Robust observer-based absolute stabilization for Lur’e singularly perturbed systems with state delay

This paper is concerned with the problem of robust observer-based absolute stabilization for Lur’e singularly perturbed time-delay systems. The aim is to design a suitable observer-based feedback control law such that the resulting closed-loop system is absolutely stable. First, a full-order state observer is constructed. Based on the linear matrix inequality (LMI) technique, a delay-dependent sufficient condition is presented such that the observer error system is absolutely stable. Then, for observer-based feedback control, by introducing some slack matrices, a sufficient condition for input-to-state stability (ISS) of the closed-loop system with regard to the observer error is presented. Thus, the absolute stabilization of the closed-loop system can be guaranteed based on the ISS property. In addition, the criteria presented are both independent of the small parameter and the upper bound for the absolute stability can be obtained in a workable algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the developed methods.     

Robust absolute stability criteria for uncertain Lurie interval time-varying delay systems of neutral type

This study investigates the delay-dependent robust absolute stability analysis for uncertain Lurie systems with interval time-varying delays of neutral type. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov–Krasovskii functional (LKF) for each subinterval of delay, much less conservative delay-dependent absolute and robust stability criteria are derived. Second, a new delay-dependent robust stability condition for uncertain Lurie neutral systems with interval time-varying delays, which expressed in terms of quadratic forms of linear matrix inequalities (LMIs), and has been derived by constructing the LKF from the delayed decomposition approach (DDA) and integral inequality approach (IIA). Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.     

高精度稳定平台伺服系统的自抗扰控制

提出了一种应用于高精度稳定平台伺服系统的设计方法。为满足稳定平台快速隔离扰动、稳定视轴的要求,将自抗扰控制应用于平台系统的速度环,和常规PID控制的电流环一起构成ADRC-PID控制。Simulink仿真结果表明,与传统PID控制相比,采用自抗扰控制后系统响应速度快,隔离度有较大的提高。ADRC-PID控制可满足高精度光电稳定平台的性能要求,系统具有响应速度快,隔离度好,鲁棒性强,稳定性高等特点。     

永磁同步电机调速系统的自抗扰控制

提出了一种利用反双曲正弦函数的一阶自抗扰控制器,以提高永磁同步电机正弦波脉宽调制(SPWM)调速系统的跟踪精度。研究了永磁同步电机转速环的数学模型;分别设计了一阶跟踪微分器和二阶扩张状态观测器,利用李雅普诺夫函数分析了它们的收敛性;构造了转速环的一阶自抗扰控制器,同时证明了一阶自抗扰控制误差系统的渐近稳定性。最后,将该新型一阶自抗扰控制器作为永磁同步电机的转速调节器,分析了自抗扰控制永磁同步电机的SPWM调速系统。仿真实验表明:自抗扰控制调速系统速度阶跃跟踪的调整时间约为0.15 s,稳态误差小于0.28 r/min;同一调速系统正弦响应的最大跟踪误差约为17 r/min。与PI控制调速系统相比,自抗扰控制永磁同步电机调速系统阶跃响应快速而平稳,无超调,稳态误差小;另外,系统正弦响应的跟踪性能好,跟踪误差小。     

基于控制增益实时辨识的BLDCM自抗扰控制

自抗扰控制具有算法简单、性能优良等优点,控制增益b对控制效果的影响较大,高效稳定地在线辨识出该参数对提高控制效果具有重要意义。设计了一种基于模型参考自适应参数辨识的新型自抗扰控制器,核心参数自适应变化使该控制器拥有更好的性能,仿真结果表明参数b辨识准确并且该控制器相对于传统自抗扰控制具有更好的控制效果。     

Robust stability and performance for interval process plants

In this paper, a two-degrees-of-freedom control design methodology for interval plants to guarantee both the robust stability and performance has been considered. A simple necessary condition and sufficient condition for robust Hurwitz stability of interval polynomial has been obtained using the results of Nie [Nie YY. A new class of criterion for the stability of the polynomials. Acta Mechnica Sinica 1976;110-6] for fixed polynomials. The proposed design methodology based on the obtained necessary condition and sufficient condition is then applied to design a robust control system for a second-order unstable plant in the presence of unknown but bounded parameter uncertainties. Subsequently, a pre-filter is constructed to ensure the desired system performance. Simulation results are used to establish the efficacy of the proposed method for interval plants.     

Probabilistic robust stabilization of fractional order systems with interval uncertainty

This study investigates effects of fractional order perturbation on the robust stability of linear time invariant systems with interval uncertainty. For this propose, a probabilistic stability analysis method based on characteristic root region accommodation in the first Riemann sheet is developed for interval systems. Stability probability distribution is calculated with respect to value of fractional order. Thus, we can figure out the fractional order interval, which makes the system robust stable. Moreover, the dependence of robust stability on the fractional order perturbation is analyzed by calculating the order sensitivity of characteristic polynomials. This probabilistic approach is also used to develop a robust stabilization algorithm based on parametric perturbation strategy. We present numerical examples demonstrating utilization of stability probability distribution in robust stabilization problems of interval uncertain systems.     

