类Chen-Qi混沌系统的固定时间自适应同步控制

类Chen-Qi四维混沌系统的渐近稳定控制的同步误差不能在有限时间内收敛到零,有限时间控制的同步误差收敛到零的状况与初值有关.因此,本文应用固定时间控制技术,设计了自适应控制器和参数估计律,试图使得驱动系统与同类型的参数未知的响应系统在固定时间内达到同步,完成了理论证明.应用数值仿真考察同步误差收敛到零的状况.选取不同参数值,不同状态初值,考察状态时程图、同步误差曲线等.结果表明:混沌运动时,固定时间内同步误差收敛到零的效果较好,与状态初值无关,收敛时间符合理论计算值;周期运动时,固定时间内前三个状态的同步误差收敛到零的效果较好,收敛时间符合理论计算值,但第四个状态的同步误差的收敛时间不符合理论计算值,其原因是系统存在的三次非线性项的不平衡、不匹配.

TCM-HIN2Vec:A strategy for uncovering biological basis of heart qi deficiency pattern based on network embedding and transcriptomic experiment

Objective:To elucidate the biological basis of the heart qi deficiency(HQD)pattern,an in-depth understanding of which is essential for improving clinical herbal therapy.Methods: We predicted and characterized HQD pattern genes using the new strategy,TCM-HIN2Vec,which involves heterogeneous network embedding and transcriptomic experiments.First,a heterogeneous network of traditional Chinese medicine(TCM)patterns was constructed using public databases.Next,we predicted HQD pattern genes using a heterogeneous network-embedding algorithm.We then analyzed the functional characteristics of HQD pattern genes using gene enrichment analysis and examined gene expression levels using RNA-seq.Finally,we identified TCM herbs that demonstrated enriched interactions with HQD pattern genes via herbal enrichment analysis.Results: Our TCM-HIN2Vec strategy revealed that candidate genes associated with HQD pattern were significantly enriched in energy metabolism,signal transduction pathways,and immune processes.Moreover,we found that these candidate genes were significantly differentially expressed in the transcriptional profile of mice model with heart failure with a qi deficiency pattern.Furthermore,herbal enrichment analysis identified TCM herbs that demonstrated enriched interactions with the top 10 candidate genes and could potentially serve as drug candidates for treating HQD.Conclusion: Our results suggested that TCM-HIN2Vec is capable of not only accurately identifying HQD pattern genes,but also deciphering the basis of HQD pattern.Furthermore our finding indicated that TCM-HIN2Vec may be further expanded to develop other patterns,leading to a new approach aimed at elucidating general TCM patterns and developing precision medicine.

Exploring the therapeutic potential of Qi Teng Mai Ning recipe in ischemic stroke and vascular cognitive impairment

Background:This study aims to explore the therapeutic effects of the Qi Teng Mai Ning recipe on ischemic stroke and vascular cognitive impairment through its potential to modulate cellular autophagy,with a focus on identifying its active ingredients and their target proteins.Methods:The study began with the identification of active ingredients in the Qi Teng Mai Ning recipe.It proceeded to screen the gene expression omnibus database for ischemic stroke and vascular cognitive impairment-associated differentially expressed mRNAs and to identify cellular autophagy-related proteins via the Human Autophagy Database.These proteins were annotated with Gene Ontology and Kyoto Encyclopedia of Genes and Genomes functions and subjected to molecular docking with the recipe’s core active ingredients.In vitro cell experiments were conducted on hypoxic HT22 cells,involving CCK8 assay,lentiviral transfection to silence autophagy related 9B(ATG9B),immunofluorescence staining,and qPCR validation to investigate the effects of the recipe on autophagy.Results:The analysis identified 104 active ingredients targeting 408 proteins and forming a complex ingredient-target network.Intersecting 55 ischemic stroke-related and 909 vascular cognitive impairment-related differentially expressed mRNAs revealed 14 co-expressed mRNAs.Molecular docking showed quercetin,kaempferol,myrcene,and conferone as key ingredients targeting autophagy-related proteins.Cellular experiments indicated that the recipe significantly enhanced cell viability under hypoxic conditions,reduced apoptosis,and modulated the expression of autophagy-related factors,thereby decreasing apoptosis rates in HT22 cells.Conclusion:The Qi Teng Mai Ning recipe offers protective effects against ischemic stroke and vascular cognitive impairment by modulating autophagy-related proteins.Its efficacy highlights the potential of traditional Chinese medicine in treating these conditions,though further research is needed to fully understand its mechanisms and clinical applications.

