Abstract:
The passivity-based interaction measure is studied in this special research project with objective of controller design and analysis. Case study processes consists of, 1). Process system with time delay is a matrix transfer function which has time delay term in off-diagonal elements, 2). Process system with RHP zeros is high-purity distillation column, and 3). Process with large interaction is the process of furnace which operates with 4 burners and 4 heating coils. The studies obtain their passivity-based interaction, optimum controller, and closed-loop stability of system. The passivity-based interaction measure can be used to predict the stability of decentralized control systems and to evaluate their performance loss. The steady state value of this measure provides a sufficient condition for offset free decentralize control. The optimum controllers are designed by H? synthesis procedure. The case studies are analyzed the stability of closed-loop system after implementing the optimum controllers by Nyquist stability criterion for multi-loop system. The simulation results of passivity-based interaction measure of all case studies at steady state are less than unity therefore the proposed controllers can be designed to achieve the offset free specification. Then, the Simulink models are developed to investigate the closed-loop responses. These closed-loop responses of all case studies with the optimum controller show that the controllers reach the setpoint without any offset and can reject disturbances from interaction between the loops very well even some oscillates occurred. Furthermore, Kalman filer algorithm is implemented to the models to reduce this closed-loop oscillation. In the system with time delay, setpoints are stepped from 1 to 2. The time for achieving the new setpoint is 25 seconds for optimum controller and 2 seconds for optimum controller with Kalman filter. The setpoints of system with RHP zeros are increased from 0.7 to 0.9. The optimum controller itself manipulates the system to reach the new setpoint with in 800 seconds while the settling time for the one attached with Kalman filter is only 30 seconds. The settling times for changing setpoint of system with large interaction from 150 to 200 ?C are 2.5 seconds and 25 seconds for optimum controller with and without Kalman filter, respectively. The closed-loop responses of all case studies after implementing Kalman filter have less oscillation and achieve the setpoint faster.