Zero-assignment and complex coefficient gain design of generalized proportional-integral observer for robust fault detection

Aiming at early detection of faults in dynamic systems subject to external periodic disturbances, this paper proposes a new generalized proportional-integral observer (GPIO) fault detection scheme with zero-pole joint optimization and novel complex coefficient gain (CCG) of residual evaluation. The focus of the proposed scheme is to reduce the adverse impacts caused by the semi-stationary periodic disturbance whose spectrum is uneven, with most energy being at some dominant frequencies. The proposed GPIO with a complex coefficient gain is designed in a two-stage procedure. In the first stage of zero assignment and pole optimization, the additional zeros introduced by the GPIO’s integration action are allocated to near the disturbance frequency. The gain of the transfer function matrix relating from the disturbances to the fault indicator signals is minimized by pole optimization. In the second stage of designing complex coefficient gain in residual evaluation, the unique feature of rank-deficient caused by the additional zeros assigned in stage one is further exploited to cancel the disturbances in the fault indicator signals (which is also referred to as the fault detection residual in this article). It is proved that, for an arbitrary periodic disturbance with a specific spectrum, the remnant components of the disturbance in the indicator signals generated by the GPIO can cancel each other by a complex gain vector, which can be determined by the zero eigenvalue’s left eigenvector of the rank-deficient of the disturbance transfer function matrix. The sufficient conditions for the convergence of the proposed fault detection filter are also given. Numerical examples illustrate the proposed method’s better performance in detecting minor faults.     

Continuous output feedback sliding mode control for underactuated flexible-joint robot

The tracking control based on output feedback for a category of flexible-joint robot (FJR) systems is investigated in this brief. Control performance of the systems is inevitably bearing the brunt of various unknown time-varying disturbances, which can be categorized to be matched and mismatched and generally cover internal parameter uncertainties, couplings, unmodelled dynamics, and external load or changing operating environments. To cope with these disturbances, the mismatched disturbances are first transferred to the matched ones by a flatness method, which eliminates the computational cost of estimating mismatched disturbances. Then, a generalized proportional integral observer (GPIO) is constructed to estimate the unavailable states and disturbances. By integrating the estimated disturbance and states provided by the GPIO, a novel dynamic sliding surface is constructed. Finally, a continuous sliding mode control (CSMC)-based output feedback control framework is further designed. The presented control strategy only requires link position information and is continuous, which can effectively reduce the chattering driven by the high-frequency switching item in the traditional SMC method. Asymptotic convergence of output tracking error is guaranteed by theoretical analysis under some mild conditions. Comparative tests on a two-link FJR verify the claimed control performance.     

Disturbance observer-based repetitive control with application to optoelectronic precision positioning system

Rejection of periodic disturbance and/or tracking of periodic reference is of importance in high-precision control systems. Conventional repetitive control is often used to solve the problem, but it cannot precisely set effective frequency points and adversely amplify the non-periodic component disturbance. Therefore, it is not applicable in actual systems where external disturbances exist in the whole frequency domain. In this paper, we propose an improved discrete-time repetitive control method based on the disturbance observer to correct the undesired deviation at repetitive frequencies and mitigate the amplification of the non-components. Moreover, in the observer structure, an intuitive and flexible Q-filter design is presented to suppress low-frequency broadband and intermediate-frequency narrowband disturbances. The conditions of closed-loop stability, performance analysis, and the implementation of the proposed scheme are provided in detail. Finally, the effectiveness of the method is verified by simulation and experimentation on an optoelectronic precision positioning system under the condition of disturbances, and the disturbance suppression and tracking error attenuation are improved.     

Disturbance rejection for nonlinear systems with mismatched disturbances based on disturbance observer

A disturbance rejection approach based on disturbance observer is proposed for a class of nonlinear systems subject to mismatched disturbances. The mismatched disturbances are described by exogenous systems and satisfy partially-known information, which enter the system in the different channels with the control input. The disturbance observer is designed to estimate the mismatched disturbances, which can be introduced separately from the controller design. By integrating disturbance observer with back-stepping method, the disturbance observer plus back-stepping (DOPBS) controller can be constructed to reject the mismatched disturbances. And the asymptotically stability for the closed-loop system can be achieved. Finally, simulation examples are given to demonstrate the feasibility and effectiveness of the proposed scheme compared with existing methods.     

