Robust Decentralized Control Algorithms for a Multivariable Liquid Level System

Abstract

Multivariable liquid level system is featured as a benchmark control problem due to a number of control challenges involved such as nonlinearity, coupling effects arise in such system. Coupled tank system (CTS) provides an useful control application platform for verifying the effectiveness of control algorithms for a multivariable liquid level system with nonlinear and interacting dynamics that are usually encountered in almost all process industries. Control of multivariable liquid level system is a very challenging problem owing to its nonlinear, coupling and non-minimum phase behaviour. The control objectives in a multivariable liquid level system is to maintain the desired level in the individual tank while reducing coupling effects. Although a number of controller algorithms have been proposed for multivariable liquid level system, however in view of addressing control issues such as uncertainties and
disturbances, robust control algorithms need to be developed for achieving perfect level regulation in the face of uncertainties. Development of robust control algorithms necessitates accurate mathematical model of such multivariable liquid level system.
But, indeed in real-world, many physical systems are not only nonlinear but also are
highly uncertain. Hence, it is necessary that robust controller needs to be designed such that good set-point tracking and robust disturbance can be achieved. A lot of research works have been directed in the past several years to develop control strategies for a multivariable liquid level system. However, it was found that very few works have been reported for validating the developed control strategy through real-time evaluation. Most of the controllers have been designed considering (Single Input Single Output) SISO configuration of a liquid level system. Further, it is observed that very few works reported on (Multiple Input Multiple Output) MIMO configuration of liquid level system. Implementation of control algorithms for a MIMO system is more complex than a SISO system; because there exist loop interactions
among different control loops in a MIMO system. Thus, there lies an opportunity
to develop control strategies for MIMO configuration of liquid level system and implement them in real-time on an experimental setup of CTS in the laboratory.
Hence, in this thesis, it is intended to design various robust decentralized control algorithms for a multivariable liquid level system, for achieving both efficient set-point tracking performance and disturbance attenuation performances. In this thesis, all the proposed controllers are designed with two distinct control parts. The decoupling controller is exclusively employed for minimizing the coupling effects among different loops in system, and then a suitable controller is designed that takes care of SISO performance of the decoupled subsystem. In this work, a system identification approach is employed to obtain the model of the liquid level system. Further, based on the identified model, dynamic decouplers are designed. However, the dynamic decoupler comprises of large time delays. Hence, for ease in practical realization, a model reduction technique is adopted to simplify further the higher order decoupled subsystem. Then the resulting reduced order decoupled subsystems are used for robust decentralized controller design. The developed control algorithms are first implemented using Simulink and then in real-time on the physical CTS set-up to verify their efficacies.
The thesis first describes the design of robust decentralized PI controller (RDPI), by formulating the problem as frequency matching problem of a predefined reference model with the actual closed-loop system transfer function. Then, this decentralized control algorithm is synthesized using MATLAB/Simulink. Further to show the robustness of the proposed controller, _10% parametric uncertainties are incorporated in time delay, static gain and time constant in the nominal system. Then, to illustrate the effectiveness of the proposed decentralized controller, real-time experimentation is pursued on a CTS set-up. Robust stability analysis of the proposed decentralized controller is studied considering multiplicative
input and multiplicative output uncertainties. From the obtained simulation and experimental results, it is observed that the proposed controller exhibits good loop performance with adequate robustness. Although this control algorithm exhibits satisfactory performance, however, the performance of the closed-loop system depends on the accuracy of the chosen reference model. Thus, if the reference model is not precisely chosen, then the performance of the closed-loop system may be degraded. Hence, to resolve this issue, a Optimal Robust Decentralized PI (ORDPI) controller has been proposed next. In this proposed approach, nonlinear constraint optimization is performed to obtain the parameters of the proposed decentralized PI controller. From the results obtained, it is confirmed that the proposed controller maximizes the closed-loop bandwidth for specified gain margin and phase margin, with constraints on overshoot ratio to achieve both the closed-loop performance and robustness together. In this proposed controller, on imposing constraints on closed-loop amplitude ratio (PT ) and gain margin and phase margin (GPM) specification, robustness is ensured together with limits for the peak overshoot in a specified bound. The performance of the proposed ORDPI controller is verified in the simulation and then validated experimentally on the CTS experimental set-up. The obtained simulation and experimental results reveal that the proposed ORDPI controller exhibits excellent loop performance and also provide
the robust performance in the face of uncertainty.
Although this robust optimal decentralized PI controller provides good loop performance for both set-point tracking and disturbance attenuation as well as better robustness, but it is very difficult to choose an appropriate value of the upper bound of maximum amplitude ratio om _ while solving optimization. Besides this, also the performances of the above two developed decentralized controllers, i.e., robust decentralized controller and robust optimal decentralized PI controller are influenced by accurate mathematical modelling of the CTS. But in practice, to obtain an exact dynamic model of a complex multivariable liquid level system is quite difficult. Therefore, to resolve this issue, a new robust decentralized controller has been developed by employing a modifying active disturbance rejection approach (MLADRC), in which the exact mathematical model of the multivariable liquid system is not necessary. The fundamental idea behind an ideal Active Disturbance Rejection Controller (ADRC) is that, in this method, the disturbances and lumped disturbance are considered as a generalized disturbance which is estimated by using an Extended State Observer (ESO) that are cancelled out by employing the control law. In this work, the proposed controller is designed in a two degree of freedom internal model structure to overcome the limitations associated with ESO in an ideal ADRC control structure. First, this proposed Decentralized Controller based on Disturbance Rejection Control structure (DCDR) is synthesized by simulation in MATLAB and Simulink and then by real-time experimentation in CTS. Also, the robustness of this controller is pursued from the singular value plot of the modelling error and the designed controller. From the obtained results, it is confirmed that the proposed robust decentralized disturbance rejection controller exhibits excellent loop performances for both the desired set-point tracking as well as disturbance rejection.
From the obtained simulation and experimental results of all the developed robust decentralized controllers, it is observed that all the developed control algorithms exhibit robust performances for both set-point tracking and disturbance attenuation. The performances of all the developed robust decentralized controllers have been compared with each other in terms of smoothness of control signal measuring by total variance (TV) of input, Root Mean Square Tracking Error (RMSE) and also maximum sensitivity (Ms) values. From the comparative assessment, it is envisaged that the proposed Optimal Robust Decentralized PI (ORDPI) controller (ORDPI), exhibits smaller RMSE value and also good robustness as compared to the other two developed robust decentralized controllers. Moreover, the proposed Optimal Robust Decentralized PI possess a simple structure, ease in tuning and real-time implementation.