Unified Control Theory from PID to ACPID

To address the challenge of achieving unified control across diverse nonlinear systems, a comprehensive control theory spanning from PID (Proportional-Integral-Derivative) to ACPID (Auto-Coupling PID) has been proposed. The primary concept is to unify all intricate factors, including internal dynamics and external bounded disturbance, into a single total disturbance. This enables the mapping of various nonlinear systems onto a linear disturbance system. Based on the theory of PID control and the characteristic equation of a critically damping system, Zeng’s stabilization rules (ZSR) and an ACPID control force based on a single speed factor have been designed. ACPID control theory is both simple and practical, with significant scientific significance and application value in the field of control engineering.

Impact of spatially varying rock disturbance on rock slope stability

Degradation of rock mass produced by rock blasting,stress relief,and other causes is an important factor in the assessment of rock strength.Quantified as a disturbance factor,such degradation varies depending on blasting control,stress state and stress relief,and rock mass quality.This study focuses on the impact of disturbance on the safety of slopes.The disturbance in the rock mass is characterized by the geometry of the disturbed zone,its size,the magnitude,and the decaying rate with the distance away from the slope surface.A method accounting for decay of rock disturbance is presented.A study of the impact of rock disturbance characteristics on the quantitative stability measures of slopes was carried out.These characteristics included disturbed zone geometry,its thickness,the maximum magnitude of the disturbance factor,and the rate of disturbance decaying.The thickness of the disturbed zone and the maximum factor of disturbance were found to have the greatest impact.For example,the factor of safety for a 45slope in low-quality rock mass can decrease from 1.96 to 1.09 as the thickness of the disturbed zone increases from 1/4 of slope height H to the double of H and the maximum disturbance factor increases from 0.5 to 1.Uniform thickness of a disturbed zone was found to yield more conservative outcomes than the triangular zones did.The critical failure surfaces were found to be shallow for high rates of disturbance decay,and they were the deepest for spatially uniform disturbance factors.

A combination of climate,tree diversity and local human disturbance determine the stability of dry Afromontane forests

Background:Anthropogenic disturbances are increasingly affecting the vitality of tropical dry forests.The future condition of this important biome will depend on its capability to resist and recover from these disturbances.So far,the temporal stability of dryland forests is rarely studied,even though identifying the important factors associated with the stability of the dryland forests could serve as a basis for forest management and restoration.Methodology:In a degraded dry Afromontane forest in northern Ethiopia,we explored remote sensing derived indicators of forest stability,using MODIS satellite derived NDVI time series from 2001 to 2018.Resilience and resistance were measured using the anomalies(remainders)after time series decomposition into seasonality,trend and remainder components.Growth stability was calculated using the integral of the undecomposed NDVI data.These NDVI derived stability indicators were then related to environmental factors of climate,topography,soil,tree species diversity,and local human disturbance,obtained from a systematic grid of field inventory plots,using boosted regression trees in R.Results:Resilience and resistance were adequately predicted by these factors with an R^(2) of 0.67 and 0.48,respectively,but the model for growth stability was weaker.Precipitation of the wettest month,distance from settlements and slope were the most important factors associated with resilience,explaining 51%of the effect.Altitude,temperature seasonality and humus accumulation were the significant factors associated with the resistance of the forest,explaining 61%of the overall effect.A positive effect of tree diversity on resilience was also important,except that the impact of species evenness declined above a threshold value of 0.70,indicating that perfect evenness reduced the resilience of the forest.Precipitation of the wettest month was the most important factor explaining 43.52%of the growth stability variation.Conclusion:A combination of climate,topographic factors and local human disturbance controlled the stability of the dry forest.Also tree diversity is an important stability component that should be considered in the management and restoration programs of such degraded forests.If local disturbances are alleviated the recovery time of dryland forests could be shortened,which is vital to maintain the ecosystem services these forests provide to local communities and global climate change.

Practical Stability Analysis and Synthesis of Linear Descriptor Systems with Disturbances

This paper considers the problems of practical stability analysis and synthesis of linear descriptor systems subject to timevarying and norm-bounded exogenous disturbances. A sufficient condition for the systems to be regular, impulsive-free and practically stable is derived. Then the synthesis problem is addressed and a state feedback controller is designed. To deal with the computational issue, the conditions of the main results are converted into linear matrix inequality （LMI） feasibility problems. Furthermore, two optimization algorithms are formulated to improve the system performances. Finally, numerical examples are given to illustrate the obtained results.

