| Summary: | 碩士 === 臺灣大學 === 化學工程學研究所 === 98 === ABSTRACT
Some of industrial chemical processes are open loop unstable. The unstable process can behave either as a runaway or growing oscillation response. Recent studies shown that the simple models which can represent those open loop behaviors are
FODUP (First Order Delay Unstable Processes)
SODUP (Second Order Delay Unstable Processes)
For unstable open loop process, the feedback is an essential feature to stabilize the process. This makes the model based controller which have been recognized as a powerful method for controller design can not be implemented easily. This is due to the requirement to guarantee the internal stability. This fact has attracted many researchers to study and modify the implementation of model based controller (i.e. Internal Model Controller or Smith predictor).
The other study is to reveal the fundamental limitation and important characteristic of control system containing unstable process. The important characteristic such as the stabilizability of a particular process by PID controller or its special cases, the lower and upper bound of PID tuning parameters to stabilize the process, etc. That information is particularly useful to get insight the controllability of the process prior to the controller design. These control abilities can be studied in the frequency or time domain. The recent study reveals the lower bound of the overshoot for these two process model controlled by a unity feedback subjected to the step input. Since then, many control structure which can be regarded as two degree of freedom controller has been proposed to improve the control performance.
This thesis begins from a literature survey on control system design for unstable open loop processes. The published literature will be categorized into three parts:
1. The stabilizability condition by PID controller,
2. PID controller design and
3. Advanced control system design.
This survey can describe the research direction which has been developed in this area. In the first part of this thesis, we propose the PID predictive controller which is related to the PIMC (Partial Internal Model Controller, Wang et.al). The feature of the proposed control structure can virtually remove the RHP zero to the outside of feedback loop. Therefore the main PID controller can be designed regardless of the RHP zero. This control structure can be implemented either for unstable or stable process. Thus, it generalizes the original predictor proposed by Iinoya and Altpeter. In the second part of this thesis, we derive the desired closed loop response which has optimal performance for step input either from set point or input disturbance. From this, the corresponding PID controller is designed by utilizing MacLaurin series to approximate the ideal controller which posses the optimal performance. Then, we compare with some of recently proposed controller design. This step is an essential for designing a stabilizing controller. And then, due to the performance limitation of 1 DOF (i.e. there is a lower bound on the overshoot of step set point tracking response), the set point weighting PID controller is used to improve the performance. Thus, the set point weighting parameter is derived based on the IMC principle. As have been mentioned, the behavior of unstable process can be shown as a runaway or growing oscillation response. It has been well known that the runaway process is essentially due to the existence of real positive eigenvalue. On the other hand, the growing oscillation comes from a pair of complex conjugate positive eigenvalue. Based on this basic knowledge, it is natural to make question regarding the fundamental different between those two in case of controllability, stabilizability and controller design. Therefore, we study those issues for a process contains time delay and a pair of RHP complex conjugate poles. The desired closed loop response, its corresponding controller and its difficulty is investigated and solved. In the last part of this thesis, we will investigate the multiloop controller design when the system has transmission RHP pole(s). The design method will be based on its effective open loop transfer function. By using the desired closed loop response developed in the previous section, the controller design for system is broken down into designing n-single loop system and treat the mismatch of the benchmark as a model uncertainty.
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