State Observer Gain Research Articles

Fuzzy neural network adaptive AUV control based on FTHGO

ABSTRACT A fuzzy radial basis function neural network (Fuzzy RBFNN) adaptive control scheme, based on fixed-time high gain state observer (FTHGO), is proposed to address the unpredictability of real-time state and composite interference in the trajectory tracking of the fully driven Autonomous Underwater Vehicle (AUV), ensuring fixed-time system convergence regardless of initial conditions. Firstly, a fixed-time backstepping controller is designed and a first-order fixed-time filter is introduced to tackle the differential explosion issue. Secondly, an FTHGO is developed to observe the real-time states of the AUV without assuming global known state signal. Then, the composite interference in the AUV system is effectively compensated by integrating the Fuzzy RBFNN technique. Finally, the fixed-time stability of the entire closed-loop system is proven utilising the Lyapunov stability theory. The effectiveness of the proposed algorithm is proved by the simulation experiment.

Tracking and Disturbance Suppression of the Radio Telescope Servo System Based on the Equivalent-Input-Disturbance Approach

This paper presents a composite control algorithm for the radio telescope servo control system to address the target tracking and matched/mismatched disturbance suppression problems. The algorithm consists of the equivalent-input-disturbance (EID) approach and the optimal control method. An EID estimator is developed using the difference between the estimated output of the state observer and the measurement output and then the estimate of the EID is fed forward into the control input to reject the disturbance. A cost function with clear physical meaning is selected and the weighting parameters are adjusted for the optimal controller to improve tracking performance. Considering the nonminimum phase characteristics of the radio telescope system, the state observer gain is computed using the linear matrix inequality (LMI) method. The system stability is analyzed using the small gain theorem, and the linear quadratic regulator (LQR) control method is utilized to determine the state feedback gain. Finally, the composite controller is designed for an identified telescope model. Simulation results show that for the tracking performance, the settling time of proposed method is 1.13 s and reduces by about 0.32 s and 0.87 s than that of the ADRC controller and PI controller, respectively. For the antidisturbance performance, the RMS value and the maximum error of the proposed method are 0.0039 and 0.0128, which are 42.86% and 40.38% of the ADRC controller and 30.71% and 27.77% of the PI controller, respectively, which indicates that the proposed method has better control performance. In addition, the proposed controller has certain robustness to systematic parameter perturbations.

Adaptive Event-Triggered Model Predictive Load Frequency Control for Power Systems

This paper investigates the adaptive event-triggered (AET) output feedback model predictive control (MPC) method for the load frequency control (LFC) problem of hybrid power system involving the thermal power and the photovoltaic power. First, an AET communication mechanism, which possesses the ability to dynamically adjust the trigger threshold parameter according to an adaptive law, is addressed to reducing the communication overhead, while keeping the required control performance; Second, the output feedback model predictive controller which is composed of an off-line designed state observer and an on-line solved optimization problem, is proposed using the techniques of quadratic boundedness and S-procedure. The state observer gain is obtained by off-line maximizing the trace of a matrix which is closely related to minimal positively invariant set; While the output feedback MPC strategy is acquired by expressing the infinite horizon control moves as a free control move and a linear feedback law based on the estimated state; Third, the recursive feasibility of the on-line optimization problem and the stability of the closed-loop system are analyzed by the fact that the estimated state and estimation error will converge to the presented minimal positively invariant set. Finally, MATLAB and its linear matrix inequality (LMI) toolbox are used to solve the optimization problem, and the LFC system with load disturbance is simulated and analyzed. The simulation results show that the proposed method is feasible and effective.

Ellipsoidal tube‐based output feedback robust MPC for linear systems with bounded disturbances and noises

AbstractThis paper designs an ellipsoidal tube‐based output feedback robust model predictive control approach for linear systems with bounded disturbances and noises subject to physical constraints. The ellipsoidal tube‐based output feedback robust model predictive control approach combines the off‐line optimization to compute controller parameters and deal with system uncertainties, and the on‐line optimization to stabilize the nominal system with time‐varying tightened constraints. In the off‐line optimization, the state observer gain, ancillary feedback controller gain, and tightened constraint sets on the nominal system are synthesized in one optimization. Then, an ellipsoidal terminal constraint set with terminal controller gain and terminal cost matrix, and tightened constraint sets related to different sizes of estimation error bounds are computed. In the on‐line model predictive control optimization with time‐varying tightened constraints, a sequence of nominal control inputs is receding horizon optimized to steer the nominal system state to the ellipsoidal terminal constraint set. When the current nominal system state is bounded within the ellipsoidal terminal constraint set, the nominal control inputs are switched to the feedbacks on the closed‐loop nominal system states. Recursive feasibility of the proposed algorithm and robust stability of the controlled system are guaranteed.

Suppression of Packet Losses and Disturbances in Networked Control Systems Based on Equivalent-Input-Disturbance Approach.