The Essential Role of Zheng Qi in Promoting Health: From the Perspective of Chinese Medicine and Modern Medicine

The concept of Zheng Qi in traditional Chinese medicine (TCM) refers to the vital energy produced by the interaction of Yin and Yang forces in the body. Zheng Qi performs two main functions: Wei Qi (defensive Qi), which shields the body from external pathogens, and Ying Qi (nutritive Qi), which sustains the internal organs and enhances their functionality. In TCM, Chinese tonifying herbs can help restore the balance of Yin/Yang and Qi/Blood function in visceral organs (i.e., optimal physiological functions), thereby fostering the efficient production of Zheng Qi and enhancing health. To ensure the quality of Chinese herbal products, functional assays to measure Yin/Yang, Qi/Blood functions, and Zheng Qi production should be implemented. The efficacy of Yang and Qi herbs can be evaluated by their ability to increase mitochondrial ATP in cultured mouse cardiomyocytes, while Yin and Blood herbs are tested through their immunostimulatory effects on antigen-induced T/B cell proliferation in mouse splenocytes and the production of erythropoietin/nitric oxide in hepatocytes/vascular endothelial cells, respectively. Additionally, Zheng Qi’s effect can be gauged by examining natural killer cell activity and antigen-induced T/B cell proliferation in mice ex vivo. These assays act as biomarkers for assessing the quality and effectiveness of herbal health products within TCM theory.

Network pharmacology-based exploration of molecular mechanisms underlying therapeutic effects of Jianpi Huatan Quyu recipe on chronic heart failure with spleen Qi deficiency syndrome

BACKGROUND Chronic heart failure is a complex clinical syndrome.The Chinese herbal compound preparation Jianpi Huatan Quyu recipe has been used to treat chronic heart failure;however,the underlying molecular mechanism is still not clear.AIM To identify the effective active ingredients of Jianpi Huatan Quyu recipe and explore its molecular mechanism in the treatment of chronic heart failure.METHODS The effective active ingredients of eight herbs composing Jianpi Huatan Quyu recipe were identified using the Traditional Chinese Medicine Systems Pharmacology Database and Analysis Platform.The target genes of chronic heart failure were searched in the Genecards database.The target proteins of active ingredients were mapped to chronic heart failure target genes to obtain the common drugdisease targets,which were then used to construct a key chemical componenttarget network using Cytoscape 3.7.2 software.The protein-protein interaction network was constructed using the String database.Gene Ontology and Kyoto Encyclopedia of Genes and Genomes enrichment analyses were performed through the Metascape database.Finally,our previously published relevant articles were searched to verify the results obtained via network pharmacology.RESULTS A total of 227 effective active ingredients for Jianpi Huatan Quyu recipe were identified,of which quercetin,kaempferol,7-methoxy-2-methyl isoflavone,formononetin,and isorhamnetin may be key active ingredients and involved in the therapeutic effects of TCM by acting on STAT3,MAPK3,AKT1,JUN,MAPK1,TP53,TNF,HSP90AA1,p65,MAPK8,MAPK14,IL6,EGFR,EDN1,FOS,and other proteins.The pathways identified by KEGG enrichment analysis include pathways in cancer,IL-17 signaling pathway,PI3K-Akt signaling pathway,HIF-1 signaling pathway,calcium signaling pathway,cAMP signaling pathway,NF-kappaB signaling pathway,AMPK signaling pathway,etc.Previous studies on Jianpi Huatan Quyu recipe suggested that this Chinese compound preparation can regulate the TNF-α,IL-6,MAPK,cAMP,and AMPK pathways to affect the mitochondrial structure of myocardial cells,oxidative stress,and energy metabolism,thus achieving the therapeutic effects on chronic heart failure.CONCLUSION The Chinese medicine compound preparation Jianpi Huatan Quyu recipe exerts therapeutic effects on chronic heart failure possibly by influencing the mitochondrial structure of cardiomyocytes,oxidative stress,energy metabolism,and other processes.Future studies are warranted to investigate the role of the IL-17 signaling pathway,PI3K-Akt signaling pathway,HIF-1 signaling pathway,and other pathways in mediating the therapeutic effects of Jianpi Huatan Quyu recipe on chronic heart failure.

