A graph theoretic approach to multivariable control system design

A graph theoretic approach is described for the design of multivariable control for large systems as an alternative to geometric methods. An example is given f⊙r a distillation column to demonstrate the technique, with a particular reference to aspects of disturbance rejection and the possibilities for pole assignment.     

Globally linearized control system design of a constrained multivariable distillation column

The goal of this paper is to develop a discrete-time multivariable globally linearized control (GLC) algorithm, which provides low computational requirements with constraint handling ability. The control strategy is constructed with four elements: a transformer that accounts for process nonlinearities; an estimator, which observes the required unmeasured states; a variable constraint mapping optimizer that transforms the input constraints of the nonlinear process into constraints on the manipulated inputs of the globally linearized system and a quadratic dynamic matrix controller (QDMC) that provides constraints handling ability. The effectiveness of the designed controller has been tested on a multi-input multi-output (MIMO) nonlinear distillation column through extensive numerical simulations. The control law showed a high quality performance for set point tracking and disturbance rejection in presence of parametric uncertainty. The effect of unmeasured disturbance also has been studied through the simulation experiment. In the comparative study, the proposed GLC-QDMC control technique outperformed the GLC-DMC control law.     

Object-oriented approach applied to ANFIS modeling and control of a distillation column

Neurofuzzy networks are hybrid systems that combine neural networks with fuzzy systems, and the Adaptive Neuro-Fuzzy inference system (ANFIS) is a particular case in which a fuzzy system is implemented in the framework of an adaptive neural network. This neurofuzzy approach represents an effective structure to the modeling of plant dynamics, and the oriented-object programming environments offer an intuitive way to address this task. In this paper the MODELICA object-oriented environment has been applied to the ANFIS modeling and indirect control of the heavy and light product composition in a binary methanol-water distillation column by using the adaptive Levenberg–Marquardt approach. The results obtained demonstrate the potential of the adaptive ANFIS scheme under MODELICA for the dual control of composition both for changes in set points with null stationary error even when disturbances are present.     

Application of predictive control techniques to a distillation column

Model-based predictive control techniques are widely recognized as having useful application to control problems characterized by complex dynamics and severe time delay. The establishment of a representative process model is the key step in the procedure and for anything other than trivially simple systems is a major hurdle. This paper describes the application of predictive control techniques to a distillation problem which embodies a pure time delay of 2–3 h and time constants of 3–4 h. A sampled-data process model is identified from monitored input/output data and from this a predictive control algorithm is designed. The application of the controller has resulted in very effective closed-loop control of the base composition of the distillation column, where previously only manual supervision was possible.     

Constrained multivariable control of a distillation column using a simplified model predictive control algorithm

Distillation columns are important process units in petroleum refining and need to be maintained close to optimum operating conditions because of economic incentives. Model predictive control has been used for control of these units. However, the constrained optimization problem involved in the control has generally been solved in practice in a piece-meal fashion. To solve the problem without decomposition, the use of a linear programming (LP) formulation using a simplified model predictive control algorithm has been suggested in the literature. In this paper, the LP approach is applied for control of an industrial distillation column. The approach involved a very small size optimization problem and required very modest computational resources. The control algorithm eliminated the large cycling in the product composition that was present using SISO controllers. This resulted in a 2.5% increase in production rate, a 0.5% increase in product recovery, and a significant increase in profit.     

Adaptive dynamic matrix control of a distillation column with closed-loop online identification

This paper presents an online identification technique where a process is identified in terms of pseudo impulse response coefficients and subsequently used to update convolution type models to accommodate process-model mismatch. As an example, dynamic matrix control has been applied adaptively to control the top product composition of a distillation column for both servo and regulatory problems. The algorithm automatically detects a large step-like disturbance requiring fresh identification of the process and subsequently adapts the controller to the new model. Simulation studies using an analytical dynamic full order model of a distillation column demonstrated the usefulness of the adaptation scheme. Experimentation on a pilot scale distillation unit vindicated the simulation results.     