This article presents a method of suppressing packet losses and exogenous disturbances for a networked control system (NCS) subject to network-introduced delays. The NCS has two feedback loops: 1) a local one and 2) a main one. The local feedback loop contains a state observer, an equivalent-input-disturbance (EID) estimator, and state feedback. It is used to ensure prompt disturbance suppression. The controller in the main feedback loop contains an internal model to track a reference input. The system is divided into two subsystems for the design of controllers. The state-observer gain is designed for one subsystem using the concept of perfect regulation to ensure disturbance estimation performance. The state-feedback gains of the other subsystem are designed based on a stability condition in the form of a linear matrix inequality (LMI). A tracking specification is embedded in the LMI-based stability condition to ensure satisfactory tracking performance. A case study on a two-finger robot hand control system and a comparison with a Smith-EID and H∞ controller approach validate the effectiveness and superiority of the presented method.

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.

A Robust Nonlinear Controller With Low-Gain-State-Observer for Wire Rope Tension Active Control of Hoisting Systems

In this paper, a modified double-rope winding hoisting system (MDWHS) is proposed for ultra-deep mines. Nevertheless, the MDWHS has wire rope tension imbalance issues due to lift inconsistency of two wire ropes. A combined control algorithm is designed for wire rope tension active control considering the nonlinear uncertainties subjected to the MDWHS, where a low gain state observer (LGSO) and a robust nonlinear adaptive controller are employed via backstepping theory. Firstly, to investigate the wire rope tension active control method, the dynamics model of the MDWHS is established. Then, the LGSO is employed to estimate unmeasured system state variables and to optimize perturbed system state variables. Finally, a robust nonlinear control method is employed to acquire prospective control input. The combined control algorithm can ensure the desired transient and final tracking accuracy, which is essential for tracking control of wire rope tension active adjustment. The stability of the overall closed-loop system with the presented control algorithm can be verified referring to the Lyapunov theory. Experimental results conducted on the established double-rope winding hoisting simulation experimental system demonstrate that the proposed active control method exhibit more advantageous performance on wire rope tension balance control compared with the conventional Proportion Integration (PI) and adaptive backstepping controller (ABC).

Observer-based anti-windup compensator design for nonlinear systems

This paper presents a method for observer-based nonlinear anti-windup compensator (AWC) design using decoupled architecture for the class of nonlinear systems under input saturation by considering the unavailability of state variables. Novel observer-based nonlinear decoupled and equivalent decoupled anti-windup compensator architectures are proposed for the class of nonlinear systems with input saturation and unmeasured states. The designed constraints are formulated by utilizing Lyapunov function, L2 gain reduction, global sector condition and Lipschitz inequality. Linear matrix inequality (LMI) based conditions are derived for simultaneous design of dynamic nonlinear anti-windup compensator and the state observer gain. Global design of dynamic nonlinear anti-windup compensator and observer gain is provided in order to ensure global exponential L2 stability of the closed-loop system. Furthermore, anti-windup compensation constraints using local exponential L2 stability are also provided to ensure regional closed-loop stability and performance. In contrast to the conventional dynamic AWC schemes for nonlinear systems, the proposed approach can be employed when states of a system are not measurable. Numerical example of the nonlinear DC motor under input saturation is considered to demonstrate effectively of the proposed technique.

Discrete-Time LPV Observer With Nonlinear Bounded Varying Parameter and Its Application to the Vehicle State Observer

In this paper, we designed a unique structure and developed a novel linear parameter varying (LPV) formulation design for a vehicle-model-based state observer. The design problem for a vehicle state observer was totally reformulated into an LPV system that depended on online accessible time-varying parameters. The proposed LPV formulation, which is presented for the first time in this paper, did not require high computational costs compared to a conventional approach using an extended Kalman filter (EKF) including a nonlinear term. With regard to vehicle state estimation using a global positioning system, we considered the measured course angle as a varying parameter. Observer gain scheduling was determined using an $H_2$ filter based on the linear matrix inequality approach. The state observer gain using a discrete-time $H_2$ filter could minimize the error from a disturbance to a state. The stability of the proposed algorithm is proven, and the performance of the proposed method was demonstrated with an experimental test through a performance comparison with the EKF.

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.

Adaptive observer design for a class of nonlinear systems. Application to speed sensorless induction motor

This paper investigates the problem of designing an adaptive high gain observer for a class of MIMO non uniformly observable systems involving some unknown constant parameters. The considered systems are not necessarily linear with respect to the unknown parameters up to a well defined parameter structure involving the parameter characteristic indices. The observer design model is elaborated from the state system dynamics augmented with the dynamics of the unknown parameters. An adaptive observer whose gain is derived from the resolution of a Lyapunov differential equation is proposed and its exponential convergence is established under an appropriate persistent excitation property up to the classical high gain state observer design assumptions. Moreover, it is shown that the equations of the observer can be put under an adaptive form emphasizing thereby its versatility to include several available adaptive observers. The main steps of the observer design and its convergence properties are illustrated through a typical problem involving an induction motor where one aims at estimating the mechanical speed, the load torque and rotor fluxes as well as the rotor inductance and resistance from the measurements of the stator currents.