Pharmacological Investigation on the Qi-Invigorating Action of Schisandrin B: Effects on Mitochondrial ATP Generation in Multiple Tissues and Innate/Adaptive Immunity in Mice

Schisandrae Fructus, containing schisandrin B (Sch B) as its main active component, is recognized in traditional Chinese medicine (TCM) for its Qi-invigorating properties in the five visceral organs. Our laboratory has shown that the Qi-invigorating action of Chinese tonifying herbs is linked to increased mitochondrial ATP generation and an enhancement in mitochondrial glutathione redox status. To explore whether Sch B can exert Qi-invigorating actions across various tissues, we investigated the effects of Sch B treatment on mitochondrial ATP generation and glutathione redox status in multiple mouse tissues ex vivo. In line with TCM theory, which posits that Zheng Qi generation relies on the Qi function of the visceral organs, we also examined Sch B’s impact on natural killer cell activity and antigen-induced splenocyte proliferation, both serving as indirect measures of Zheng Qi. Our findings revealed that Sch B treatment consistently enhanced mitochondrial ATP generation and improved mitochondrial glutathione redox status in mouse tissues. This boost in mitochondrial function was associated with stimulated innate and adaptive immune responses, marked by increased natural killer cell activity and antigen-induced T/B cell proliferation, potentially through the increased generation of Zheng Qi.

Clinical Observation of the Hot and Humid Compress Therapy of Traditional Chinese Medicine in the Treatment of Qi Stagnation and Blood Stasis Type of Lumbar Disc Herniation

Background: Although a number of studies have reported that the hot and humid compress from traditional Chinese medicine (TCM) is effective in treating lumbar disc herniation (LDH) with qi stagnation and blood stasis, clinical evidence is limited. Objective: The purpose of this study is to provide high-quality evidence to support the effectiveness of the traditional Chinese hot and humid compress in the treatment of LDH with qi stagnation and blood stasis. Methods: From October 2021 to November 2023, 86 patients with LDH of qi stagnation and blood stasis type were recruited in our hospital and divided into a control (n = 43) and an observation group (n = 43) according to the random number table method. The control group was given routine clinical treatment, and the observation group was treated with the hot and humid compress therapy for two weeks. The visual analogue scale (VAS) score, Japanese Orthopaedic Association (JOA) score, TCM syndrome score, serum interleukin-6 (IL-6), serum interleukin-1β (IL-1β), and tumor necrosis factor-α (TNF-α) were observed and compared between the two groups before and after treatment, and the clinical efficacy of the two groups was evaluated. Results: After treatment, the VAS score, TCM symptom score, and serum IL-6, IL-1β, and TNF-α levels decreased in both groups (P P P P P Conclusions: The hot and humid compress of traditional Chinese medicine can effectively relieve pain, restore lumbar function, improve TCM syndromes, reduce the level of inflammatory factors, and have a curative effect in treating LDH.

Observation on the Nursing Effect of Ginger Moxibustion on Gastrointestinal Symptoms in Patients with Heart Failure Due to Yang Qi Deficiency

Objective:To evaluate the nursing measures and effects of ginger moxibustion in the treatment of heart failure(yang qi deficiency type)with gastrointestinal symptoms.Methods:86 patients with heart failure(yang qi deficiency type)accompanied by gastrointestinal symptoms who were admitted to the hospital between January 2023 and January 2024 were selected and divided into 43 cases in each group by random number table grouping;Group I implemented integrated care,while Group II adopted conventional care.The indicators of care were compared between the two groups.Results:After the nursing care,the digestive symptom scores of Group I were lower than those of Group I,and the psychological scores were lower than those of Group II(P<0.05).Conclusion:Ginger moxibustion can improve gastrointestinal symptoms and enhance the psychological health of patients with heart failure(yang qi deficiency type)with gastrointestinal symptoms.

Exploring the Effect of Qi Cross-Shaped Moxibustion on the Recovery of Gastrointestinal Function after Hip Fracture in the Elderly

Objective:To explore the effect of Qi cross-shaped moxibustion on the recovery of gastrointestinal function in elderly hip fracture patients after surgery.Methods:62 elderly hip fracture surgery patients were selected as the base analysis sample,enrolled in January 2023-May 2024,and divided into an observation group(n=31)and a control group(n=31)using the digital table random draw scheme.The patients in the control group underwent conventional dietary intervention,and the patients in the observation group underwent Qi cross-shaped moxibustion intervention,comparing the gastrointestinal function recovery time and quality of life scores(PAC-QOL)of patients with constipation between the two groups.Results:The gastrointestinal function recovery time of the observation group was lower than that of the control group(P<0.05);the PAC-QOL score of the observation group was lower than that of the control group after the intervention(P<0.05).Conclusion:Qi cross-shaped moxibustion can shorten the recovery time of gastrointestinal function and improve the quality of life of elderly hip fracture patients after surgery,and it has the value of promotion and application.