A hybrid genetic algorithm to optimize simple distillation column sequences

Based on the principles of Genetic Algorithms (GAs), a hybrid genetic algorithm used to optimize simple distillation column sequences was established. A new data structure, a novel arithmetic crossover operator and a dynamic mutation operator were proposed. Together with the feasibility test of distillation columns, they are capable to obtain the optimum simple column sequence at one time without the limitation of the number of mixture components, ideal or non-ideal mixtures and sloppy or sharp splits. Compared with conventional algorithms, this hybrid genetic algorithm avoids solving complicated nonlinear equations and demands less derivative information and computation time. Result comparison between this genetic algorithm and Underwood method and Doherty method shows that this hybrid genetic algorithm is reliable.     

Effect of interaction multiplicity on control system design for a MTBE reactive distillation column

The control strategy of a reactive distillation for synthesis of MTBE is investigated. Although steady state multiplicities occur in the column, a linear control is still possible since a controlled and manipulated variable-pairing scheme that exhibits a sufficiently large range of near linear relations can be found, if we operate at constant reflux ratio. Reboiler duty is used to control the temperature of a stage just below the reaction section and near the top of the stripping section. Stoichiometric balance is controlled by a feed ratio plus internal composition control scheme, using a control valve installed on the C4 feed-line as the manipulated variable. Such a scheme is capable of maintaining the desirable steady state that achieves high product purity and reactant conversion. However, a similar scheme that uses a control valve installed on the methanol feed-line as the manipulated variable shows severe oscillation. It is caused by multiplicity in the interaction between the temperature and stoichiometric control loops.     

Sliding mode control assisted by GPI observers for tracking tasks of a nonlinear multivariable Twin-Rotor aerodynamical system

This paper explores the techniques based on Generalized Proportional Integral Observers (GPI), under the approach of active disturbance rejection, applied to the control of multivariable nonlinear systems with the same number of inputs and outputs (square). As a central axis, a sliding mode control scheme assisted by GPI observers is proposed. These observers are responsible for estimating the disturbances associated with the dynamics of the sliding surfaces produced by non-linearities, not modeled elements, parameter uncertainty and external disturbances. This process allows the creation of sliding regimes under the point of view of decoupled control. As a case study, the position control of a small-scale 2-DOF helicopter affected by adverse operating conditions, such as unknown external disturbances and actuator faults, is considered. Finally, experimental results that validate the proposed control strategy and a comparison with a linear GPI observer-based active disturbance rejection control scheme are presented.     

Multivariable adaptive predictive control of a binary distillation column

This paper presents a tutorial review of an adaptive predictive control system (APCS). Special emphasis is given to the key issues involved in the practical application of APCS to real processes. These practical issues are illustrated by actual application of SISO and MIMO control of a pilot scale binary distillation column. The experimental evaluation of this method reveals the simplicity of the adaptive algorithm and its excellent performance in an industrial type environment. The experimental results easily outperformed well-tuned classical PID controllers. A brief review of other applications of adaptive control to chemical processes is also included in this paper.     

Experimental investigation of conventional control strategies for a heterogeneous azeotropic distillation column

In this work, a laboratory scale sieve plate distillation column was constructed to investigate the conventional control strategies of an isopropyl alcohol (IPA), cyclohexane (CyH) and water (H₂O) heterogeneous azeotropic distillation column. Steady state process analysis showed that the optimal operation point should be located at a critical reflux, a transition point at which the distillation path switches from a route that passes through IPA+H₂O azeotrope to one that passes through IPA+CyH azeotrope. At this critical reflux, a high purity IPA product can be obtained with minimum energy consumption and maximum product recovery. However, the steady state is extremely sensitive to feed disturbances. A good control strategy must be able to maintain a steady column temperature profile that shows a plateau near 70°C to ensure passage around IPA+CyH azeotrope. In this study, an inverse double loop control strategy is recommended. Through experimental testing, the proposed control strategy was demonstrated to keep the product IPA purity at the desired high-purity level under all feed disturbance changes while other conventional control strategies fail.     

