is considered as an unmatched disturbance. For this purpose, the unknown perturbation is estimated by a disturbance observer and compensated in the control law to drive the steady-state error to zero. With a fast disturbance estimation, the composite controller is able to retain the nominal transient performance specified with the FBL. The effectiveness of the proposed approach was verified by both simulation and experimental results, and a remarkable agreement was obtained while exhibiting excellent performances.

Fuzzy Dynamic Output Feedback Control for T-S Fuzzy Discrete-Time Systems With Multiple Time-Varying Delays and Unmatched Disturbances

This paper addressed the fuzzy dynamic output feedback control problem for a class of nonlinear discrete-time Takagi–Sugeno (T-S) fuzzy systems with multiple time-varying delays and unmatched disturbances. Based on the control input matrix and output matrix, the T-S fuzzy model is employed to approximate the nonlinear discrete-time system. Based on the stochastic system theory and the Bernoulli distribution, the fuzzy dynamic output feedback controller is constructed for the nonlinear discrete-time T-S fuzzy system with multiple time-varying delay and unmatched disturbance. The $H_{\infty } $ performance analysis is presented, and the cone complementarity linearization algorithm is employed for the stability analysis to deal with the non-convex problem caused by the basis-dependent linear matrix inequalities conditions. Compared with the previous works, the developed controller in this paper is smooth and only uses the system output. The control design conditions are relaxed because of the developed cone complementarity linearization algorithm. The results are further extended to the chemical process case and the mobile robot case. Finally, two simulation examples are performed to show the effectiveness of the proposed methods.

Active Disturbance Rejection for a Three Degrees of Freedom Gyroscope

This paper deals with the active disturbance rejection problem for a three degrees of freedom gyroscope. The goal is to design a robust tracking controller for the underactuated coordinate. A nonlinear model of the gyroscope, affected by matched and unmatched disturbances, is first obtained. Then, a high order sliding mode observer (HOSMO) estimates, theoretically in finite time, the disturbance signals. Such information is thus injected into the tracking controller to counteract the disturbances effect on the gyroscope dynamics. Stability of the closed-loop observer-controller system is analyzed through Lyapunov theory. Simulation results show the effectiveness of the proposed method.

Tuning function-based adaptive backstepping fault-tolerant control for nonlinear systems with actuator faults and multiple disturbances

The aim of this paper is to deal with the tracking control problem of strict-feedback nonlinear systems subject to unknown actuator faults and multiple disturbances simultaneously. To tackle the problem, a novel adaptive backstepping fault-tolerant control algorithm which is based on the tanh function, the tuning function, and neural networks is proposed. During the procedure of controller design, the effects of unknown actuator faults modeled as loss of effectiveness are eliminated without a fault detection and isolation mechanism. The multiple disturbances composed of the matched disturbance and the unmatched disturbance are approximated by neural networks and compensated by the tuning function-based adaptive technique, respectively. Moreover, the over-parametrization phenomenon resulting from unknown parameters is avoided via the tuning function. The sufficient condition for the closed-loop system to be asymptotically stable is gained through constructing an appropriate Lyapunov function. The presented scheme is reduced to two numerical examples, in which the practical system for high-speed trains is considered. Simulation results prove that the chattering phenomenon is eliminated via tanh function and the presented fault-tolerant strategy is feasible and effective.

Neural network-based H∞ sliding mode control for nonlinear systems with actuator faults and unmatched disturbances

Abstract By combining integral sliding mode control with nonlinear H∞ optimal control theory, a novel nonlinear control scheme is proposed for uncertain nonlinear systems with actuator faults and unmatched disturbances. The effect of the actuator faults and the separated matched disturbance component can be reduced by a properly designed discontinuous sliding mode controller, while unmatched disturbance component is attenuated by a nonlinear H∞ control obtained by approximately solving HJI equations for equivalent sliding mode dynamics. An adaptive dynamic program (ADP) algorithm based on three neural networks (NNs) is applied to solve the HJI equation. Lyapunov techniques are used to demonstrate the convergence of the NN weight errors in the sense of uniform ultimate bounded. Some simulation results are presented to verify the feasibility of the proposed control scheme.

Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation

In this paper we present a method for the addition of integral action to nonpassive outputs of a class of port-Hamiltonian (pH) systems. The proposed integral controller is a dynamic extension, constructed from the open-loop system, such that the closed loop preserves the pH form. It is shown that the controller is able to reject the effects of both matched and unmatched disturbances, preserving the regulation of the nonpassive outputs. Previous solutions to this problem have relied on a change of coordinates whereas the presented solution is developed using the original state vector and, therefore, retains its physical interpretation. In addition, the resulting closed-loop dynamics have a natural interpretation as a control by interconnection scheme.

Backstepping State Feedback Regulator Design for an Unstable Reaction-Diffusion PDE with Long Time Delay

We consider the output regulation of an unstable reaction-diffusion PDE in the presence of regulator delay and unmatched disturbances, which are generated by an exosystem. The systematic design procedure of a backstepping state feedback regulator is first presented by mapping the reaction-diffusion PDE cascaded with a transport equation into an error system, which is shown to be exponentially stable with a prescribed rate in a suitable Hilbert space. The regulator design relies on solving regulator equations, and the solvability condition of the regulator equations is then characterized by a transfer function and eigenvalues of the exosystem. Finally, the numerical simulations are provided to illustrate the effect of the regulator.

Cooperative Fault Tolerant Tracking Control for Multiagent Systems: An Intermediate Estimator-Based Approach.

This paper studies the observer based fault tolerant tracking control problem for linear multiagent systems with multiple faults and mismatched disturbances. A novel distributed intermediate estimator based fault tolerant tracking protocol is presented. The leader's input is nonzero and unavailable to the followers. By applying a projection technique, the mismatched disturbances are separated into matched and unmatched components. For each node, a tracking error system is established, for which an intermediate estimator driven by the relative output measurements is constructed to estimate the sensor faults and a combined signal of the leader's input, process faults, and matched disturbance component. Based on the estimation, a fault tolerant tracking protocol is designed to eliminate the effects of the combined signal. Besides, the effect of unmatched disturbance component can be attenuated by directly adjusting some specified parameters. Finally, a simulation example of aircraft demonstrates the effectiveness of the designed tracking protocol.

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.

Sliding mode control for underactuated overhead cranes suffering from both matched and unmatched disturbances

Overhead cranes, which are known as typical underactuated systems, are extensively studied in recent years. However, many existing methods for overhead cranes are developed based on a relatively ideal model, with little consideration for persistent external disturbances, unmodeled dynamics, uncertain system parameters and so on. Thus, their performance may badly degrade when it comes to practical applications, and this problem is made even worse when the system suffers from unmatched disturbances. To tackle this issue, a sliding mode control (SMC) method is proposed in this paper, which ensures satisfactory control performance even when the crane works under unfavorable conditions. The asymptotic stability of the desired equilibrium point is backed up with rigorous Lyapunov-based analysis. Furthermore, to alleviate the chattering problem inherent to SMC, a disturbance observer is further designed for overhead cranes to estimate and then eliminate the influence of the disturbances. Both simulation and hardware experimental results are provided to validate the efficiency and robustness of the proposed control strategy. To the best of our knowledge, this paper proposes the first method that can solve the control problem of overhead cranes suffering from both matched and unmatched disturbances, without tuning to linearizations or approximations.

Robust Control of Discrete‐time Singular Systems via Integral Sliding Surface

AbstractIn this paper, the sliding mode control for a class of uncertain discrete‐time singular system with performance constraint is studied. By taking the singular matrix E into consideration, a new type of integral sliding mode surface is firstly introduced, based on which a sufficient condition is derived to guarantee the sliding mode dynamics admissible with a given γ‐level disturbance attenuation of the unmatched disturbance. A controller law is also given to keep the system trajectory staying in a neighborhood of the ideal sliding surface. Finally, a numerical example is given to show the effectiveness of the proposed approach.