A study on the treatment of chloasma with moxibustion based on the theory of“Yang transforming Qi,and Yin shaping”

Background:“Yang Transforming Qi and Yin shaping”comes from“Plain Question Yin and Yang should be like the theory”.Chinese medicine believes that the imbalance of yin and yang is the cause of human diseases.One of the strengths of TCM in treating diseases is holistic regulation.The theory of“Yang transforming Qi,and Yin shaping”implies a strong holistic view.Chloasma,one of the common skin diseases,seriously affects the physical and mental health of patients due to its unclear etiology,difficult treatment and easy recurrence.The occurrence and development of chloasma are closely related to internal organs.This paper is based on the theory of internal meridian,“Yang transforming Qi,and Yin shaping”which attaches importance to the concept of“Yang Qi”,from a new understanding of the pathogenesis etiology of chloasma.Methods:The author believes that the incidence of the disease is the deficiency of Yang Qi,which can’t promote the movement of Qi and blood to nourish the face,resulting in tangible material condensation,so proposes that this disease needs to be promoted by Yang transforming Qi and warm to dissipate.Moxibustion belongs to the fire,and its warming effect can dissipate the tangible evil.Results:Combined with clinical practice and the theory of internal meridian,the author elaborated that moxibustion is one of the effective methods for treating chloasma,which provides a new way of thinking for the treatment of chloasma.Conclusion:“Yang Transforming Qi and Yin shaping”can be used to guide the treatment of chloasma.

Optimal timing for the oral administration of DaCheng-Qi decoction based on the pharmacokinetic and pharmacodynamic targeting of the pancreas in rats with acute pancreatitis

AIM To identify the optimal oral dosing time of Da-Cheng-Qi decoction(DCQD) in rats with acute pancreatitis(AP) based on the pharmacokinetic and pharmacodynamic parameters.METHODS First, 24 male Sprague-Dawley rats were divided into a sham-operated group [NG(a)] and three model groups [4 h G(a), 12 h G(a) and 24 h G(a)]. The NG(a) and model groups were administered DCQD(10 g/kg.BW) intragastrically at 4 h, 4 h, 12 h and 24 h, respectively, after AP models induced by 3% sodium taurocholate. Plasma samples were collected from the tails at 10 min, 20 min, 40 min, 1 h, 2 h, 4 h, 8 h, 12 h and 24 h after a single dosing with DCQD. Plasma and pancreatic tissue concentrations of the major components of DCQD were determined by high-performance liquid chromatography tandem mass spectroscopy. The pharmacokinetic parameters and serum amylase were detected and compared. Second, rats were divided into a sham-operated group [NG(b)] and three treatment groups [4 h G(b), 12 h G(b) and 24 h G(b)] with three corresponding control groups [MG(b)s]. Blood and pancreatic tissues were collected 24 h after a single dosing with DCQD. Serum amylase, inflammatory cytokines and pathological scores of pancreatic tissues were detected and compared.RESULTS The concentrations of emodin, naringin, honokiol, naringenin, aloe-emodin, chrysophanol and rheochrysidin in the 12 h G(a) group were higher than those in the 4 h G(a) group in the pancreatic tissues(P < 0.05). The area under the plasma concentration-time curve from time 0 to the time of the last measurable concentration values(AUC0→t) for rhein, chrysophanol, magnolol and naringin in the 12 h G(a) group were larger than those in the 4 h G(a) or 24 h G(a) groups. The 12 h G(a) group had a higher Cmax than the other two model groups. The IL-10 levels in the 12 h G(b) and 24 h G(b) groups were higher than in the MG(b)s(96.55 ± 7.84 vs 77.46 ± 7.42, 251.22 ± 16.15 vs 99.72 ± 4.7 respectively, P < 0.05), while in the 24 h G(b) group, the IL-10 level was higher than in the other two treatment groups(251.22 ± 16.15 vs 154.41 ± 12.09/96.55 ± 7.84, P < 0.05). The IL-6 levels displayed a decrease in the 4 h G(b) and 12 h G(b) groups compared to theMG(b)s(89.99 ± 4.61 vs 147.91 ± 4.36, 90.82 ± 5.34 vs 171.44 ± 13.43, P < 0.05). CONCLUSION Late-time dosing may have higher concentrations of the most major components of DCQD, with better pharmacokinetics and pharmacodynamics of antiinflammation than early-time dosing, which showed the late time to be the optimal dosing time of DCQD for AP.