Comparison of pressure-swing distillation and extractive distillation with varied-diameter column in economics and dynamic control

Pressure-swing distillation and extractive distillation are two common methods for azeotrope separation. The economics and controllability are two crucial factors for evaluating the feasibility of a separation process. A varied-diameter column (VDC) was used in the process design to evaluate its economics and controllability. Five azeotropic systems were investigated in order to compare the economics of pressure-swing distillation and extractive distillation with a VDC. Results indicate that pressure-swing distillation with a VDC saves more money than extractive distillation. The dynamic control were evaluated in the acetone-methanol system for both processes with a VDC. The improved control structure for pressure-swing distillation with a VDC can handle ±20% disturbances effectively, while the improved control structure for extractive distillation with a VDC can only handle ±10% disturbances. A comparison of the two methods from the viewpoint of economics and controllability demonstrates that pressure-swing distillation is more suitable when using a VDC.     

An approach to multivariable combustion control design

In this paper, an approach to multivariable combustion control design within the Individual Channel Design (ICD) framework for analysis and control design is presented. ICD is a framework which involves an interplay between customer specification, uncertain plant characteristics, and the multivariable feed-back design itself. Established multivariable methods and process engineering knowledge can be incorporated or evaluated within the ICD framework. The combustion control has been designed and evaluated with a computer simulation of both a linearized model and a nonlinear model of the closed-loop system. The ICD multivariable framework shows in a highly transparent manner, by way of simple graphical frequency response indicators, what the main possibilities and difficulties posed by a combustion process for multivariable control are, and how much trade-off between control specifications is possible. Solutions are also presented for problems such as: integrity of closed-loop control, balance of input-output channels, simple and transparent controller structure, and robustness.     

Role of multiplicity in reactive distillation control system design

The impact of steady-state multiplicities on the control of a simulated industrial scale methyl acetate reactive distillation (RD) column is studied. At a fixed reflux rate, output multiplicity, with multiple output values for the same reboiler duty, causes the column to drift to an undesirable steady-state under open loop operation. The same is avoided for a fixed reflux ratio policy. Input multiplicity, where multiple input values give the same output, leads to “wrong” control action under feedback control severely compromising control system robustness. A new metric, rangeability, is defined to quantify the severity of input multiplicity in a steady-state input–output (IO) relation. Rangeability is used in conjunction with conventional sensitivity analysis for the design of robust control structures for the RD column. Results for the two synthesized control structures show that controlling the most sensitive reactive tray temperature results in poor robustness due to low rangeability causing “wrong” control action for large disturbances. Controlling a reactive tray temperature with acceptable sensitivity but larger rangeability gives better robustness. It is also shown that controlling the difference in the temperature of two suitably chosen reactive trays further improves robustness of both the structures as input multiplicity is avoided. The article brings out the importance of IO relations for control system design and understanding the complex dynamic behavior of RD systems.     

Nonfragile containment control of nonlinear multi-agent systems via a disturbance observer-based approach

In this article, we consider the nonfragile containment control problem of nonlinear multi-agent systems (MASs) with exogenous disturbance where the communication links among agents under consideration is directed. Firstly, based on relative output measurements between the agent and its neighbors, a disturbance observer-based control protocol is proposed to solve the containment control problem of MASs with inherent nonlinear dynamics and exogenous disturbances. Secondly, because of the additional tuning of parameters in the real control systems, uncertainties in the designing of observer and controller gains always occur, and as a result, an output feedback controller with disturbance rejection is conceived and the containment control problem of nonlinear MASs with nonfragility is thoroughly investigated. Then, depending on matrix transformation and inequality technique, sufficient conditions of the designed controller gains exist, which is derived from the asymptotic stability analysis problem of some containment error dynamics of MASs. Finally, two simulation examples are exploited to illustrate the effectiveness of the proposed techniques.     