Robust stability analysis of fractional order interval polynomials

The paper deals with the robust stability analysis of a Fractional Order Interval Polynomial (FOIP) family. Some new results are presented for testing the Bounded Input Bounded Output (BIBO) stability of dynamical control systems whose characteristic polynomials are fractional order polynomials with interval uncertainty structure. It is shown that the Kharitonov theorem is not applicable for this type of polynomial. A procedure is given for computation of the value set of FOIP. Based on the value set, an algorithm is presented for testing the stability of FOIP. The results presented in the paper are useful for the analysis and design of Fractional Order Interval Control Systems (FOICS). Examples are given to show how the proposed method can be used to assess the effects of parametric variations on the stability in feedback loops with fractional order interval transfer functions.     

A numerical investigation for robust stability of fractional-order uncertain systems

This study presents numerical methods for robust stability analysis of closed loop control systems with parameter uncertainty. Methods are based on scan sampling of interval characteristic polynomials from the hypercube of parameter space. Exposed-edge polynomial sampling is used to reduce the computational complexity of robust stability analysis. Computer experiments are used for demonstration of the proposed robust stability test procedures.     

Active disturbance rejection boundary control of Timoshenko beam with tip mass

In this paper, the active disturbance rejection control (ADRC) is utilized to stabilize the vibration of perturbed Timoshenko beam model with tip mass. The boundary control design is based on a hybrid PDE–ODE model, and is accompanied with designing a high-gain extended state observer (ESO) that is used to estimate the boundary disturbances. By transforming the model into the appropriate state space, the semigroup theory is employed to prove the well-posedness of the closed-loop system. To this end, it is proved by a frequency domain method that the semigroup generated by the system operator is exponentially stable, which allows to conclude the boundedness of perturbed closed-loop system response. The stability of the closed-loop system is further analyzed using the Lyapunov approach. Simulation results are presented to illustrate the efficacy of the suggested method.     

驾驶员对汽车行驶方向稳定性影响的分析方法

在驾驶员一汽车闭环系统操纵动力学模型基础上，将驾驶员参数变化范围用区间数表示，用直接优化法对非对称区间矩阵特征值问题进行求解，从系统与控制理论角度定量地揭示了驾驶员对汽车行驶方向稳定性的影响。分析结果表明，汽车行驶方向稳定性的区间分析方法可以应用于使车适合于人的汽车操纵动力学设计。     

Control design for the SISO system with the unknown order and the unknown relative degree

For the uncertain system whose order, relative degree and parameters are unknown in the control design, new research is still in need on the parameter tuning and close-loop stability. During the last 10 years, much progress is made in the application and theory research of the active disturbance rejection control (ADRC) for the uncertain system. In this study, the necessary and sufficient conditions are established for building the ADRC for the minimum-phase system and the open-loop stable system when the plant parameters, orders and relative degrees are unknown, the corresponding ideal dynamics are analyzed, and the theoretical results are verified by the simulations. Considering the wide application and the long history of the PID/PI controller, a method is given to design ADRC quickly based on the existing (generalized or conventional) PID/PI controller. A plenty of simulations are made to illustrate this PID/PI-based design method and the corresponding close-loop performances. The simulation examples include the minimum/nonminimum-phase plants, the stable/integrating plants, the high/low-order plant, and the plants with time delays. Such plants are from a wider scope than the theoretical result, and representative of many kinds of the industrial processes. That leads to a new way to simplify the ADRC design via absorbing the engineering experience in designing the PID/PI controller.     

A robust decentralized load frequency controller for interconnected power systems

A novel design of a robust decentralized load frequency control (LFC) algorithm is proposed for an inter-connected three-area power system, for the purpose of regulating area control error (ACE) in the presence of system uncertainties and external disturbances. The design is based on the concept of active disturbance rejection control (ADRC). Estimating and mitigating the total effect of various uncertainties in real time, ADRC is particularly effective against a wide range of parameter variations, model uncertainties, and large disturbances. Furthermore, with only two tuning parameters, the controller provides a simple and easy-to-use solution to complex engineering problems in practice. Here, an ADRC-based LFC solution is developed for systems with turbines of various types, such as non-reheat, reheat, and hydraulic. The simulation results verified the effectiveness of the ADRC, in comparison with an existing PI-type controller tuned via genetic algorithm linear matrix inequalities (GALMIs). The comparison results show the superiority of the proposed solution. Moreover, the stability and robustness of the closed-loop system is studied using frequency-domain analysis.     