Clinical Observation of the Therapeutic Effects of Wenzhong Hewei Formula in Treating Spleen and Stomach Qi Deficiency Syndrome in Internal Medicine Diseases

Objective:To observe the clinical efficacy and safety of Wenzhong Hewei Formula in treating spleen and stomach qi deficiency syndrome in internal medicine diseases.Methods:Sixty patients with spleen and stomach qi deficiency syndrome admitted to the hospital from April 2022 to June 2023 were randomly divided into observation and control groups,with 30 patients in each group.The control group received conventional internal medicine treatment,while the observation group was additionally treated with Wenzhong Hewei Formula on the basis of conventional treatment.Both groups were treated for 4 weeks.Results:The total effective rate of treatment in the observation group was higher than that of the control group(P<0.05).After treatment,the traditional Chinese medicine syndrome scores of both groups were significantly lower than before treatment,with the observation group showing a more pronounced reduction(P<0.05).There was no statistically significant difference in the incidence of adverse reactions between the two groups(P>0.05).Conclusion:Wenzhong Hewei Formula can effectively improve clinical symptoms in patients with spleen and stomach qi deficiency syndrome,enhance clinical efficacy,and have a high level of safety,making it worthy of clinical promotion.

Integration of 1H-NMR-Based Metabolomics Approach with Traditional Chinese Pulse Diagnosis to Evaluate the Qi-Enhancing Activity of Herbal Tea

Human metabolism is intricately linked to an individual’s health status. Regardless of living habits, it will be reflected in the metabolic characteristics of urine. The utilization of the 1H NMR-based metabolomics method has enabled examine the metabolomic changes in urine under various physiology conditions, providing valuable insights into metabolites. In this particular study, volunteers were divided into two groups based on the strength of their spleen pulses, using the pulse diagnosis method employed in traditional Chinese medicine. Subsequently, their urine samples were analyzed, revealing notable variances in urea, creatinine, citric acid, succinic acid, trimethylamine-N-oxide (TMAO), alanine, hippuric acid, and glycine between the two groups. Interestingly, individuals with weak spleen pulses showed significant improvements after consuming herbal tea. Furthermore, we conducted LC-MS analysis on herbal tea and performed adenosine triphosphate (ATP) activity tests on the C2C12 mouse skeletal muscle cell line. The results indicated that within a reasonable concentration range, exposure to herbal tea led to an increase in the mitochondrial ATP production capacity of C2C12 cells. These findings shed light on the relationship between traditional Chinese medicine pulse diagnosis and urine metabolites, highlighting their potential as non-invasive and straightforward health assessment indicators. They can aid in the preliminary determination of necessary dietary and lifestyle changes to enhance overall bodily health.

扶阳罐治疗尿毒症维持性血液透析患者不安腿综合征的效果及对PSQI评分的影响

目的探析尿毒症维持性血液透析患者不安腿综合征采用扶阳罐治疗的效果。方法选取2021年7月—2023年12月在本院住院并进行规律维持性血液透析的尿毒症患者60例为研究对象,并将患者随机分为试验组(n=30)和对照组(n=30)。其中,对照组采取常规治疗,试验组加用扶阳罐治疗,比较两组治疗效果、临床症状积分、RLS评分、PSQI评分。结果试验组治疗有效率高于对照组,组间差异有统计学意义(P<0.05)。干预前,两组临床症状积分比较差异无统计学意义(P>0.05);干预后,试验组临床症状积分(下肢酸胀、下肢麻木、下肢灼烧感、下肢蚁行感、下肢瘙痒、下肢刺痛)低于对照组,组间差异有统计学意义(P<0.05)。干预后,试验组RLS评分、PSQI评分低于对照组,组间差异有统计学意义(P<0.05)。结论扶阳罐治疗尿毒症维持性血液透析患者不安腿综合征的效果明显,其临床症状显著缓解,患者的睡眠质量提升,临床上可借鉴及推广。

Qi系统的Hopf分叉分析与幅值控制

通过非线性状态反馈,不改变Hopf分叉点,实现对四维Qi系统极限环的幅值控制.推导出Qi系统在第一类非零平衡点上产生Hopf分叉的条件,绘制第一类平衡点的分叉图.采用washout filter非线性控制律,利用中心流形定理对受控系统降维,得到极限环的幅值与控制增益之间的近似解析式.通过数值模拟以及幅值解析解与数值解的比较,验证幅值预测的正确性与控制的有效性.