Robust H∞ control of an observer-based repetitive-control system

This paper concerns the problem of designing a robust observer-based modified repetitive-control system with a prescribed H_∞ disturbance rejection level for a class of strictly proper linear plants with unknown aperiodic disturbances and time-varying structural uncertainties. A correction to the amount of the delay in the repetitive controller is introduced that leads to a significant improvement in tracking performance. An integrated performance index is defined to quantify the overall effect of rejecting the aperiodic disturbances and tracking the periodic reference input. A Lyapunov functional with two tuning parameters is used to derive a linear-matrix-inequality based robust stability condition for the system with a prescribed disturbance-rejection bound. Combining the performance indices, an optimization algorithm that searches for the best combination of state-observer gain and the feedback control gains is developed. A numerical example illustrates the design procedure and demonstrates the effectiveness of the method.     

Disturbance rejections and synchronization of fractional-order fuzzy complex networks

This paper deals with the problem of disturbance rejection and synchronization of fractional-order complex dynamical networks subject to nonlinear coupling strength and discontinuous nonlinear functions. Notably, the nonlinear coupling strength is linearised by using a well-known Takagi-Sugeno fuzzy approach. The considered system is transformed into a nominal form by employing the uncertainty and disturbance estimator-based control approach, which simplifies the control objective and improves the system performance. Second, the uncertainty and disturbance estimator is incorporated into the traditional feedback control scheme to reject the unknown disturbance and uncertainty. Then, the required synchronization conditions for both the discontinuous and continuous fractional-order systems are obtained by using Lyapunov stability and fractional calculus theories. Last, numerical examples are provided to illustrate the efficiency of the proposed control strategy, wherein it is shown that the system yields better satisfactory tracking performance and high robustness against possible disturbance and uncertainties and finite set of jump discontinuous nonlinear functions. Moreover, the selection of appropriate filter design is discussed for various kinds of disturbance signals.     

Consensus disturbance rejection for Lipschitz nonlinear multi-agent systems with input delay: A DOBC approach

In this paper, a new predictor-based consensus disturbance rejection method is proposed for high-order multi-agent systems with Lipschitz nonlinearity and input delay. First, a distributed disturbance observer for consensus control is developed for each agent to estimate the disturbance under the delay constraint. Based on the conventional predictor feedback approach, a non-ideal predictor based control scheme is constructed for each agent by utilizing the estimate of the disturbance and the prediction of the relative state information. Then, rigorous analysis is carried out to ensure that the extra terms associated with disturbances and nonlinear functions are properly considered. Sufficient conditions for the consensus of the multi-agent systems with disturbance rejection are derived based on the analysis in the framework of Lyapunov–Krasovskii functionals. A simulation example is included to demonstrate the performance of the proposed control scheme.     

Performance assessment for non-Gaussian systems by minimum entropy control and dynamic data reconciliation

Control performance of the industrial process is inevitably influenced by the measurement noises and non-Gaussian external disturbances. This influence has not been fully considered in the traditional variance-based controller design. To reduce the influence, a novel scheme that can enhance the control performance is developed by integrating dynamic data reconciliation (DDR) into minimum rational entropy control (MREC) in this paper. Firstly, the influence of measurement noise is fully considered, and a novel DDR method is proposed to deal with the minimum entropy control (MEC) process such that the influence of measurement noise can be reduced, and the control performance will be improved. Then, based on the DDR-MREC performance index, a benchmark for evaluating the control performance of non-Gaussian systems is established. Finally, the proposed control performance assessment (CPA) method is applied to the wind energy conversion system and compared with the CPA method based on DDR-minimum variance control. The experimental results have demonstrated that the proposed new method is more effective than existing works.     

Disturbance rejection for time-delay systems based on the equivalent-input-disturbance approach

This paper presents a disturbance rejection method for time-delay systems. The configuration of the control system is constructed based on the equivalent-input-disturbance (EID) approach. A modified state observer is applied to reconstruct the state of the time-delay plant. A disturbance estimator is designed to actively compensate for the disturbances. Under such a construction of the system, both matched and unmatched disturbances are rejected effectively without requiring any prior knowledge of the disturbance or inverse dynamics of the plant. The presentation of the closed-loop system is derived for the stability analysis and controller design. Simulation results demonstrate the validity and superiority of the proposed method.     

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.     

