Generalized-Extended-State-Observer and Equivalent-Input-Disturbance Methods for Active Disturbance Rejection: Deep Observation and Comparison

Active disturbance-rejection methods are effective in estimating and rejecting disturbances in both transient and steady-state responses. This paper presents a deep observation on and a comparison between two of those methods: the generalized extended-state observer (GESO) and the equivalent input disturbance (EID) from assumptions, system configurations, stability conditions, system design, disturbance-rejection performance, and extensibility. A time-domain index is introduced to assess the disturbance-rejection performance. A detailed observation of disturbance-suppression mechanisms reveals the superiority of the EID approach over the GESO method. A comparison between these two methods shows that assumptions on disturbances are more practical and the adjustment of disturbance-rejection performance is easier for the EID approach than for the GESO method.      

Compensation for state‐dependent nonlinearity in a modified repetitive control system

This paper presents an estimation and compensation of state‐dependent nonlinearity for a modified repetitive control system. It is based on the equivalent‐input‐disturbance (EID) approach. The nonlinearity is estimated by an EID estimator and compensated by incorporation of the estimate into the repetitive control input. A two‐dimensional model of the EID‐based modified repetitive control system is established that enables the preferential adjustment of control and learning actions by means of 2 tuning parameters. The singular‐value‐decomposition technique and Lyapunov stability theory are used to derive a linear‐matrix‐inequality–based asymptotic stability condition. Exploiting the stability condition and an overall performance evaluation index, a design algorithm is developed. Simulation results for the tracking control of a chuck‐workpiece system show that the method not only compensates state‐dependent nonlinearity but also improves the tracking performance for the periodic reference input, thereby demonstrating the validity of the method.     

Generalized extended state observer–based repetitive control for systems with mismatched disturbances

A generalized extended state observer (GESO) is devised to improve the disturbances rejection performance in a repetitive‐control system (RCS) for a class of single‐input, single‐output nonlinear plants with nonintegral chain form and mismatched disturbances. By appropriately choosing a disturbance compensation gain and incorporating the disturbance estimate into a repetitive control law, a GESO‐based RCS is established. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of the disturbance compensation into the control input enables attenuating the lumped disturbance from the system output. Stability criteria and design algorithms have been developed for the system. A case study on the speed control of a rotational control system exhibits that the GESO‐based RCS delivers not only a promising disturbance rejection performance but also a superior property of tracking performance.     

Active Disturbance Rejection in Affine Nonlinear Systems Based on Equivalent‐Input‐Disturbance Approach

This paper presents a disturbance rejection method for an affine nonlinear system. The control system is constructed based on the equivalent‐input‐disturbance (EID) approach. An affine nonlinear state observer is used to reconstruct the state of the affine nonlinear system and to estimate an EID. The well‐known differential mean value theorem enables us to describe the closed‐loop system in the state space as a linear‐parameter‐varying system. This makes it easy to derive sufficient conditions of global uniform ultimate boundedness in term of linear matrix inequalities (LMIs) by using a Lyapunov function and convexity theory. Controllers are designed based on the LMIs. A numerical example is used to illustrate the design of the control system. And a comparison between the EID‐based control and the sliding‐mode control demonstrates the effectiveness and advantages of the EID‐based control method.     

Low dimensional disturbance observer‐based control for nonlinear parabolic PDE systems with spatio‐temporal disturbances

In this paper, a design problem of low dimensional disturbance observer‐based control (DOBC) is considered for a class of nonlinear parabolic partial differential equation (PDE) systems with the spatio‐temporal disturbance modeled by an infinite dimensional exosystem of parabolic PDE. Motivated by the fact that the dominant structure of the parabolic PDE is usually characterized by a finite number of degrees of freedom, the modal decomposition method is initially applied to both the PDE system and the PDE exosystem to derive a low dimensional slow system and a low dimensional slow exosystem, which accurately capture the dominant dynamics of the PDE system and the PDE exosystem, respectively. Then, the definition of input‐to‐state stability for the PDE system with the spatio‐temporal disturbance is given to formulate the design objective. Subsequently, based on the derived slow system and slow exosystem, a low dimensional disturbance observer (DO) is constructed to estimate the state of the slow exosystem, and then a low dimensional DOBC is given to compensate the effect of the slow exosystem in order to reject approximately the spatio‐temporal disturbance. Then, a design method of low dimensional DOBC is developed in terms of linear matrix inequality to guarantee that not only the closed‐loop slow system is exponentially stable in the presence of the slow exosystem but also the closed‐loop PDE system is input‐to‐state stable in the presence of the spatio‐temporal disturbance. Finally, simulation results on the control of temperature profile for catalytic rod demonstrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Torque tracking control of electric load simulator with active motion disturbance and nonlinearity based on T‐S fuzzy model