Finite-time state observer for delayed reaction-diffusion genetic regulatory networks

This paper focus on the finite-time state estimation problem for delayed reaction-diffusion genetic regulatory networks (DRDGRNs) under Dirichlet boundary conditions. The purpose is to design a finite-time state observer which is used to estimate the concentrations of mRNAs and proteins via available measurement outputs. By constructing a Lyapunov–Krasovskii functional (LKF) concluding quad-slope integrations, we establish a reaction-diffusion-dependent and delay-dependent finite-time stability criterion for the error system. The derivative of LKF is estimated by employing the Wirtinger-type integral inequality, Gronwall inequality and convex (reciprocally convex) technique. The stability criterion is to check the feasibility of a set of linear matrix inequalities (LMIs), which can be easily realized by the toolbox YALMIP of MATLAB. In addition, the expected finite-time state observer gain matrices can be represented by a feasible solution of the set of LMIs. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results.

Anti-windup design for uncertain nonlinear systems subject to actuator saturation and external disturbance

Summary A novel anti-windup design method is provided for a class of uncertain nonlinear systems subject to actuator saturation and external disturbance. The controller considered incorporates both an active disturbance rejection controller as well as an anti-windup compensator. The dynamical uncertainties and external disturbance are treated as an extended state of the plant, and then estimate it using an extended state observer and compensate for it in the control action, in real time. The anti-windup compensator produces a signal based on the difference between the controller output and the saturated actuator output, and then augment the signal to the control to deal with the windup phenomenon caused by actuator saturation. We first show that, with the application of the proposed controller, the considered nonlinear system is asymptotically stable in a region including the origin. Then, in the case that the controller in linear form, we establish a linear matrix inequality-based framework to compute the extended state observer gain and the anti-windup compensation gain that maximize the estimate of the domain of attraction of the resulting closed-loop system. The effectiveness of the proposed method is illustrated by a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.

State Observer for Continuous Oscillating Systems with Pulsatile Feedback⋆

AbstractThe paper introduces a static gain state observer for linear continuous systems under sustained oscillations driven by intrinsic and inaccessible for measurement pulse-modulated feedback. This kind of hybrid dynamics arises in e.g. modeling of endocrine systems with pulsatile regulation. Conditions under which the observer state estimation error converges to zero and the sequence of pulse modulation instances estimated by the observer asymptotically synchronizes with that of the plant are presented.

설계사양을 고려한 컨테이너 크레인의 RCGA기반 상태 관측기 설계

대규모 컨테이너항만의 건설과 함께 컨테이너 크레인의 생산성 향상으로 선박 체항시간을 단축시켜 항만의 서비스 수준을 높이려는 노력이 가속화되고 있다. 컨테이너 크레인 시스템에 가해지는 입력에 대하여 바람직한 성능을 보이도록 설계사양을 고려한 상태 퍼드백 제어시스템을 사용한다. 컨테이너 크레인에서 측정이 까다롭거나 측정 잡음이 클 것으로 예상되는 상태 변수를 추정하는 방법으로 상태 관측기를 설계하고자 한다. 기존의 연구에서는 상태 피드백 제어시스템의 피드백 이득행렬과 상태 관측기 이득행렬을 분리하여 구하였다. 그러나 본 연구에서는 피드백 이득행렬과 상태 관측기 이득행렬을 선정함에 있어 최근 강인한 탐색법으로 많이 사용되는 REGAs를 사용해 설계사양을 만족하도록 동시에 구하고자 한다. Construction of large-scale container ports with the productivity improvements in container cranes shortened time of staying port to increase the level of service it harbors efforts accelerated. About container crane system exerted on the input, which is designed to look good performance considering the states feedback control system. The states observer designed of container cranes state variables that are expected to measurement noise or particular measurement signal. In the status of existing research, the feedback gain matrix and the state observer gain matrix are searched by being separated solving. But the feedback gain matrix and the state observer gain matrix are searched by RCGAs at once that be used robust search method in this paper.

A New Output Feedback Control for Nonlinear Differential-Algebraic-Equation Systems

This note considers the problem of stabilization by output feedback for a class of nonlinear Differential-Algebraic-Equation systems. The output feedback controller is constructed which ensures the closed-loop systems asymptotically stable. Not based on separation-principle that is commonly adopted in the literature, the output feedback controller design is coupled with that of the non-initialized linear high gain state observer. The numerical simulation results illustrate the effectiveness of the proposed scheme.

Robust State Observer and Variable Sampling Technique for Performance Improvement of a Motor Drive System

A microprocessor-based digital control system of motor speed is discussed with respect to the dynamic response and the accuracy of controlled speed. Two methods for improving both the dynamics and the accuracy are examined in this paper. One is a method of variable gain state observer and the other is a variable sampling technique. Comparing their effects in improving the accuracy of controlled speed, it is shown that the former is preferable to the latter. The validity of the above discussion is confirmed by several simulations.