Partial state estimation for linear systems with output and input time delays

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov–Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.     

Design of an observer for quantized output systems using orthogonal projection

This paper presents a state observer for linear systems with quantized outputs. The observer employs an orthogonal projection operation at quantizer output discontinuities to enhance its convergence rate for quantized output systems. Although there may be a significant quantization error on average, it is possible to design observers with an exponentially stable tracking error. We explain how to construct the orthogonal projection operation in a Hilbert space and prove the stability of the proposed observer by using the Lyapunov second method. In order to assess the value of the orthogonal projection operation in the proposed observer, the simple motor system with an optical encoder has been analyzed numerically.     

Discrete state space modeling and control of nonlinear unknown systems

A novel procedure for integrating neural networks (NNs) with conventional techniques is proposed to design industrial modeling and control systems for nonlinear unknown systems. In the proposed approach, a new recurrent NN with a special architecture is constructed to obtain discrete-time state-space representations of nonlinear dynamical systems. It is referred as the discrete state-space neural network (DSSNN). In the DSSNN, the outputs of the hidden layer neurons of the DSSNN represent the system's (pseudo) state. The inputs are fed to output neurons and the delayed outputs of the hidden layer neurons are fed to their inputs via adjustable weights. The discrete state space model of the actual system is directly obtained by training the DSSNN with the input–output data. A training procedure based on the back-propagation through time (BPTT) algorithm is developed. The Levenberg–Marquardt (LM) method with a trust region approach is used to update the DSSNN weights. Linear state space models enable to use well developed conventional analysis and design techniques. Thus, building a linear model of a system has primary importance in industrial applications. Thus, a suitable linearization procedure is proposed to derive the linear state space model from the nonlinear DSSNN representation. The controllability, observability and stability properties are examined. The state feedback controllers are designed with both the linear quadratic regulator (LQR) and the pole placement techniques. The regulator and servo control problems are both addressed. A full order observer is also designed to estimate the state variables. The performance of the proposed procedure is demonstrated by applying for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear control problems.     

基于并联RSO优化自抗扰的PMSM速度控制

为提高永磁同步电机调速系统的速度精度及抗干扰能力,提出一种并联降阶状态观测器优化线性自抗扰控制的方法.对传统线性扩张状态观测器进行改进,设计了降阶状态观测器.为了提升控制器在有限带宽内的抗扰动能力,设计并联型的降阶状态观测器.仿真结果表明,控制系统的速度精度和鲁棒性得到明显的提升.     

State and actuator fault estimation observer design integrated in a riderless bicycle stabilization system

This paper deals with an observer design for Linear Parameter Varying (LPV) systems with high-order time-varying parameter dependency. The proposed design, considered as the main contribution of this paper, corresponds to an observer for the estimation of the actuator fault and the system state, considering measurement noise at the system outputs. The observer gains are computed by considering the extension of linear systems theory to polynomial LPV systems, in such a way that the observer reaches the characteristics of LPV systems. As a result, the actuator fault estimation is ready to be used in a Fault Tolerant Control scheme, where the estimated state with reduced noise should be used to generate the control law. The effectiveness of the proposed methodology has been tested using a riderless bicycle model with dependency on the translational velocity v, where the control objective corresponds to the system stabilization towards the upright position despite the variation of v along the closed-loop system trajectories.     

Fractional active disturbance rejection control

A fractional active disturbance rejection control (FADRC) scheme is proposed to improve the performance of commensurate linear fractional order systems (FOS) and the robust analysis shows that the controller is also applicable to incommensurate linear FOS control. In FADRC, the traditional extended states observer (ESO) is generalized to a fractional order extended states observer (FESO) by using the fractional calculus, and the tracking differentiator plus nonlinear state error feedback are replaced by a fractional proportional-derivative controller. To simplify controller tuning, the linear bandwidth-parameterization method has been adopted. The impacts of the observer bandwidth ω_o and controller bandwidth ω_c on system performance are then analyzed. Finally, the FADRC stability and frequency-domain characteristics for linear single-input single-output FOS are analyzed. Simulation results by FADRC and ADRC on typical FOS are compared to demonstrate the superiority and effectiveness of the proposed scheme.     

