時滯分?jǐn)?shù)階微積分若干理論及其在水輪機調(diào)節(jié)系統(tǒng)中應(yīng)用
發(fā)布時間：2019-07-08 20:31
【摘要】：水輪機調(diào)節(jié)系統(tǒng)由壓力引水管道、水輪發(fā)電機機組、液壓調(diào)速系統(tǒng)和發(fā)電機端口側(cè)電力負(fù)荷組成,是一個集水機電磁為一體的非線性控制系統(tǒng)。生產(chǎn)實踐表明,液壓隨動系統(tǒng)具有時延性,水輪機傳遞系數(shù)隨機組工況變化表現(xiàn)時變性,并且發(fā)電機端口側(cè)電力負(fù)荷存在隨機擾動。上述因素的存在不僅威脅著水輪機調(diào)節(jié)系統(tǒng)的穩(wěn)定可靠運行,而且難以保證電網(wǎng)系統(tǒng)的供電質(zhì)量。鑒于此,非常有必要對系統(tǒng)的不穩(wěn)定性因素進(jìn)行考慮來建立系統(tǒng)的非線性數(shù)學(xué)模型,進(jìn)而探究系統(tǒng)保持穩(wěn)定運行的充分條件。本畢業(yè)論文通過將時滯引入液壓隨動系統(tǒng)、將分?jǐn)?shù)階微積分非線性理論引入壓力引水管道系統(tǒng),建立了一個較符合工程實際的水輪機調(diào)節(jié)系統(tǒng)非線性動力學(xué)模型。此外,研究了一類時滯分?jǐn)?shù)階非線性系統(tǒng)解的存在性和唯一性定理、系統(tǒng)有限時間穩(wěn)定和漸進(jìn)穩(wěn)定的充分條件。論文主要內(nèi)容和結(jié)論如下:(1)研究系統(tǒng)穩(wěn)定性的最基本條件是要保證系統(tǒng)解的存在性和唯一性。將水輪機調(diào)節(jié)系統(tǒng)數(shù)學(xué)模型歸納為一類時滯分?jǐn)?shù)階非線性系統(tǒng),利用分?jǐn)?shù)階微積分性質(zhì)和廣義Gronwall不等式,給出該類系統(tǒng)解存在的充分必要條件以及系統(tǒng)存在唯一解的充分條件,并推導(dǎo)系統(tǒng)解的預(yù)估計值。(2)運用拉普拉斯變換、Mittag-Leffler函數(shù)及其性質(zhì),給出時滯分?jǐn)?shù)階非線性系統(tǒng)滿足有限時間穩(wěn)定的充分條件,即當(dāng)系統(tǒng)滿足該條件時,不論系統(tǒng)初始狀態(tài)如何,該系統(tǒng)總能在有限時間內(nèi)趨于穩(wěn)定狀態(tài)。通過數(shù)值仿真,驗證所得穩(wěn)定性理論的有效性。(3)研究一類離散時滯分?jǐn)?shù)階非線性系統(tǒng)滿足漸進(jìn)穩(wěn)定的充分條件,并將其與已有的穩(wěn)定性理論進(jìn)行比較,得出本定理的優(yōu)越性;進(jìn)而,給定兩個三維混沌非線性系統(tǒng),應(yīng)用本定理使其滿足漸近穩(wěn)定條件,驗證所推理論。(4)在壓力引水管道為復(fù)雜管系情況下,將分?jǐn)?shù)階微積分理論引入壓力引水管道系統(tǒng),建立分?jǐn)?shù)階復(fù)雜管系混流式水輪機調(diào)節(jié)系統(tǒng)的非線性數(shù)學(xué)模型。利用分?jǐn)?shù)階非線性系統(tǒng)穩(wěn)定性定理,我們給出隨分?jǐn)?shù)階階次變化時系統(tǒng)分岔點的變化規(guī)律;同時,詳盡分析系統(tǒng)穩(wěn)定域隨分?jǐn)?shù)階階次的變化情況。通過分?jǐn)?shù)階分岔圖、時域圖、相軌跡圖、龐加萊映射圖、功率譜圖以及頻譜圖,系統(tǒng)地分析不同階次下系統(tǒng)的具體動力學(xué)行為,從而得出機組振動情況。(5)考慮到液壓隨動系統(tǒng)主配壓閥死區(qū)造成接力器靜止不動,以及接力器活塞速度響應(yīng)滯后等因素,將時滯引入液壓隨動系統(tǒng),建立時滯分?jǐn)?shù)階非線性動態(tài)模型。進(jìn)而利用改進(jìn)的ABM(Admas-Bashforth-Moulton)算法,基于MATLAB進(jìn)行數(shù)值仿真,結(jié)合統(tǒng)計物理學(xué)原理,研究系統(tǒng)在時滯和分?jǐn)?shù)階共同作用下的穩(wěn)定域變化趨勢。本論文雖然對水輪機調(diào)節(jié)系統(tǒng)的穩(wěn)定性特征進(jìn)行了一定研究,也給出了一類離散時滯分?jǐn)?shù)階非線性系統(tǒng)的有限時間穩(wěn)定性定理和漸近穩(wěn)定性定理,但將該定理應(yīng)用在水輪機調(diào)節(jié)系統(tǒng)中以控制系統(tǒng)的動態(tài)特征使其保持穩(wěn)定尚需繼續(xù)研究。
文內(nèi)圖片：
圖片說明：技術(shù)路線圖 1
[Abstract]:The water turbine regulating system is composed of a pressure water diversion pipe, a hydro-generator unit, a hydraulic speed regulating system and a generator port side power load, and is a non-linear control system integrated with the water machine. The production practice shows that the hydraulic follow-up system has the time ductility, the transfer coefficient of the water turbine is modified with the change of the working condition of the unit, and there is a random disturbance on the power load on the side of the generator port. The existence of the above factors not only threatens the stable and reliable operation of the turbine regulation system, but also makes it difficult to guarantee the power supply quality of the power grid system. In view of this, it is necessary to consider the unstable factors of the system to establish the nonlinear mathematical model of the system, and then to explore the sufficient conditions for the stable operation of the system. In this thesis, by introducing the time-delay into the hydraulic follow-up system, the nonlinear theory of the fractional-order calculus is introduced into the pressure-diversion pipe system, and a non-linear dynamic model of the turbine governing system is established. In addition, the existence and uniqueness theorems of solutions of a class