THE STABILITY UNDER DISTURBANCES FROM THE HULL H（f） AND ALMOST PERIODIC SOLUTION

In this paper, We investigate the almost periodic systems (1)and(2) where g(t,x) ∈H(f). By using the inherited property of Liapunov function, under the suitable conditions, we prove that the bounded solution of (1 ) and (2) are stable under disturbances from H(f) with respect to the compact set. From this, we obtain some theorems of the existence of the almost periodic solutions for systems (1) and (2).

Robust Control Based on Feedback Linearization for Roll Stabilizing of Autonomous Underwater Vehicle Under Wave Disturbances

In the case of Autonomous Underwater Vehicle （AUV） navigating with low speed near water surface, a new method for design of roll motion controller is proposed in order to restrain wave disturbance effectively and improve roll stabilizing performance. Robust control is applied, which is based on uncertain nonlinear horizontal motion model of AUV and the principle of zero speed fin stabilizer. Feedback linearization approach is used to transform the complex nonlinear system into a comparatively simple linear system. For parameter uncertainty of motion model, the controller is designed with mixed-sensitivity method based on H-infinity robust control theory. Simulation results show better robustness improved by this control method for roll stabilizing of AUV navigating near water surface.

Influence of a liquid-filled compartment structure on the incoming shaped charge jet stability

Liquid-filled compartment structure consists of a bulk steel plate with matrix blind holes which are filled with liquid and a steel front plate to seal up the liquid with rings and bolts.The liquid-filled compartment structure can resist the shaped charge warhead effectively.This paper presents experimental and theoretical investigations of the penetration ability of the residual shaped charge jet emerging from the liquid-filled compartment structure after the penetration process at different impact angles.On the basis of shock wave propagation theory,the influence of the liquid-filled compartment structure on jet stability is analysed.The interferences of the liquid backflow caused by a reflected shock wave and a back plate on jet stability under different impact angles are also examined.In addition,the range of the disturbed velocity segments of the jet at different impact angles and the penetration ability of the residual jet are obtained.A theoretical model is validated against the experimental penetration depths.

Numerical modeling for the coupled thermo-mechanical processes and spalling phenomena in sp Pillar Stability Experiment (APSE)

In this paper, the coupled thermo-mechanical （TM） processes in the AEspoe Pillar Stability Experiment （APSE） carried out by the Swedish Nuclear Fuel and Waste Management Company （SKB） were simulated using both continuum and discontinuum based numerical methods. Two-dimensional （2D） and three- dimensional （3D） finite element method （FEM） and 2D distinct element method （DEM） with particles were used. The main objective for the large scale in situ experiment is to investigate the yielding strength of crystalline rock and the formation of the excavation disturbed/damaged zone （EDZ） during excavation of two boreholes, pressurizing of one of the boreholes and heating. For the DEM simulations, the heat flow algorithm was newly introduced into the original code. The calculated stress, displacement and temperature distributions were compared with the ones obtained from in situ measurements and FEM simulations. A parametric study for initial microcracks was also performed to reproduce the spalling phenomena observed in the APSE.

DISTURBANCES TO A ROTATING FLUID WITH A SPHEREMOVING ALONG THE AXIS OF ROTATION

In this paper, the disturbances to a uniformly rotating ideal fluid with a sphere moving steadily along the axis of rotation are analysed by using linearization theory, the equations of disturbance pressure and disturbance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric. The equation of disturbance stream function is analysed with the method of normal modes, and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral disturbances are obtained. The conclusion is drawn that there are three kinds of possible forms of neutral disturbances.

Some Aspects of the Characteristics of Monsoon Disturbances Using a Combined Barotropic－Baroclinic Model

A standing Rossby wave of wavelength 30°longitude with a finite amplitude along the meridional direction is superimposed on the zonal mean component of the monsoon flow and the stability of such a flow is examined by a quasi-geostrophic barotropic.as well as by a quasi-geostrophic combined barotropic and baroclinic model on a beta plane centered at 18°N latitude. It is found that the growth of synoptic scale disturbance increases with the amplitude of the meridional wind. The barotropic stability analysis at 700 hPa pressure level shows that there is a critical value (Umaz=11 m/s) of the maximum mean zonal wind below which the computed disturbance moves to the west due to the wave-wave superposition. For maximum mean zonal wind greater that 11m /s, the westerly wind dominates and the disturbance moves to the east. In another analysis the stability of the zonally asymmetric basic now is studied with a combined barotropic-barotropic model where cumulus heating is included. The growth rate, intensity, horizontal scale and the westward velocity of computed disturbances reasonably agree with those of observed monsoon disturbances. The fastest growing mode has a horizontal wavelength of 2000 kms and the e-folding time is about 3 days,when the meridional amplitude of the Rossby wave is 4m/ s at 700 hPa pressure level. When cumulus heating is included in the analysis the intensity of geopotential perturbation at 700 hPa disturbance is -304 m2 / s2. Energy calculations show that the kinetic energy of the mean zonal flow is the main source of energy for the perturbation to grow.It is also t'ound that the contribution of the kinetic energy of the basic Rossby wave to the growth of perturbation is more in comparison to the available potential energy.