过滤精度对煤焦油QI的组成和结构的影响

采用精度为2~5μm和20~40μm的滤芯分别对煤焦油进行热过滤,从得到的滤渣中提取出喹啉不溶物(QI)。然后利用元素分析(EA)、激光粒度仪(LPSA)、扫描电子显微镜/X射线能量色散光谱(SEM/EDS)、傅里叶红外光谱(FT-IR)、X射线衍射仪(XRD)、X射线光电子能谱(XPS)等对所得煤焦油QI组分进行对比分析。结果表明:煤焦油QI组分芳构化程度高,有机物多为稠环类物质并带有很多侧链或杂质原子,同时存在少量石英石、方解石以及煤灰等无机物;当煤焦油热过滤时采用的滤芯精度较低时,最终提取出的QI组分缩聚度相对较高,并且稠环结构中所含侧链和杂原子也相对较少。经精度较低的滤芯热过滤后提取的QI组分中金属杂原子含量相对较高,这些金属杂原子主要存在于大颗粒无机物中,部分存在于小颗粒有机物中。当滤芯精度较高时所得QI组分中主要含酚类、醚类和羧酸类有机物,酮类含量相对较少;反之,QI中则主要含酚类、醚类和酮类有机物。因此,煤焦油热过滤所选的滤芯精度不宜过高,尤其不宜选精度在5μm以下的滤芯。

建立结点上弧－弧拓扑关系的Qi算法

建立结点上弧－弧拓扑关系的Ｑｉ算法齐华，刘文熙（成都西南交通大学，６１００３１）１引言在地理信息系统中，“自动生成多边形拓扑关系”是一个使用频率很高的过程。如何优化算法来提高这个过程的时间效率是一个十分有意义的问题。对于这个过程的研究引起了学者们的关...

基于Qi算法的Delaunay三角网逐点插入法

Delaunay三角网在很多领域都有着广泛的应用,快速高效地生成Delaunay三角网十分重要。逐点插入法是构建Delaunay三角网中使用最广泛的方法之一。本文深入研究了使用逐点插入法构建不带约束条件Delaunay三角网的过程。在使用该方法生成Delaunay三角网中建立结点拓扑关系这一影响构网效率的关键步骤中引入了Qi算法,简化了该方法生成Delaunay三角网的复杂度。然后在向Delaunay三角网内插入约束边的过程中,再次引入Qi算法,从而提高了构网的效率。为了验证上述模型,我们在Microsoft Visual Studio 2005开发环境下,以C#为开发工具,采用底层开发模式实现了改进的逐点插入法,实验证明引入Qi算法能够提高逐点插入法Delaunay三角网构建及插入约束边的效率。

煤沥青中原生QI性质分析

利用元素分析、红外光谱、激光粒度仪、原子发射光谱仪等分析手段对攀钢中温煤沥青的原生QI进行了结构组成分析。结果表明,原生QI粒径90%以上小于2μm,为无定型的微晶乱堆结构,其灰分质量分数达到5.8%。元素分析和红外光谱分析表明,QI有机成分主要为高度缩合的炭黑状物质,金属分析表明无机成分主要由耐火材料粉屑和铁件的氧化物构成。这为原生QI的脱除提供了科学依据。

规范形Qi系统的Hopf分岔分析及控制

文章研究了一个Qi系统的Hopf分岔控制问题.根据计算的极限环曲率系数,判定原系统的Hopf分岔类型,并采用washout滤波器控制该系统的分岔行为.首先讨论了控制器的线性增益对Hopf分岔点位置的影响,然后引入规范形计算方法,求出受控系统的Hopf分岔规范形.分析了规范形中系数对控制参数的选择原则所产生之影响,以及对Hopf分岔类型及极限环幅值的影响.理论和仿真结果表明,控制器的线性增益能使原系统的Hopf分岔点延迟或消失,而非线性增益能则改变极限环的稳定性和极限环幅值的大小.最后把washout滤波器和线性控制器的控制效果作了对比,发现washout滤波器比之线性控制器具有一定的优势.