Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.

Reduced-Order Observer-Based Leader-Following Formation Control for Discrete-Time Linear Multi-Agent Systems

Formation control of discrete-time linear multi-agent systems using directed switching topology is considered in this work via a reduced-order observer, in which a formation control protocol is proposed under the assumption that each directed communication topology has a directed spanning tree. By utilizing the relative outputs of neighboring agents, a reduced-order observer is designed for each following agent. A multi-step control algorithm is established based on the Lyapunov method and the modified discrete-time algebraic Riccati equation. A sufficient condition is given to ensure that the discrete-time linear multi-agent system can achieve the expected leader-following formation.Finally, numerical examples are provided so as to demonstrate the effectiveness of the obtained results.

Study on unknown input reduced-order observer for fault diagnosis

A novel unknown input reduced-order observer (UIRO) design scheme is presented. It is proved that unknown input appearing in measurement can be eliminated by a simple algebraic transformation. Then, a new UIRO design scheme is proposed via a transformation under no unknown input existing in measurement. Compared with other known results, the condition is weaker than others. So it was further reasonable. The design procedure proposed is simple and straightforward enough to be applied. An example is given to show its efficiency in fault diagnosis.

The Design of Reduced-order Observer for Systems with Monotone Nonlinearities

与单调非线性为系统关于存在和完整顺序的观察员的设计方法基于讨论，一个还原剂顺序观察员设计方法在线性矩阵不平等(LMI ) 有的假设下面被开发积极明确的矩阵答案和还原剂顺序观察员获得矩阵被 LMI 的解决方案计算。由线性转变，不包含系统产量的衍生物的信息的一个还原剂顺序观察员被提供。一个模型被模仿，一些结论基于还原剂顺序观察员的结果的比较被得出到完整顺序的观察员的。模拟证明这份报纸开发的设计方法有好性能。

Design and analysis of switching reduced-order observer and separation principle for T-S fuzzy system

This paper designs and analyzes switching fuzzy reduced-order observer and proves that the corre- sponding separation principle does hold. A numerical simulation and comparison with smooth fuzzy full-order observer are given to assess switching fuzzy reduced-order observer and the validity of the separation principles.

Target tracking for non-identical high-order networks based on reduced-order observers

In this paper,target tracking for non-identical high-order networks is presented under the digraph network topology.The target agent has different dimensions with the followers.We first address a distributed dynamic state feedback control law to solve the output tracking problem.Then a reduced-order observer is designed,and an observer-based dynamic output feedback control law is given for the case that the states of the agents are not fully measurable.Finally,some simulation results are given to illustrate the validity of the theoretical results.

Observer based projective reduced-order synchronization of different chaotic systems

The projective reduced-order synchronization of two different chaotic systems with different orders is investigated based on the observer design in this paper.According to the observer theory,the reduced-order observer is designed.The projective synchronization can be realized by choosing the transition matrix of the observer as a diagonal matrix.Further,the synchronization between hyperchaotic Chen system(fourth order)and Rssler system(third order)is taken as the example to demonstrate the effectiveness of the proposed observer.Numerical simulations confirm the effectiveness of the method.

Sensor Fault Estimation and Fault-Tolerant Control for a Class of Takagi-Sugeno Markovian Jump Systems with Partially Unknown Transition Rates Based on the Reduced-Order Observer

This paper addresses the problem on sensor fault estimation and fault-tolerant control for a class of Takagi-Sugeno Markovian jump systems,which are subjected to sensor faults and partially unknown transition rates.First,the original plant is extended to a descriptor system,where the original states and the sensor faults are assembled into the new state vector.Then,a novel reduced- order observer is designed for the extended system to simultaneously estimate the immeasurable states and sensor faults.Second,by using the estimated states obtained from the designed observer,a state- feedback fault-tolerant control strategy is developed to make the resulting closed-loop control system stochastically stable.Based on linear matrix inequality technique,algorithms are presented to compute the observer gains and control gains.The effectiveness of the proposed observer and controller are validated by a numerical example and a compared study,respectively,and the simulation results reveal that the proposed method can successfully estimate the sensor faults and guarantee the stochastic stability of the resulting closed-loop system.