自适应线性自抗扰控制器的设计

自抗扰控制器对于抑制不确定的扰动有良好的效果,但其控制器参数较多且整定困难。为了实现自适应的线性自抗扰控制器,对线性自抗扰控制器的参数整定策略展开了研究。首先,设计了基于观测误差的线性扩张观测器参数自适应整定算法。接着,设计了自抗扰控制器线性反馈环节的参数的自适应整定算法。最后,利用李雅普诺夫方法,证明上述自适应整定算法得到的参数可以保证扩张状态观测器的观测误差和被控系统最终输出误差都收敛至零。实验结果表明:精密气浮运动平台低速工况下,自适应线性自抗扰控制器的参数在0.8s内即可迅速完成整定计算;线性扩张观测器观测误差绝对值小于2nm;被控精密气浮运动平台的速度波动不大于5%。自适应线性自抗扰控制器实现了控制器参数在线整定,控制器的性能表现满足要求。     

Dissipative proportional integral observer for a class of uncertain nonlinear systems

For a class of uncertain nonlinear systems with sector-bounded nonlinearity, a proportional-integral state observer is designed in a dissipativity framework. The dissipativity ensures the bounded estimation errors against the bounded disturbance and an integral term in the observer structure can provide additional degrees of freedom in the observer design that can be used to improve the estimation performance. In this study, a dissipative condition for the proposed observer is found in terms of a linear matrix inequality (LMI). In order to specify the dissipativity, the L2 gain between the disturbance and the weighted sum of estimation errors is adopted as the supply rate in the dissipativity framework. In addition, the notion of the proposed design method is extended to the exponential dissipativity. The effectiveness of the proposed observer is demonstrated through a numerical example.     

交流电机位置伺服系统的扰动补偿控制

针对交流电机伺服系统在未知负载条件下进行准确位置控制的需求,提出了一种参数化复合控制方案。该方案建立在交流电机磁场定向矢量控制构架的基础上,以转矩电流作为控制信号(电流内环的给定值),以电机转角位置信号作为可量测的系统输出量,设计了基于极点配置的状态反馈与扰动前馈补偿组成的参数化控制律,并利用一个降阶线性扩展状态观测器对电机转速(未量测)和未知负载扰动加以估计。该控制律通过TMS320F28335DSP编程,在一台永磁同步电机伺服系统上进行了实验测试,实验结果验证了伺服系统能在未知负载情况下对各目标位置进行平稳且准确地跟踪。研究结果表明,这种基于扩展状态观测器的复合控制方案可以有效地实现交流伺服系统的高性能位置调节,且对负载幅值和模型参数差异具有较好的鲁棒性。     

一类混合时滞系统的观测器设计

对于一类具有状态和有限自动机输出时滞的离散混合系统,给出了混合观测器的设计方法。观测器由一个位置观测器和一个离散状态观测器组成。前者应用自动机观测器来确定混合系统的当前位置,后者应用龙伯格观测器对系统离散状态的演化进行估计。对于每一个独立的观测器,系统的信息往往不完全,为了在这种情况下仍能应用混合观测器对系统进行观测,在两类独立观测器的基础上给出了一个新的信号产生器,将两类观测器有机结合起来。同时给出了信号产生器中决策函数的充分条件,进一步得到了整个混合观测器指数收敛的充分条件。保证该混合观测器能在有限步内判断出系统的当前位置,同时指数收敛于真实离散时间状态。最后,给出了仿真例子说明设计方法的可行性和有效性。     

Fault Detection of continuous time linear switched systems using combination of Bond Graph method and switching observer

