Decoupling Controller Design Based on Gain and Phase Margin Specifications for a Coupled Tank System Model

Abstract

The objective of a multi-variable control involves maintaining various control variables at independent set points. The interactions present in the system affects more than one controlled variables because of the manipulated variable. Decouplers are designed to reduce the interactions in between the loops in to achieve a satisfactory responses when there is presence of non-minimum phase zeros,multiple time delays and large uncertainty. The dynamic and static decoupling are the two types of decoupling strategies. In this thesis, these control strategies are discussed. In practice, there exists certain process unmodelled dynamics. Hence, there is a necessity to examine the robust stability of a system to check whether the control system stability is ascertained in presence of these unmodelled dynamics. This thesis deals with designing a controller along with decoupler to achieve the desired performance of a TITO system. At first, a decoupler is being designed from the plant matrix. Then, a first order plus dead time model is obtained for each of the decoupled process on the basis of the frequency response fitting. After getting the FOPDT model a decentralized PI/PID controller for each reduced order decoupled model is designed to obtain desired gain and phase margins. The present technique is applied to a coupled tank system. The characteristics like non-minimum phase and non-linear characteristics make the control of coupled tank liquid level system, a standout amongst the most difficult benchmark control problems. The main objective of the coupled tank system is to maintain a desired level of liquid in the two tanks independent of each other when the water enters the tank and when the water flows out. The coupling impact here in this framework is a coupling switch that permits stream of water in the tank at higher level to a tank at lower level. Lastly, robust stability of the control system is analyzed in the presence of various process uncertainties like additive uncertainty and multiplicative uncertainties. The stability analysis is examined using the small gain theorem or the spectral radius criterion. The robust stability of the coupled tank system is also determined.