Observer-based output consensus of a class of heterogeneous multi-agent systems with unmatched disturbances

In this paper, the output consensus of a class of linear heterogeneous multi-agent systems with unmatched disturbances is considered. Firstly, based on the relative output information among neighboring agents, we propose an asymptotic sliding-mode based consensus control scheme, under which, the output consensus error can converge to zero by removing the disturbances from output channels. Secondly, in order to reach the consensus goal, we design a novel high-order unknown input observer for each agent. It can estimate not only each agent’s states and disturbances, but also the disturbances’ high-order derivatives, which are required in the control scheme aforementioned above. The observer-based consensus control laws and the convergence analysis of the consensus error dynamics are given. Finally, a simulation example is provided to verify the validity of our methods.

Saturated Backstepping Control of Underactuated Spacecraft Hovering for Formation Flights

Based on the inherent coupling of system states, backstepping controllers are designed for underactuated spacecraft hovering without either the radial or in-track thrust and in the presence of input saturation and unmatched disturbances. Feasible hovering positions for either saturated underactuated case are derived. A Lyapunov-based approach is used to prove the asymptotical convergence of state errors and system robustness against unmatched disturbances. The validity of theoretical analysis is verified by simulations in a J2 -perturbed environment.

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.

Neural-network-based integral sliding-mode tracking control of second-order multi-agent systems with unmatched disturbances and completely unknown dynamics

This paper investigates the tracking control problem of second-order multi-agent systems (MASs) in the presence of unmatched disturbances and completely unknown dynamics. The extended state observer (ESO) and neural networks (NNs) are utilized to estimate and compensated the unmatched disturbances and unknown dynamics, respectively. By constructed a novel integral sliding-mode manifold incorporated with ESO output, a neural-network-based control algorithm is developed. Meanwhile, by Lyapunov theoretical analysis, the UUB stability of the tracking errors as well as within a sufficiently small region is guaranteed by the appropriate choice of the parameters. Simulation results show that the proposed method exhibits much better control performances than the traditional I-SMC method, such as great robustness, reduced chattering and more accurate.

Ultimate state boundedness of underactuated spacecraft subject to an unmatched disturbance

Ultimate state boundedness for underactuated spacecraft subject to large non-matched disturbances is attained. First, non-smooth time-invariant state feedback control laws that make the origin asymptotically stable are obtained. Then, the controller is extended to make the closed-loop system globally uniformly ultimately bounded under the following conditions: 1) the disturbances acting on the directly actuated states are known and 2) the disturbance acting on the unactuated state is bounded and its profile need not be known. Finally, numerical simulations are presented to verify the analytical results. A large step disturbance is considered, and it is shown that the proposed controller makes the closed-loop system globally uniformly ultimately bounded. The proposed method is rather general and can be extended to other systems.

Output Feedback Stabilization of Inertial Stabilized Platform with Unmatched Disturbances Using Sliding Mode Approach

Inertial stabilized platforms are extensively used to keep the light of sight free from the effects of vehicle motion or vibration. In order to reduce the assembly difficulty and cost as well as achieve an accurate pointing in the presence of disturbances, a finite-time output feedback control strategy is proposed. On the basis of the dynamic model with both matched and unmatched uncertainties, two high-order sliding mode observers are designed to estimate the newly defined virtual state and the lumped uncertainty, respectively. Combing with the nonsingular terminal sliding mode technique, an output feedback control based on the estimates and the output is developed. The proposed method can achieve not only stability and robustness against uncertainties but also the finite-time convergence to the desired angular rate without control chattering. Finally, the comparative simulations are performed to show the effectiveness of the proposed method.

Output regulation of a reaction-diffusion PDE with long time delay using backstepping approach

In this paper, we are concerned with the output regulation of an unstable reaction-diffusion PDE with regulator delay and unmatched disturbances, which are generated by an exosystem. A backstepping regulator design procedure is presented by mapping the reaction-diffusion PDE cascaded with a transport equation into an error system, which is shown to be exponentially stable with a prescribed rate in a suitable Hilbert space. The output regulation is then verified by solving cascaded regulator equations. The solvability condition of the cascaded regulator equations is characterized by a transfer function and eigenvalues of the exosystem. Finally, the numerical simulations are provided to illustrate the effect of the regulator.