In this paper, a new Fault Detection (FD) scheme based on combination of switching observer and Bond Graph (BG) method for linear continuous time switched systems with Average Dwell Time (ADT) approach is proposed. The proposed scheme is a BG-based two-stage FD system in which the compact state space representation and Global Analytical Redundancy Relations (GARRs) are derived based on the BG model. In the first stage, a switched observer is designed considering disturbance attenuation level, fault sensitivity and rapid fault detection criteria by solving a weighted Linear Matrix Inequality (LMI) optimization problem. Next, a new form of GARRs which is based on output estimation error of the observer and is called Error-based Global Analytical Redundancy Relations (EGARRs) is developed to combine the observer and BG method. The output estimation errors from the observer, which are adequately sensitive to faults and simultaneously the effects of disturbances are attenuated therein, are given to the EGARRs to generate the residuals of the FD system. The proposed method may be used for fault detection of switched linear systems with ADT based on the BG model of the system. Finally, two case studies including a two-tank system and a buck converter-driven DC motor are considered to show the efficiency and real-time implementation of the proposed method.     

Input fault detection and estimation using PI observer based on the ARX-Laguerre model

This work is dedicated to the synthesis of a new fault detection and identification scheme for the actuator and/or sensor faults modeled as unknown inputs of the system. The novelty of this scheme consists in the synthesis of a new structure of proportional-integral observer (PIO) reformulated from the new linear ARX-Laguerre representation with filters on system input and output in order to estimate the unknown inputs presented as faults. The designed observer exploits the input/output measurements to reconstruct the Laguerre filter outputs where the stability and the convergence properties are ensured by using Linear Matrix Inequality. However, a significant reduction of this model is subject to an optimal choice of both Laguerre poles which is achieved by a new proposed identification approach based on a genetic algorithm. The performances of the proposed identification approach and the resulting PIO are tested on numerical simulation and validated on a 2 ^{n d} order electrical linear system.     

Observer-based reliable stabilization of uncertain linear systems subject to actuator faults,saturation, and bounded system disturbances

A matrix inequality approach is proposed to reliably stabilize a class of uncertain linear systems subject to actuator faults, saturation, and bounded system disturbances. The system states are assumed immeasurable, and a classical observer is incorporated for observation to enable state-based feedback control. Both the stability and stabilization of the closed-loop system are discussed and the closed-loop domain of attraction is estimated by an ellipsoidal invariant set. The resultant stabilization conditions in the form of matrix inequalities enable simultaneous optimization of both the observer gain and the feedback controller gain, which is realized by converting the non-convex optimization problem to an unconstrained nonlinear programming problem. The effectiveness of proposed design techniques is demonstrated through a linearized model of F-18 HARV around an operating point.     

Finite-time sliding mode controller for perturbed second-order systems

This paper presents a novel finite-time sliding mode controller applied to perturbed second order systems. The proposed scheme employs a disturbance observer that can identify growing in time disturbances. Then, the observer is combined with a sliding mode controller to achieve finite-time stabilization of the second-order system. The convergence of the observer as well as the finite-time stability of the closed-loop system is theoretically demonstrated. Besides, it is also shown that the finite-time convergence properties of a given controller can be enhanced when using a compensation term based on the disturbance observer. The proposed controller is compared with a twisting algorithm and a finite-time sliding mode controller with disturbance estimation. Also, a conventional proportional integral derivative (PID) controller is combined with the proposed disturbance observer in a trajectory tracking task. Numerical simulations indicate that the proposed controller attains finite-time stabilization of the second order system by requiring a less amount of power than that demanded by the other control schemes and without being affected by the peaking phenomenon. Besides, the performance of the PID technique is enhanced by applying the proposed control methodology.     