Active disturbance rejection control based human gait tracking for lower extremity rehabilitation exoskeleton

This paper presents an active disturbance rejection control (ADRC) based strategy, which is applied to track the human gait trajectory for a lower limb rehabilitation exoskeleton. The desired human gait trajectory is derived from the Clinical Gait Analysis (CGA). In ADRC, the total external disturbance can be estimated by the extended state observer (ESO) and canceled by the designed control law. The observer bandwidth and the controller bandwidth are determined by the practical principles. We simulated the proposed methodology in MATLAB. The numerical simulation shows the tracking error comparison and the estimated errors of the extended state observer. Two experimental tests were carried out to prove the performance of the algorithm presented in this paper. The experiment results show that the proposed ADRC behaves a better performance than the regular proportional integral derivative (PID) controller. With the proposed ADRC, the rehabilitation system is capable of tracking the target gait more accurately.     

Modified active disturbance rejection control for time-delay systems

Industrial processes are typically nonlinear, time-varying and uncertain, to which active disturbance rejection control (ADRC) has been shown to be an effective solution. The control design becomes even more challenging in the presence of time delay. In this paper, a novel modification of ADRC is proposed so that good disturbance rejection is achieved while maintaining system stability. The proposed design is shown to be more effective than the standard ADRC design for time-delay systems and is also a unified solution for stable, critical stable and unstable systems with time delay. Simulation and test results show the effectiveness and practicality of the proposed design. Linear matrix inequality (LMI) based stability analysis is provided as well.     

车载光电侦察平台视轴稳定技术研究

为了进一步提高光电平台伺服控制系统的抗扰动能力,提出一种基于自抗扰控制器的改进型速度稳定回路。首先,分析了平台视轴稳定回路的数学模型并引入电流环对其进行了化简,通过伺服控制系统中扰动作用原理,引入扰动总和的思想。然后,设计含有降阶扩张状态观测器的自抗扰控制器,对扰动总和实时观测并进行线性化前馈补偿。最后,以某型车载光电平台为控制对象,进行了PI控制器与自抗扰控制器的对比实验。实验结果表明,采用自抗扰控制器伺服控制系统相比PI控制法的阶跃响应速度更快,超调幅值仅为PI控制法的26.98%。使用摇摆台引入的频率为2.5Hz的正弦扰动,系统稳态误差幅值仅为PI控制法的9.76%。在系统模型参数改变±15%范围内,自抗扰控制器仍具有良好的抗扰能力,表现出很强的鲁棒性,满足光电平台的性能要求,对提升平台抗扰能力有着较高的实用性。     

Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system

A robust fuzzy control method for fractional order hydro-turbine governing system (FOHGS) in the presence of random disturbances is investigated in this paper. Firstly, the mathematical model of FOHGS is introduced, and based on Takagi-Sugeno (T-S) fuzzy rules, the generalized T-S fuzzy model of FOHGS is presented. Secondly, based on fractional order Lyapunov stability theory, a novel T-S fuzzy control method is designed for the stability control of FOHGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed fractional order T-S fuzzy control scheme works well compared with the existing method.     

Direct energy balance based active disturbance rejection control for coal-fired power plant

The conventional direct energy balance (DEB) based PI control can fulfill the fundamental tracking requirements of the coal-fired power plant. However, it is challenging to deal with the cases when the coal quality variation is present. To this end, this paper introduces the active disturbance rejection control (ADRC) to the DEB structure, where the coal quality variation is deemed as a kind of unknown disturbance that can be estimated and mitigated promptly. Firstly, the nonlinearity of a recent power plant model is analyzed based on the gap metric, which provides guidance on how to set the pressure set-point in line with the power demand. Secondly, the approximate decoupling effect of the DEB structure is analyzed based on the relative gain analysis in frequency domain. Finally, the synthesis of the DEB based ADRC control system is carried out based on multi-objective optimization. The optimized ADRC results show that the integrated absolute error (IAE) indices of the tracking performances in both loops can be simultaneously improved, in comparison with the DEB based PI control and H_∞ control system. The regulation performance in the presence of the coal quality variation is significantly improved under the ADRC control scheme. Moreover, the robustness of the proposed strategy is shown comparable with the H_∞ control.     

一种参数不确定系统的鲁棒二次保稳定设计方法

研究了不确定线性系统的鲁棒二次保稳定设计问题。在建立的鲁棒回差方程的基础上,给出了闭环系统鲁棒二次保稳定的一个充分条件,以及增益和相位裕度描述形式。进一步还给出了相应的鲁棒二次保稳定控制系统设计方法     

Lurie型时滞系统的稳定性与镇定

研究了Lurie时滞系统的绝对稳定性问题，导出了用一个线形矩阵不等式系统的可行性表示的时滞依赖绝对稳定性判据，进而通过求解线性矩阵不等式，给出使得闭环系统绝对稳定的无记忆状态反馈控制器设计方法，最后用仿真例子验证了文中所提出的结果。