Multimodel identification for control of an ill-conditioned distillation column

Identification for control of an ill-conditioned system requires special techniques. The directionality of such a system should be taken into account in the design of identification experiments. In distillation, information about the directionality properties can be obtained from certain flow gains, which are easy to determine in practice. Based on such information, the high- and low-gain directions of the plant can be explicitly excited. In this paper, a pilot-scale distillation column is identified by this approach at two different operating points. At each operating point, a nominal second-order plus time-delay model with logarithmic outputs is determined. This model structure makes it possible to capture the dynamic directionality of the plant. In addition, models describing variations and uncertainties in the high- and low-gain directions are determined by a special technique. The models obtained are superior to models determined via traditional step tests. The former satisfy integral controllability requirements, while the latter tend to violate them.     

Observer-based multivariable flatness control of a cold rolling mill

The synthesis methodology developed by Kimura (1985) based on the design theory of output regulators essentially due to Wonham (1974) has been applied successfully to the flatness control system for a 6-high cold rolling mill. The system has the following remarkable features.

1. (1) The structure of the controller is simple. This makes it easy to tune the control system.

2. (2) The controller copes well with the detection time delay, and thus high performance is obtained even at a low rolling speed.

3. (3) The flatness error caused by the rolling force variation in mill acceleration and deceleration time would be kept to a minimum by the function to adjust roll bending force using the signal of rolling force.

A multivariable MRAC scheme with application to a nonlinear aircraft model

This paper revisits the multivariable model reference adaptive control (MRAC) problem, by studying adaptive state feedback control for output tracking of multi-input multi-output (MIMO) systems. With such a control scheme, the plant-model matching conditions are much less restrictive than those for state tracking, while the controller has a simpler structure than that of an output feedback design. Such a control scheme is useful when the plant-model matching conditions for state tracking cannot be satisfied. A stable adaptive control scheme is developed based on LDS decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. A simulation study of a linearized lateral-directional dynamics model of a realistic nonlinear aircraft system model is conducted to demonstrate the scheme. This linear design based MRAC scheme is subsequently applied to a nonlinear aircraft system, and the results indicate that this linearization-based adaptive scheme can provide acceptable system performance for the nonlinear systems in a neighborhood of an operating point.     

Plant-wide design and control of acetic acid dehydration system via heterogeneous azeotropic distillation and divided wall distillation

Energy-saving plant-wide design and plant-wide control of an acetic acid dehydration system with the feed containing methyl acetate and p-xylene are investigated in the study. A heterogeneous azeotropic distillation using isobutyl acetate as an entrainer is designed to obtain high-purity acetic acid at the column bottom and to keep a small acetic acid loss through the top aqueous draw. The accumulation of p-xylene in the column is avoided by adding a side product stream. The mixture in the aqueous phase of decanter, containing mostly water, methyl acetate, and isobutyl acetate is separated using a divided wall distillation column. The whole acetic acid dehydration system includes a heterogeneous azeotropic distillation column and a divided wall distillation column.The control strategies using temperature loops are proposed for this acetic acid dehydration system. For the heterogeneous azeotropic distillation column, the requirements for acetic acid compositions in both the aqueous phase of the decanter and the column bottom can be satisfied by designing entrainer inventory temperature control and cascade temperature control simultaneously. The stages of controlled temperatures are chosen by singular value decomposition and closed-loop analysis methods based on the criteria of minimum entrainer makeup. For the divided wall distillation column, steady-state analysis methods are used for the selection of proper controlled and manipulated variables and the determination of their pairings. Dynamic simulation results demonstrate that the proposed plant-wide control strategy can maintain product purities and reject external disturbances in feed flow and composition changes as well as internal disturbances such as changes in liquid and vapor splits.     

The active disturbance rejection control approach to stabilisation of coupled heat and ODE system subject to boundary control matched disturbance

We consider stabilisation for a linear ordinary differential equation system with input dynamics governed by a heat equation, subject to boundary control matched disturbance. The active disturbance rejection control approach is applied to estimate, in real time, the disturbance with both constant high gain and time-varying high gain. The disturbance is cancelled in the feedback loop. The closed-loop systems with constant high gain and time-varying high gain are shown, respectively, to be practically stable and asymptotically stable.