Nonlinear Control of an Induction Motor Using a Reduced-Order Extended Sliding Mode Observer for Rotor Flux and Speed Sensorless Estimation

This article proposes an innovative strategy to the problem of non-linear estimation of states for electrical machine systems. This method allows the estimation of variables that are difficult to access or that are simply impossible to measure. Thus, as compared with a full-order sliding mode observer, in order to reduce the execution time of the estimation, a reduced-order discrete-time Extended sliding mode observer is proposed for on-line estimation of rotor flux, speed and rotor resistance in an induction motor using a robust feedback linearization control. Simulations results on Matlab-Simulink environment for a 1.8 kW induction motor are presented to prove the effectiveness and high robustness of the proposed nonlinear control and observer against modeling uncertainty and measurement noise.

New LMI Conditions for Reduced-order Observer of Lipschitz Discrete-time Systems: Numerical and Experimental Results

The objective of this paper is to propose a reduced-order observer for a class of Lipschitz nonlinear discrete-time systems.The conditions that guarantee the existence of this observer are presented in the form of linear matrix inequalities(LMIs). To handle the Lipschitz nonlinearities, the Lipschitz condition and the Young′s relation are adequately operated to add more degrees of freedom to the proposed LMI. Necessary and sufficient conditions for the existence of the unbiased reduced-order observer are given. An extension to H_∞ performance analysis is considered in order to deal with H_∞ asymptotic stability of the estimation error in the presence of disturbances that affect the state of the system. To highlight the effectiveness of the proposed design methodology, three numerical examples are considered. Then, high performances are shown through real time implementation using the ARDUINO MEGA 2560 device.

Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles

This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.

Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

Reduced-order method for nuclear reactor primary circuit calculation

Accurate real-time simulations of nuclear reactor circuit systems are particularly important for system safety analysis and design.To effectively improve computational efficiency without reducing accuracy,this study establishes a thermal-hydraulics reduced-order model(ROM)for nuclear reactor circuit systems.The full-order circuit system calculation model is first established and verified and then used to calculate the thermal-hydraulic properties of the circuit system under different states as snapshots.The proper orthogonal decomposition method is used to extract the basis functions from snapshots,and the ROM is constructed using the least-squares method,effectively reducing the difficulty in constructing the ROM.A comparison between the full-order simulation and ROM prediction results of the AP1000 circuit system shows that the proposed ROM can improve computational efficiency by 1500 times while achieving a maximum relative error of 0.223%.This research develops a new direction and perspective for the digital twin modeling of nuclear reactor system circuits.

Observer-Based Adaptive Robust Precision Motion Control of a Multi-Joint Hydraulic Manipulator

Hydraulic manipulators are usually applied in heavy-load and harsh operation tasks.However,when faced with a complex operation,the traditional proportional-integral-derivative(PID)control may not meet requirements for high control performance.Model-based full-state-feedback control is an effective alternative,but the states of a hydraulic manipulator are not always available and reliable in practical applications,particularly the joint angular velocity measurement.Considering that it is not suitable to obtain the velocity signal directly from differentiating of position measurement,the low-pass filtering is commonly used,but it will definitely restrict the closed-loop bandwidth of the whole system.To avoid this problem and realize better control performance,this paper proposes a novel observerbased adaptive robust controller(obARC)for a multi-joint hydraulic manipulator subjected to both parametric uncertainties and the lack of accurate velocity measurement.Specifically,a nonlinear adaptive observer is first designed to handle the lack of velocity measurement with the consideration of parametric uncertainties.Then,the adaptive robust control is developed to compensate for the dynamic uncertainties,and the close-loop system robust stability is theoretically proved under the observation and control errors.Finally,comparative experiments are carried out to show that the designed controller can achieve a performance improvement over the traditional methods,specifically yielding better control accuracy owing to the closed-loop bandwidth breakthrough,which is limited by low-pass filtering in fullstate-feedback control.

Disturbance Observer-Based Predictive Tracking Control of Uncertain HOFA Cyber-Physical Systems

Dear Editor,In this letter,an output tracking control problem of uncertain cyber-physical systems(CPSs)is considered in the perspective of high-order fully actuated(HOFA)system theory,where a lumped disturbance is used to denote the total uncertainties containing parameters perturbations and external disturbances.

