Performance index analysis of control systems synthesized for a counter-current process

Master Thesis


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University of Cape Town

Indices which quantitatively predict the ability of a particular MIMO control system design to meet certain performance objectives are discussed in this dissertation. These performance objectives include: * Input and output rejection of noise and disturbances. * Input and output insensitivity to changes in the process. * Good output regulation and minimal control effort. A counter-current heat exchanger process (simulating the carbon-in-pulp gold extraction process) has been designed and constructed. The quality of control systems synthesized for this process is gauged using these performance indices. The control of this large-scale process has been decentralized to reduce the design complexity. The strategy adopted is to regulate the process flows and levels using a cascade compensator, and then to use these setpoints as inputs to control the temperatures at various points on the heat exchange cascade standard PI-type controllers were designed for the regulation of the flow and level outputs. The outputs were regulated accurately in the presence of process disturbances, and the relatively slow level dynamics were improved considerably. Performance index analysis of control systems is achieved by observing frequency-dependent plots of the singular values of certain characteristic matrices describing the system. These matrices are obtained as ratios of the plant and controller matrices. A CAD software package has been developed to enable this type of analysis on state-space control systems with state observers. The package enables the synthesis of LQG optimal control systems and the quantitative assessment of the ability of such systems to meet their design objectives. A package has been developed to run the heat exchanger and to implement control systems for the process. Two LQG control systems were synthesized for the process in which the two flow inputs (setpoints) were used to regulate the two outlet temperature outputs. The performance of the systems were predicted quantitatively using performance indices. The systems were tested by digital simulation. Good correlation between the predicted and simulated performance was observed. One of the systems was successfully implemented on the heat exchanger process, and the controlled system revealed that the predictions made by the indices were indeed accurate. This analysis technique is a powerful indicator of the general performance of a MIMO control system. It also provides a means of analysing the frequency-dependent performance of state-space control systems. Bibliography: pages 219-223.