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.

Stability and Robustness Analysis of an Adaptive Algorithm for Quasi-periodic Disturbances Rejection

Winding and web transport systems are subjected to quasi-periodic disturbances of the web tension due to the eccentricity and the non-circularity of the reel and rolls. The disturbances induced by the non-circularity and eccentricity of the rolls are quasi-periodic with a frequency that varies with their rotation speed. An adaptive method of rejection of these disturbances is proposed in this paper. It is based on a phase-locked loop structure that estimates simutaneously the phase and magnitude of the perturbation and then cancels it. This algorithm can be plugged in an existing industrial controller. The stability and robustness of the algorithm are also discussed. The ability of the algorithm to reject quasi-periodic disturbances with slowly varying frequencies is shown through simulation results.

Disk Stability of the Milky Way Near the Sun

By solving Poisson's equation for logarithmic density disturbance in three-dimensional (3D) spiral galaxies, the disturbed potential can be given on the disk. Combining it with the corresponding dispersion relation, the local gravitational stability of our galaxy is discussed here. We have generalized the Toomre's stability criterion to the more realistic 3D galaxy models. The generalized Toomre's parameter Q near the sun is 2.08 or 2.20 for two or four armed spiral galaxy models, respectively.

STABILITY OF THE BURGERS SHOCK WAVE

This paper considers the stability of the Burgers shock wave solution with respect to infinitesimal disturbance. It is found that the Burgers shock wave is asymptotically stable in the Liapunov sense.

Error reachable set based stabilization of switched linear systems with bounded peak disturbances

This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.

并网逆变器非线性特性建模及稳定性研究综述

并网逆变器作为连接新能源分布式发电和电网之间的关键接口,发挥着将电能高效、高质量馈入电网的重要作用。随着新能源渗透率的持续提高,并网点处电网存在诸如高电网阻抗、丰富的低频谐波、电压幅值/频率波动甚至故障等复杂状况。鉴于并网逆变器本质上是一个多输入、强耦合的非线性系统,沿用传统的线性建模与分析方法已难以解释工程中的复杂谐波振荡现象,并网逆变器的稳定性分析及其稳定运行受到巨大挑战。为此,该文首先具体阐述了线性与非线性和系统受扰大小之间的关系,指出大干扰稳定性分析更依赖于非线性建模及分析方法的应用。在此基础上,对已见诸报道的并网逆变器稳定性分析方法进行了归纳和对比。然后,详细阐述了稳定性分析方法在并网逆变器特定非线性环节中的应用。最后,总结并讨论了现有研究的不足,以期进一步促进“双高”背景下并网装置非线性建模和稳定性分析的研究。

线性自抗扰控制系统的稳定性分析方法

针对二阶线性系统和二阶线性自抗扰控制,提出了基于误差的稳定性分析方法。该方法通过观测误差、跟踪误差状态量建立闭环系统状态空间模型,借助状态空间模型的特征值分析闭环系统的收敛性,并运用李雅普诺夫法判断系统的稳定性。与基于劳斯判据的稳定性分析方法相比较,二者的分析结论一致,算例和仿真结果验证了所提方法的简单性和有效性。此外,通过仿真和蒙特卡洛实验验证了自抗扰控制相比于PID控制在跟踪性能、抗扰能力和鲁棒性等方面的优势。

四旋翼无人机改进自抗扰姿态控制

针对四旋翼无人机姿态控制过程中模型不确定及外部扰动问题,设计了一种自抗扰控制的姿态控制器。将模糊控制方法与传统的自抗扰控制理论相结合,增加了一个集模糊化、模糊推理和清晰化为一体的模糊控制单元,采用改进天牛须算法整定自抗扰控制器参数,提高了参数整定效率。为解决fal函数拐点处不平滑,易产生小幅抖振以及误差较大时系统增益较大等问题,引入了改进的yfal函数替代扩张状态观测器中的fal函数,并对改进后的状态观测器进行了收敛性判断。仿真结果表明,改进后的自抗扰控制器具有更快的响应速度和抗干扰能力。