Quantum Realities and Observer-Dependent Universes: An Advanced Observer Model

This paper presents a novel observer model that integrates quantum mechanics, relativity, idealism, and the simulation hypothesis to explain the quantum nature of the universe. The model posits a central server transmitting multi-media frames to create observer-dependent realities. Key aspects include deriving frame rates, defining quantum reality, and establishing hierarchical observer structures. The model’s impact on quantum information theory and philosophical interpretations of reality are examined, with detailed discussions on information loss and recursive frame transmission in the appendices.

A Novel Disturbance Observer Based Fixed-Time Sliding Mode Control for Robotic Manipulators With Global Fast Convergence

This paper proposes a new global fixed-time sliding mode control strategy for the trajectory tracking control of uncertain robotic manipulators.First,a fixed-time disturbance observer(FTDO) is designed to deal with the adverse effects of model uncertainties and external disturbances in the manipulator systems.Then an adaptive scheme is used and the adaptive FTDO(AFTDO) is developed,so that the priori knowledge of the lumped disturbance is not required.Further,a new non-singular fast terminal sliding mode(NFTSM) surface is designed by using an arctan function,which helps to overcome the singularity problem and enhance the robustness of the system.Based on the estimation of the lumped disturbance by the AFTDO,a fixed-time non-singular fast terminal sliding mode controller(FTNFTSMC)is developed to guarantee the trajectory tracking errors converge to zero within a fixed time.The settling time is independent of the initial state of the system.In addition,the stability of the AFTDO and FTNFTSMC is strictly proved by using Lyapunov method.Finally,the fixed-time NFESM(FTNFTSM) algorithm is validated on a 2-link manipulator and comparisons with other existing sliding mode controllers(SMCs) are performed.The comparative results confirm that the FTNFTSMC has superior control performance.

基于Observer的典型飞行学员起飞阶段操作行为差异研究

为了研究飞行学员起飞训练阶段的行为特性,选取某航校培训的150名飞行学员,在实训固态模拟机(DA-40)上执行大侧风起飞航线任务,通过多角度录像的方法记录下飞行的全过程,并选取A、B两组飞行学员(表现最好和最差)的操作视频,对其操纵动作进行编码,应用The Observer XT(12.0)行为分析软件得出两组飞行学员各行为的可视图,并结合数理统计的方法对其俯仰操纵、航向操纵、滚转操纵等行为的持续时间、发生频次、所占飞行总时长的百分比进行对比分析。结果表明:在大侧风起飞任务下,两组飞行学员的俯仰操纵和滚转操纵行为在持续时间、发生频次、所占飞行总时长的百分比差异较为明显,其他操作行为无显著性差异。

Design of integral sliding mode guidance law based on disturbance observer

With the increasing precision of guidance,the impact of autopilot dynamic characteristics and target maneuvering abilities on precision guidance is becoming more and more significant.In order to reduce or even eliminate the autopilot dynamic operation and the target maneuvering influence,this paper suggests a guidance system model involving a novel integral sliding mode guidance law(ISMGL).The method utilizes the dynamic characteristics and the impact angle,combined with a sliding mode surface scheme that includes the desired line-ofsight angle,line-of-sight angular rate,and second-order differential of the angular line-of-sight.At the same time,the evaluation scenario considere the target maneuvering in the system as the external disturbance,and the non-homogeneous disturbance observer estimate the target maneuvering as a compensation of the guidance command.The proposed system’s stability is proven based on the Lyapunov stability criterion.The simulations reveale that ISMGL effectively intercepted large maneuvering targets and present a smaller miss-distance compared with traditional linear sliding mode guidance laws and trajectory shaping guidance laws.Furthermore,ISMGL has a more accurate impact angle and fast convergence speed.

Research on fixed-time time-varying formation of heterogeneous multi-agent systems based on tracking error observer under DoS attacks

In this paper,the fixed-time time-varying formation of heterogeneous multi-agent systems(MASs) based on tracking error observer under denial-of-service(DoS) attacks is investigated.Firstly,the dynamic pinning strategy is used to reconstruct the communication channel for the system that suffers from DoS attacks to prevent the discontinuous transmission information of the communication network from affecting MASs formation.Then,considering that the leader state is not available to each follower under DoS attacks,a fixed-time distributed observer without velocity information is constructed to estimate the tracking error between followers and the leader.Finally,adaptive radial basis function neural network(RBFNN) is used to approximate the unknown ensemble disturbances in the system,and the fixed-time time-varying formation scheme is designed with the constructed observer.The effectiveness of the proposed control algorithm is demonstrated by the numerical simulation.