Observer design and stabilization for linear neutral delay systems

This paper focuses on the state observer design problem as well as the observer-based stabilization problem for linear neutral delay systems. The purpose of the former problem is to design an observer that guarantees the asymptotic stability of the estimation error dynamics. The existence condition for such an observer is established. The latter problem, which is the main problem studied in this paper, aims at designing an observer-based feedback controller, such that the closed-loop system is asymptotically stabilized. It is shown that the desired controller can be easily designed if there are solutions to several linear matrix inequalities. Finally, two simulation examples are given to demonstrate the validity and effectiveness of the proposed approach.     

三阶线性自抗扰控制器的液压伺服流量控制

针对阀控液压马达系统受非线性复杂扰动导致流量输出不稳定的问题,提出一种基于三阶线性自抗扰控制器(LADRC)的液压伺服流量控制方法。基于高阶LADRC理论,提出将ADRC应用于非线性的液压伺服系统控制,分析并验证了跟踪微分器的跟踪误差前馈增益具有抑制系统超调的作用。采用跟踪误差前馈与扩张状态观测器扰动反馈相分离的办法,提出一种针对复杂非线性三阶被控系统的改进的三阶LADRC算法。最后验证了该算法对一类大范围复杂不确定性液压伺服系统具有较PID更强的扰动抑制能力。     

Sliding mode controller with sliding perturbation observer based on gain optimization using genetic algorithm

The Stewart platform manipulator is a closed-kinematics chain robot manipulator that is capable of providing high structural rigidity and positional accuracy. However, this is a complex and nonlinear system, so the control performance of the system is not so good. In this paper, a new robust motion control algorithm is proposed. The algorithm uses partial state feedback for a class of nonlinear systems with modeling uncertainties and external disturbances. The major contribution is the design of a robust observer for the state and the perturbation of the Stewart platform, which is combined with a variable structure controller (VSC). The combination of controller and observer provides the robust routine called sliding mode control with sliding perturbation observer (SMCSPO). The optimal gains of SMCSPO, which is determined by nominal eigenvalues, are easily obtained by genetic algorithm. The proposed fitness function that evaluates the gain optimization is to put sliding function. The control performance of the proposed algorithm is evaluated by the simulation and experiment to apply to the Stewart platform. The results showed high accuracy and good performance.     

Distributed output-feedback consensus control of multi-agent systems with dynamically changing directed interaction topologies

This paper considers the distributed output-feedback consensus control problem for a multi-agent system with higher order linear dynamics and subject to external disturbance, under dynamically changing directed topologies and weighting factors. An extended state observer (ESO) is first designed to estimate not only the unmeasurable agent states but also the external disturbance. Based on the output of the ESO, a novel distributed control protocol is proposed. We show that, with the application of the proposed control protocol, the consensus can be achieved asymptotically by the group of agents if the union of the directed interaction graphs contains a spanning tree frequently enough. A numerical example is given to verify the effectiveness of the theoretical results.     

Analytical synthesis of invariant reduced-order state observers

An algorithm for the analytical synthesis of reduced-order observers for dynamic systems with an output matrix of arbitrary form is proposed, and invariance conditions for the constructed observer with respect to external disturbances are formulated. Solvability conditions for the synthesis problem are obtained in the form of a system of linear matrix equations. The proposed algorithm is based on a nondegenerate transformation of the state vector using the matrix canonization technique and methods for solving linear matrix equations of arbitrary dimension.     

Position control of a rodless cylinder in pneumatic servo with actuator saturation

In this paper, positioning control of a rodless cylinder in pneumatic servo systems with actuator saturation is investigated via an active disturbance rejection control. A linear extended state observer is designed to estimate and compensate strong friction force and other nonlinearities in the pneumatic rodless cylinder system. An actuator saturation linear feedback control law is developed to further improve the control performance. Furthermore, a linear matrix inequality-based optimization algorithm is employed to estimate a strictly invariance set for the closed-loop system. Experiment results with response time 0.5 s and accuracy 0.005 mm for a 200 mm step signal demonstrate the effectiveness of the proposed control strategy.