This paper develops a high performance nonlinear control method for an electric load simulator (ELS). The tracking performance of the ELS is mainly affected by the actuator's active motion disturbance and friction nonlinearity. First, a nonlinear model of ELS is developed, and then the Takagi‐Sugeno fuzzy model is used to represent the friction nonlinearity ofthe ELS. A state observer is constructed to estimate the speed of the load system. For converting the tracking control into a stabilization problem, a new control design called virtual desired state synthesis is proposed to define the internal desired states. External disturbances are attenuated based on an H_∞ criterion and the stability of the entire closed‐loop model is investigated using the well‐known quadratic Lyapunov function. Meanwhile, the feedback gains and the observer gains are obtained separately by solving a set of linear matrix inequalities (LMIs). Both a simulation and experiment were performed to validate the effectiveness of the developed algorithm.     

Output‐based disturbance rejection control for 1‐D anti‐stable Schrödinger equation with boundary input matched unknown disturbance

In this paper, we are concerned with the output feedback control design for a system (plant) described by a boundary controlled anti‐stable one‐dimensional Schrödinger equation. Our output measure signals are the displacements at both side. An untraditional infinite‐dimensional disturbance estimator is developed to estimate the disturbance. Based on the estimator, we propose a state observer that is exponentially convergent to the original system and then design a stabilizing control law consisting of two parts: The first part is to compensate the disturbance by using its approximated value and the second part is to stabilize the observer system by applying the classical backstepping approach. The resulting closed‐loop system is shown to be exponentially stable with guaranteeing that all internal systems are uniformly bounded. An effective output‐based disturbance rejection control algorithm is concluded. An application, namely, a cascade of ODE–wave systems, is investigated by the developed control algorithm. Numerical experiments are carried out to illustrate the effectiveness of the proposed control law. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust H∞ control of uncertain singular systems based on equivalent‐input‐disturbance approach

In this paper, a robust H_∞ control problem is considered for an uncertain singular system. An active disturbance rejection method called equivalent input disturbance (EID) is used to reduce the influence of exogenous disturbances and uncertainties on the system. At the first, there exists an EID, which can produces the same effect on the system as disturbances and uncertainties do in the control channel according to the EID concept. Then, an EID estimator is constructed to estimate the influence of EID on the system. Finally, based on Lyapunov stability theory, a static output feedback‐based robust H_∞ controller combined with EID estimate is designed, guaranteeing that closed‐loop system is admissible (regular, impulse‐free, and stable) with a prescribed H_∞ performance level. Compared with traditional H_∞ control method, H_∞ control based on EID method improve the control performance of the system. A numerical example demonstrates the validity of the method.     

Trajectory tracking control for manned submersible system with disturbances via disturbance characterization index approach

This paper investigates a novel disturbance estimation and characterization‐based robust control scheme of the manned submersible in the presence of external disturbances and model uncertainties. First of all, a finite‐time disturbance observer is designed to estimate the lumped disturbances of the manned submersible system. Then, a novel disturbance characterization index is defined via Lyapunov theory to indicate whether the lumped disturbances harm or benefit the manned submersible system. The control law is developed via the disturbance characterization–based backstepping control (DCB‐BC) method to remove the detrimental disturbances and to keep the beneficial disturbances of the manned submersible. Additionally, the rigorous stability analysis is given based on Lyapunov theory. Furthermore, some simulation results verify the effectiveness of the proposed DCB‐BC method. The key novelty of this paper is that the disturbances are explicitly used in the controller design to achieve better control performance and disturbance rejection capability.     

多星发射上面级主动抗扰姿态控制技术研究

针对多星发射的运载火箭上面级在入轨段由于卫星分离产生的质量偏移,从而引起的三轴姿态严重耦合问题展开了研究,提出了基于广义扩张状态观测器的改进预测函数控制姿态控制方法.该控制方法将质心偏移造成上面级结构参数偏差和引入的干扰力矩以及其他未知系统参数偏差、外界扰动和未建模动态视为集总扰动,并将该非匹配干扰通过等效输入扰动技术转换为匹配干扰,由广义扩张状态观测器对变化后的系统状态和未知集总扰动同时观测.将集总扰动在反馈回路予以补偿保证了预测模型与上面级真实动力学模型有较高匹配度,进一步保证预测函数控制有较高的控制跟踪精度和较快的响应速度,并对外界扰动和参数偏差有较强的鲁棒性.文中算例仿真和性能对比验证了该方法的有效性及可行性.