Cluster synchronization of fractional-order complex networks via uncertainty and disturbance estimator-based modified repetitive control

The combined problems of cluster synchronization and disturbance rejection for a family of fractional-order complex networks subject to coupling delay, unknown uncertainty and disturbances (UDs) are examined in this study. In particular, the existence of coupling delay is taken into the account with both known and unknown cases. First, a new uncertainty and disturbance estimator (UDE)-based control protocol is formulated for the concerned system to estimate and compensate for the effects of UD. Although the UDE strategy has proven to be a viable tool to deal with slowly changing UDs in control design, the presence of rapidly changing UDs or sinusoidal disturbances is not an effective tool. A well-known modified iterative control (MRC) block is built internally in a closed feedback control loop to solve this problem. After implementing UDE and MRC blocks into the feedback loop, the resulting system becomes almost UD-free. Moreover, a set of sufficient linear matrix inequality constraints are established to ensure the cluster synchronization of the resulting system. Lastly, the benefits, feasibility and robustness of the established UDE-based MRC scheme are confirmed by two illustrative examples.     

Additive-state-decomposition-based model predictive tracking control for PMSM servo system with multiple disturbances

This paper presents an additive-state-decomposition-based model predictive tracking control and disturbance rejection method for a permanent magnet synchronous motor (PMSM) servo system subject to unknown parameter perturbations, unmodeled dynamics, and time-varying load torque. The basic idea of this method is to equivalently decompose the original system into a primary system for handling the tracking control subproblem and a secondary system for dealing with the robust stabilization subproblem. A model predictive controller is designed for the primary system to achieve high-accuracy tracking of the reference speed. As for the secondary system, a novel high-order generalized extended state observer (HGESO) is constructed to estimate the multiple disturbances simultaneously, and a state feedback control law incorporating a disturbance compensator is developed to eliminate the adverse effect of the multiple disturbances on the system output. By combining the control inputs of the two subsystems together, the control objectives of the original system can be achieved. Both the stability criterion and design procedure of the closed-loop control system are developed. Finally, hardware-in-the-loop-based comparative experiments are conducted to demonstrate that the proposed method effectively suppresses the influence of the multiple disturbances on motor speed tracking accuracy and that the control system has both satisfactory dynamic performance and robustness.     

Approximate decoupling and output tracking for MIMO nonlinear systems with mismatched uncertainties via ADRC approach

In this paper, we consider output tracking for a class of MIMO nonlinear systems which are composed of coupled subsystems with vast mismatched uncertainties. First, all uncertainties influencing the performance of controlled outputs, which include internal unmodelled dynamics, external disturbances, and uncertain nonlinear interactions between subsystems, are refined into the total disturbance in the control channels of subsystems. The total disturbance is shown to be sufficiently reflected in the measured output of each subsystem so that it can be estimated in real time by an extended state observer (ESO) in terms of the measured outputs. Second, we decouple approximately the MIMO systems by cancelling the total disturbance based on ESO estimation so that each subsystem becomes approximately independent linear time invariant one without uncertainty and interaction with other subsystems. Finally, we design an ESO based output feedback for each subsystem separately to ensure that the closed-loop state is bounded, and the closed-loop output of each subsystem tracks practically a given reference signal. This is completely in comply with the spirit of active disturbance rejection control (ADRC). Some numerical simulations are presented to demonstrate the effectiveness of the proposed output feedback control scheme.     

Cascade ADRC with neural network-based ESO for hypersonic vehicle

In this paper, active disturbance rejection control (ADRC) based on a neural network has been investigated for the attitude control of the hypersonic vehicle (HV) with uncertain disturbances, which are regarded as a strongly time-varying, nonlinear, and coupled system. The structure of nonlinear state error feedback (NLSEF) with an Extended State Observer (NLSEF+ESO) utilized in ADRC is considered to have good disturbance resistance ability in engineering applications with less dependence on the mathematical model of the system. However, the strong coupling of the HV makes it complicated to separately design ADRC for each channel. In addition, the bandwidth and parameters of the ESO can seriously affect the performance of the ADRC, while jitter occurs when they are not well matched. A cascade active-rejection control scheme is designed by introducing the Radial Basis Function (RBF) Neural Network to substitute the ESO in ADRC, which mitigates the shortcoming of ADRC in addressing the control problems of the MIMO system with coupling disturbances. The NNESO can adapt well to disturbance characteristics through online training and fitting and can effectively reduce the jitter of the control. The stability of the NNESO is proved by Lyapunov stability theory, and the numerical simulations are presented to demonstrate the effectiveness of our theoretical results. In summary, the proposed NNESO-based cascade ADRC is an effective method for solving the problem of HV control with better disturbance resistance.     

Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates

In this paper, finite-time synchronization problem is considered for a class of Markovian jump complex networks (MJCNs) with partially unknown transition rates. By constructing the suitable stochastic Lyapunov–Krasovskii functional, using finite-time stability theorem, inequality techniques and the pinning control technique, several sufficient criteria have been proposed to ensure the finite-time synchronization for the MJCNs with or without time delays. Since finite-time synchronization means the optimality in convergence time and has better robustness and disturbance rejection properties, this paper has important theory significance and practical application value. Finally, numerical simulations illustrated by mode jumping from one mode to another according to a Markovian chain with partially unknown transition probability verify the effectiveness of the proposed results.     

Control design for maximal capability of disturbance rejection under general control input saturation

This paper focuses on the control problem for a basic class of nonaffine uncertain systems with general control input saturation (CIS) and piecewise constant disturbance. Instead of traditional CIS, the considered general CIS model includes the case that larger control input generates smaller control capability to capture more general engineering systems. Also, the saturation point, at which the maximum or minimum value of the saturation function of general CIS can be obtained, is assumed to be unknown. To achieve the maximal capability of disturbance rejection, this paper proposes a novel active disturbance rejection control design with online estimating both disturbance and the saturation points. Firstly, the control capability under the nominal saturation points is discussed. We demonstrate that the corresponding capability of disturbance rejection can be discussed via the domain of attraction or invariant set of the systems with general CIS despite of disturbance. Furthermore, we design an algorithm to online identify the saturation points based on the estimation of “total disturbance” obtained by extended state observer (ESO). It is proven that the maximal capability of disturbance rejection can be approached by tuning the parameters of the proposed controller. In addition, simulation results for the angular rate control of aircraft show the superiority of our control law to the traditional disturbance rejection control law.     

Design of PID controller based on a self-adaptive state-space predictive functional control using extremal optimization method

In proportional-integral-derivative (PID) controller design, obtaining high stability and desired closed-loop response are of great importance for system engineers. Most existing methodologies, which have validated their excellent control performance on the accurate mathematical model, face significant difficulties in the unavoidable model mismatches and disturbance. To overcome these drawbacks, this paper proposes a self-adaptive state-space predictive functional control (APFC) based on extremal optimization method to design PID controller called EO-APFC-PID, wherein, the self-adaptive means, i.e., a forgetting factor recursive least squares (FFRLS) mechanism is embedded into state-space predictive functional control (PFC), and the proposed EO is exploited to alleviate the challenging problem that the elements in weighting factors of APFC technique are lacking analytical knowledge. The performance of the proposed EO-APFC-PID control scheme is demonstrated and compared with one classic PID tuning method and two state-of-the-art control strategies on the chamber pressure control for a coke furnace. The experimental results fully illustrate that the proposed method is more effective and efficient than other existing control strategies for achieving a desired behavior on the most test cases considered in this paper in terms of set point tracking, input disturbance rejection and output disturbance rejection.     

Nonlinear model-predictive control with disturbance rejection property using adaptive neural networks

In this paper, a method is proposed to reject disturbances in the model predictive control (MPC) strategy. In addition, uncertainties in the system parameters (i.e., internal disturbances) are considered as well. To achieve these goals, adaptive neural networks are designed as the predictor model and as the nonlinear disturbance observer, respectively. The disturbances are rejected via the optimization problem of the MPC. Stability of the closed-loop system is studied based on the Input-to-State Stability method. The proposed method is applied to the pH neutralization process and CSTR system and its effectiveness in optimal rejection of the disturbances and satisfying the system constrains is compared with the feed-forward control method.     

Composite adaptive disturbance observer based control and back-stepping method for nonlinear system with multiple mismatched disturbances

A novel control scheme combining disturbance observer technique and back-stepping method is proposed for a class of nonlinear system with multiple mismatched disturbances. The uncertain multiple mismatched disturbances contain not only single harmonic or constant disturbances but also another unexpected nonlinear signal presented as a nonlinear function. The composite adaptive disturbance observers are designed to estimate the disturbances with partial known information. By integrating disturbance observer based control with back-stepping method, a composite controller is designed. Here, the disturbance estimations are introduced into the design of virtual control laws in each step to compensate the mismatched disturbances. Rigorous stability analysis for the closed-loop system is established by direct Lyapunov function method. It is shown that the system output asymptotically converges to zero in spite of existing multiple mismatched disturbances. Finally, a simulation example is applied to demonstrate the effectiveness of the proposed method.     

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.