Four-tank System Research Articles

Fault Diagnosis in Hybrid Systems using Possible Conflicts

Hybrid systems, whose behavior exhibit continuous and discrete event dynamics, are present in many industrial environments. The complexity of such behavior makes the online fault diagnosis task very challenging. In this work we propose an accurate and timely online fault diagnosis approach for hybrid systems. Our approach uses the Hybrid Bond Graph modeling methodology to avoid the precompilation of all possible modes in the system. Structural decomposition of Hybrid Bond Graph models, obtained by means of Possible Conflicts, together with its implementation using Block Diagrams, allows the diagnosis system be quickly reconfigured when a mode change occurs. Moreover, this diagnosis approach has the ability to track the behavior of the system during the transitory states caused by mode changes. Diagnosis results using a four-tank system demonstrate the capabilities of the proposal.

Model Predictive Control Design for a Nonlinear Four-Tank System

In recent years, especially in industrial processes, model predictive control has become a prominent advanced control technique. In this paper a nonlinear plant is considered to be controlled by linear model predictive control. Particularly this study is carried out on the Four-Tank system to show the performance of linear model predictive control for nonlinear plant. Since linear model predictive control is used instead of nonlinear model predictive control the problems of complexity of the algorithm and non-convexity of the optimization are avoided.

Adaptive Control of Multivariable Process Using Recurrent Neural Networks

Industrial processes are naturally multivariable in nature, which also exhibit non-linear behavior and complex dynamic properties. The multivariable four-tank system has attracted recent attention, as it illustrates many concepts in multivariable control, particularly interaction, transmission zero, and non-minimum phase characteristics that emerge from a simple cascade of tanks. So, the multivariable laboratory process of four interconnected water tanks is considered for modeling and control. For processes which show nonlinear and multivariable characteristics, classical control strategies like PIDs have performance limitations. Hence, intelligent approaches like Neural Networks (NN) is an important term in this juncture. The use of Recurrent Neural Network (RNN) is apt for modeling and control of nonlinear dynamic processes as it contains the past information about the process. The objective of the current study is to design and implement an adaptive control system using RNN for a nonlinear multivariable process. The proposed adaptive design comprises an estimator based on RNN, which adapts online and predicts one step ahead output. A Recursive Least Square (RLS) based back propagation algorithm is used for training the network. The controller used is also a RNN, which minimizes the difference between the predicted output and reference trajectory. The objective function is minimized using a steepest descent algorithm which gives the optimum control input. Desired performance of the system is ensured by the parallel operation of both. The proposed control strategy is implemented in a laboratory scale four tank system. The trajectory tracking and disturbance rejection response obtained are compared with the response obtained by using a well designed decoupled, decentralized IMC controller.

Modelling and Predictive Control of a Multivariable Process Using Recurrent Neural Networks

Industrial processes are naturally multivariable in nature, which exhibit non-linear behaviour and complex dynamic properties. The multivariable four-tank system has attracted recent attention as it exhibits elegantly complex dynamics, which includes interaction, transmission zero, and non-minimum phase characteristics that emerge from a simple cascade of tanks. In this paper, a neural model predictive controller (NMPC) is compared with a decentralized PI controller designed for a four-tank system. The approach adopts the approximation capabilities of a recurrent Elman network for modelling purposes. The learning process is performed with a modification of a back propagation through time (BPTT) algorithm. The algorithms are simulated using MATLAB and the performances of NMPC and decentralized PI control are compared based on integral square error (ISE) values for set point tracking and load changes. The performance comparison shows that NMPC is a suitable controller for four-tank system.

Distributed model predictive control of an experimental four-tank system

A distributed model predictive control (DMPC) framework is proposed. The physical plant structure and the plant mathematical model are used to partition the system into self-sufficient estimation and control nodes. Local measurements at the nodes are used to estimate the relevant plant states. This information is then used in the model predictive control calculations. Communication among relevant nodes during estimation and control calculations provides improvement over the performance of completely decentralized controllers. The DMPC framework is demonstrated for the level control of an experimental four-tank system. The performance of the DMPC system for disturbance rejection is compared with other control configurations. The results indicate that the proposed framework provides significant improvement over completely decentralized MPC controllers, and approaches the performance of a fully centralized design.

Robust state estimation and fault diagnosis for uncertain hybrid systems

Robust state estimation and fault diagnosis are challenging problems in the research into hybrid systems. In this paper a novel robust hybrid observer is proposed for a class of hybrid systems with unknown inputs and faults. Model uncertainties, disturbances and faults are represented as structured unknown inputs. The robust hybrid observer consists of a mode observer for mode identification and a continuous observer for continuous state estimation and mode transition detection. It is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded. Robustness to model uncertainties and disturbances can be guaranteed for the hybrid observer by disturbance decoupling. Furthermore, the detectability and mode identifiability conditions are rigorously analyzed. On the basis of the robust hybrid observer, a robust fault detection and isolation scheme is presented also in the paper. Simulations of a hybrid four-tank system show the proposed approach is effective.