of time-delay fractional-order nonlinear systems are studied, and the sufficient conditions of the system's finite-time stability and asymptotic stability are given. The main contents and conclusions are as follows: (1) The most basic condition of the system stability is to ensure the existence and uniqueness of the system solution. The mathematical model of the hydraulic turbine governing system is generalized to a class of time-delay fractional-order nonlinear systems, and the sufficient and necessary conditions for the existence of the system and the sufficient conditions for the existence of the system are given by using the fractional-order calculus and the generalized Gronwall inequality, and the pre-estimated value of the system solution is derived. (2) Using the Laplace transform, the Mittag-Leffler function and its properties, a sufficient condition for the time-delay order nonlinear system to satisfy the finite-time stability is given, that is, when the system satisfies this condition, the system can always be stable in a limited time, regardless of the initial state of the system. The validity of the stability theory is verified by numerical simulation. (3) The sufficient conditions for a class of discrete time-delay fractional-order nonlinear systems to satisfy the asymptotic stability are studied, and compared with the existing stability theory, the advantage of this theorem is obtained. This theorem is applied to satisfy the asymptotic stability conditions and to verify the theory of push. (4) Under the condition of complex piping, the fractional calculus theory is introduced into the pressure water diversion pipe system, and the nonlinear mathematical model of the mixed-flow turbine governing system of the fractional-order complex piping system is established. Using the stability theorem of fractional order nonlinear system, we give the rule of the bifurcation point of the system as the order of the fractional order is changed, and the variation of the system stability field with the order of the fractional order is analyzed in detail. The dynamic behavior of the system under different orders is systematically analyzed by the fractional-order bifurcation diagram, the time-domain diagram, the phase trace diagram, the Pincare map, the power spectrum diagram and the frequency spectrum graph, so as to obtain the vibration condition of the unit. (5) Considering that the dead zone of the main pressure valve of the hydraulic follow-up system causes the servomotor to be stationary, and the speed response of the servomotor piston is lagging and other factors, the time-delay is introduced into the hydraulic follow-up system, and the nonlinear dynamic model with the time-delay order is established. In this paper, the modified ABM (Admas-Bashar-Moulton) algorithm is used to simulate the numerical simulation based on MATLAB, and the variation trend of stability of the system under the common action of time-delay and fractional order is studied in combination with the principle of statistical physics. In this paper, the stability characteristics of the turbine governing system are studied, and the finite-time stability theorem and the asymptotic stability theorem of a class of discrete time-delay fractional-order nonlinear systems are also given. However, the application of this theorem in the water turbine regulation system to keep the stability of the control system remains to be studied.
