電漿火炬系統和離心式壓縮機之動態分析與控制設計

Abstract

本論文主要探討電漿火炬系統和離心式壓縮機的非線性現象與控制器設計。近年來，電漿火炬系統已廣泛地應用於各種的工業應用，例如：有毒廢棄物分解、電漿熔融、電漿噴塗、線電弧噴塗、電漿精鍊及奈米製程。電漿火炬系統主要是由火炬、電源供應器和空氣流量控制系統組成。由過去的研究可知，電漿火炬系統的火炬本體之物理與化學特性、電源供應器和提供氣流的壓縮機都有可能因系統內部參數值變化而發生非線性分叉現象。為了分析電漿火炬系統的動態行為，本論文應用非線性理論與分叉理論探討火炬本體與壓縮機的非線性特性。在電弧電漿的研究方面，Ghorui等人提出非線性三階振幅方程式(nonlinear third-order amplitude equation)以解釋電弧電漿的顫動現象(fluctuation phenomenon)並且利用理論分析與實驗量測發現電弧電漿的顫動現象可能為一混沌行為(Chaos)。另外，非線性振幅方程式也被用以解釋其他非線性系統的動態特性，例如：雙對流系統(double convection)、三對流系統(triple convection)等等。為了探討非線性振幅方程式的非線性行為，我們擴展三階振幅方程式以推導可能發生的靜態分叉(stationary bifurcation)與Andronov-Hopf Bifurcation之存在條件。接著，本論文利用數值模擬驗證分叉特性並延伸發現Period-Doubling和Torus bifurcation，甚至出現混沌現象。

在氣體流量控制方面，我們探討離心式壓縮機的動態特性。影響其工作穩定性的主要為壓縮機的激振現象(surge)。激振現象是指壓縮機出現流量波動之動態行為，此時的壓力差會出現一週期性振盪現象。當此非線性現象發生時，壓縮機內部溫度會升高，可能導致機械嚴重的損壞。為了避免不穩定的氣體流量影響電漿火炬系統的行為，我們應用非線性理論與分叉理論推導壓縮機發生激振的存在條件，並分析其他可能發生的動態行為。另外，本論文提供強健控制設計(robust control)與強健輸出追蹤控制(robust output tracking control)以改善離心式壓縮機的不穩定現象。在強健控制設計方面，若系統的非線性項和不確定項(uncertainty)均落於局部扇形內，則我們可利用線性控制器使系統穩定，其方法即為局部扇形非線性(local sector nonlinearity)。此控制法則可提供於實際的離心式壓縮機之激振現象改善應用。在強健輸出追蹤控制方面，我們設計線性控制器以達成系統輸出能追蹤預定的軌跡。然而，在實際應用方面，壓縮系統之部分輸出訊號可能不易擷取而導致無法狀態迴授控制。為了估測系統狀態值，本論文提出強健觀測器控制機制，由已知的輸出訊號估測無法量測到的系統狀態。因此，我們採用可變結構控制(variable structure control)觀測器以達到系統輸出可以追蹤到預定的軌跡，並且使其他系統狀態維持穩定。數值模擬的結果驗證本論文提出的控制器與觀測器設計之實用可行性。

Dynamical analysis and controller designs of the nonlinear dynamics in a plasma torch systems and centrifugal compression system are studied in this dissertation. Recently, the study of plasma technology has attracted considerable attention due to the fact that the arc plasma devices have been widely used in industrial applications. A basic plasma device is consisted of plasma torch, power supply and mass flow control system. It is known that both of the power converter and compressor might have the instability with respect to the variation of system parameter. Based on the subsystem in arc plasma device, we focus on the analysis of dynamical behavior in both the nonlinear third-order amplitude equation and centrifugal compressor. Among studies of arc plasma device, Ghorui, Sahasrabudhe, Murthy, Das and Venkatramani claimed that the inherent fluctuation appearing in arc plasma devices might be a chaotic dynamical behavior (e.g. [4]-[6]). Those studies derived the nonlinear third-order amplitude equation to describe the dynamical behavior for the arc plasma device. In this dissertation, we extend the nonlinear third-order amplitude equation to a more general case. Local bifurcation analysis for a class of the nonlinear third-order amplitude equation was employed to solve for the existence conditions of both stationary and Andronov-Hopf bifurcations. Moreover, the scenarios for the possible nonlinear behavior in the nonlinear third-order amplitude equation were also obtained with respect to the variation of system parameters via the numerical simulations, which might provide a guide for finding nonlinear phenomena in the practical application of the plasma torch.

In addition, for the analysis of surge instability in a centrifugal compressor, local bifurcation analysis is first studied for finding the existence conditions of nonlinear behavior. Due to the occurrence of bifurcated phenomena, a robust scheme was proposed to eliminate the surge phenomenon appearing in a centrifugal compressor. It is known that the surge instability in compressor might lead to reduce the operating efficiency and even damage the machinery while both of unstable compressor characteristics and compressor load torque are hard to exactly measure in the practical application. Based on the assumption of local sector nonlinearity for system dynamics, a robust control law was proposed to cover the system nonlinearity and uncertainties while guaranteeing the stability of system equilibrium. This is achieved by using the actuation of the driving torque and closed-couple valve. Numerical simulations are given to demonstrate the success of the proposed robust controller design. After that, the output tracking design for preventing the spool dynamics of a centrifugal compressor system was also presented in this dissertation. The proposed controller design not only could provide the stabilization of dynamical behavior but also regulate the system output to the desired trajectory. However, some of the state variables might also be unavailable from the signal feedback. In order to estimate the unavailable state variables, the robust observer-based control design was considered applying to the elimination of surge instability in a centrifugal compressor. Therefore, to achieve robust stabilization and observation, the output tracking control and observer were proposed via the local sector nonlinearity approach and variable structure control, respectively. Numerical simulations were obtained to verify the feasibility of output tracking design via robust observer-based control scheme.