Comparision of Multivariable Controllers for Non-Minimum Phase Systems

A system with one or more right half plane transmission (RHPT) zero is generally called a non-minimum phase system. In this paper, the authors compare two methods of designing multivariable controllers for systems with RHPT zeros. The methods used are decoupled internal model controller and a simple tuning method. In the decoupled IMC method, controller design procedure is developed with the help of a model reduction theorem. Davison has proposed a simple tuning method, which is based on inverse of the steady-state gain matrix [G(0)]. Previously the method was applied to multivariable minimum phase systems only. In the present work the Davison method is applied to systems with multivariable right half plane zero. The decoupled IMC method involves some complex calculations in designing controllers, whereas the Davison method is simple to apply. Simulation results are given for the following 2 × 2 transfer function matrix of the systems: (1) a four-tank system, a benchmark example of multivariable system; (2) a system with individual and multivariable transmission zero at s = 1; and (3) binary distillation column. The performance comparisons are given by the sum of IAE values based on response and interaction both for servo and regulatory problems. The presented simple tuning method gives an improved performance.

DISTRIBUTED MODEL PREDICTIVE CONTROL OF A FOUR-TANK SYSTEM

A distributed model predictive control (DMPC) framework is proposed. The physical plant structure and the plant mathematical model are used to partition the control duties over self-sufficient estimation and control nodes. Linear models and local measurements at the nodes are used to estimate the relevant plant states. This information is then used in the model predictive control calculations. Communication among relevant nodes during estimation and control calculations provides improvement over the performance of completely decentralized controllers. The DMPC framework is demonstrated for the level control of an interacting four-tank system. The performance of the DMPC system for disturbance rejection is compared with other control configurations. The results indicate that the performance of the proposed framework provides significant improvement over completely decentralized MPC controllers, and approaches the performance of a fully centralized design.

Subspace identification of continuous time models for process fault detection and isolation

This paper proposes a novel subspace approach towards identification of optimal residual models for process fault detection and isolation (PFDI) in a multivariate continuous-time system. We formulate the problem in terms of the state space model of the continuous-time system. The motivation for such a formulation is that the fault gain matrix, which links the process faults to the state variables of the system under consideration, is always available no matter how the faults vary with time. However, in the discrete-time state space model, the fault gain matrix is only available when the faults follow some known function of time within each sampling interval. To isolate faults, the fault gain matrix is essential. We develop subspace algorithms in the continuous-time domain to directly identify the residual models from sampled noisy data without separate identification of the system matrices. Furthermore, the proposed approach can also be extended towards the identification of the system matrices if they are needed. The newly proposed approach is applied to a simulated four-tank system, where a small leak from any tank is successfully detected and isolated. To make a comparison, we also apply the discrete time residual models to the tank system for detection and isolation of leaks. It is demonstrated that the continuous-time PFDI approach is practical and has better performance than the discrete-time PFDI approach. # 2003 Elsevier Science Ltd. All rights reserved.

Structure of Nonlinear Systems and Differential Algebra: An Example

This paper describes how differential algebra calculations can be used to investigate the structure of nonlinear systems. The tools are illustrated, using a a laboratory process in the form of a four-tank system.

Model based control of a four-tank system

A multi-disciplinary laboratory for control education has been developed at the University of Delaware to expose students to realistic process system applications and advanced control methods. One of the experiments is level control of a four-tank system. This paper describes two model-based methods students can implement for control of this interacting four-tank system. Sub-space identification is used to develop an empirical state space model of the experimental apparatus. This model is then used for model based control using internal model control (IMC). This represents an application of inner—outer factorization for non-minimum phase multivariable IMC design. Modeling is also performed using step tests and Aspen software for use with dynamic matrix control (DMC).

A Four-tank Water Recirculation System with a Hydrocyclone Prefilter and a Single Water Reconditioning Unit

Abstract In a four-tank recirculation system serviced by a single biological filter, hydrocyclone prefilters removed over 87% of the particulate matter greater than 77 μm (3 x 10-3 in) in diameter. Biological nitrification occurred on a substrate of 25 mm (1 in) diameter, Actifil (R) polypropylene biorings contained in a 0.29-m3 (10-ft3) fiberglass tank. The four 0.9 m3 (32-ft3) tanks were stocked with 1200 rainbow trout (Salmo gairdneri), averaging 66.9 g (0.148 lb) each. Fish were thinned every 2 weeks to maintain approximately constant density. During the first 62 days of the 248-day test when the filter was being conditioned, the fish had essentially no growth. Over the last 186 days the average weight increased from 71.4 to 294.1 g (0.157 to 0.648 lb) resulting in a specific growth rate of 0.76%/day. Recirculation and makeup water rates were 130 and 5 L/minute (34 and 1.3 gal/minute), respectively. Chlorinated makeup water was passed through a small ultraviolet irradiator where chlorine was oxidized ...