【學(xué)位授予單位】：西北農(nóng)林科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TV734
本文編號：2511855
文內(nèi)圖片：
圖片說明：技術(shù)路線圖 1
[Abstract]:The water turbine regulating system is composed of a pressure water diversion pipe, a hydro-generator unit, a hydraulic speed regulating system and a generator port side power load, and is a non-linear control system integrated with the water machine. The production practice shows that the hydraulic follow-up system has the time ductility, the transfer coefficient of the water turbine is modified with the change of the working condition of the unit, and there is a random disturbance on the power load on the side of the generator port. The existence of the above factors not only threatens the stable and reliable operation of the turbine regulation system, but also makes it difficult to guarantee the power supply quality of the power grid system. In view of this, it is necessary to consider the unstable factors of the system to establish the nonlinear mathematical model of the system, and then to explore the sufficient conditions for the stable operation of the system. In this thesis, by introducing the time-delay into the hydraulic follow-up system, the nonlinear theory of the fractional-order calculus is introduced into the pressure-diversion pipe system, and a non-linear dynamic model of the turbine governing system is established. In addition, the existence and uniqueness theorems of solutions of a class of time-delay fractional-order nonlinear systems are studied, and the sufficient conditions of the system's finite-time stability and asymptotic stability are given. The main contents and conclusions are as follows: (1) The most basic condition of the system stability is to ensure the existence and uniqueness of the system solution. The mathematical model of the hydraulic turbine governing system is generalized to a class of time-delay fractional-order nonlinear systems, and the sufficient and necessary conditions for the existence of the system and the sufficient conditions for the existence of the system are given by using the fractional-order calculus and the generalized Gronwall inequality, and the pre-estimated value of the system solution is derived. (2) Using the Laplace transform, the Mittag-Leffler function and its properties, a sufficient condition for the time-delay order nonlinear system to satisfy the finite-time stability is given, that is, when the system satisfies this condition, the system can always be stable in a limited time, regardless of the initial state of the system. The validity of the stability theory is verified by numerical simulation. (3) The sufficient conditions for a class of discrete time-delay fractional-order nonlinear systems to satisfy the asymptotic stability are studied, and compared with the existing stability theory, the advantage of this theorem is obtained. This theorem is applied to satisfy the asymptotic stability conditions and to verify the theory of push. (4) Under the condition of complex piping, the fractional calculus theory is introduced into the pressure water diversion pipe system, and the nonlinear mathematical model of the mixed-flow turbine governing system of the fractional-order complex piping system is established. Using the stability theorem of fractional order nonlinear system, we give the rule of the bifurcation point of the system as the order of the fractional order is changed, and the variation of the system stability field with the order of the fractional order is analyzed in detail. The dynamic behavior of the system under different orders is systematically analyzed by the fractional-order bifurcation diagram, the time-domain diagram, the phase trace diagram, the Pincare map, the power spectrum diagram and the frequency spectrum graph, so as to obtain the vibration condition of the unit. (5) Considering that the dead zone of the main pressure valve of the hydraulic follow-up system causes the servomotor to be stationary, and the speed response of the servomotor piston is lagging and other factors, the time-delay is introduced into the hydraulic follow-up system, and the nonlinear dynamic model with the time-delay order is established. In this paper, the modified ABM (Admas-Bashar-Moulton) algorithm is used to simulate the numerical simulation based on MATLAB, and the variation trend of stability of the system under the common action of time-delay and fractional order is studied in combination with the principle of statistical physics. In this paper, the stability characteristics of the turbine governing system are studied, and the finite-time stability theorem and the asymptotic stability theorem of a class of discrete time-delay fractional-order nonlinear systems are also given. However, the application of this theorem in the water turbine regulation system to keep the stability of the control system remains to be studied.
【學(xué)位授予單位】：西北農(nóng)林科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TV734
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