| Summary: | 博士 === 國立成功大學 === 化學工程學系碩博士班 === 90 === Abstract
Although a large variety of chemical processes contain rather complex or even nonlinear dynamics, linear models are often applied to describe their dynamics. Therefore, researches on the modeling and control of linear systems continually attract much attention. Using a linear model to describe nonlinear dynamics is justified if the system’s dynamic behavior in the vicinity of a specific equilibrium point is of prime interest. In the limited range of operating conditions, such linear models can still satisfy most requirements for prediction and control.
In this dissertation, a time-weighted integral transform is first presented to identify a linear continuous parametric model based on a single experimental test under open-loop or closed-loop operation. The resulting moving-horizon algorithm can arrive at unbiased estimates of the model parameters in the presence of noise. An effective technique is also developed to determine the model order and time delay from observed data in a simple manner. Furthermore, the proposed identification method can be easily applied as a model reduction technique that results in an ideal model with delay for any specified order. By selecting a suitable weighting function in the transform, the method does not require knowledge about initial and final states of the signals and hence allows the use of any interval and any state of data for identification. Consequently, the operation of a dynamic test is greatly simplified.
A novel method is then presented to identify a linear discrete parametric model under open-loop or closed-loop operation in a noisy environment. The order and time delay of the system are assumed unknown a priori. A time-weighted digital filter is introduced to convert the sampled data of input-output measurements over different sets of time horizons to a group of algebraic equations. The model parameters are then estimated by the moving horizon least-squares algorithm in a recursive fashion. An effective technique is also proposed to infer the model order and time delay from the observed data. In contrast with the conventional least-squares approach, the proposed method is able to yield unbiased parameter estimates despite the nature of noise. Furthermore, it is robust with respect to model structure mismatch and the selection of sampling period. The proposed estimator converges very rapidly to the true parameter values. This implies that the method does not require a long run to collect a large amount of data.
With a discrete parametric model, a method is developed to design a discrete-time general-structure controller the order of which is determined by the process model order. Through the modified internal model control and dominant pole placement algorithms, the direct design is achievable by specifying one to three readily understandable parameters. Simple-structure controllers with user-specified orders can then be derived based on ingenious approximations of the general-structure controller design. For example, a low-order proportional-integral- derivative and a high-order controller are obtainable in the same fashion. Furthermore, with a newly developed index for stability robustness, a procedure is presented to optimize the controller designs of various structures. It is concluded that the resultant simple-structure controllers are vastly superior to the general-structure controller in almost all respects. The method is demonstrated with a wide range of process dynamics including time delay, right-half-plane and left-half-plane zeros, low- to high-order lags, integrators, and unstable poles.
Many real processes are characterized by sophisticated or even nonlinear dynamics. The exact description demands a tedious procedure to establish a mathematical model theoretically by taking into account all nonlinear properties. In general, it is extremely difficult to understand various nonlinear dynamics by the direct use of the original nonlinear model. Furthermore, bifurcation theorem indicates that linear effects would vanish in the vicinity of singular points and nonlinear effects would dominant the dynamic behavior. In this work, a model reduction technique is developed based on bifurcation theorem to deal with the analysis of the nonlinear system effectively. The technique reduces the original nonlinear model to a simple normal form by applying center manifold projection and normal form theorem. The final normal form contains only the necessary resonance terms, which suffice to obtain the complete phase portrait and nonlinear dynamics in the vicinity of a singular point. The technique is applied to a proportional control system of two continuous stirred tank reactors with recycle connected in series. Linear stability boundaries are found and corresponding generic singular points are located for further investigation.
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