P.D. Roberts

Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

On an algorithm for combined system optimisation and parameter estimation

The paper is concerned with the determination of optimum steady-state operation of industrial plant where the optimisation is performed using a mathematical model with parameters whose values are estimated by comparing model and real plant measurements. The two associated problems of system optimisation and model parameter estimation are discussed and an algorithm is examined whose purpose is to accomplish the correct steady-state optimum operating condition on the real plant in spite of inaccuracies in the structure of the mathematical model. The aim of the paper is to investigate the performance of the algorithm which is accomplished through a theoretical analysis of its application to a linear process, where the optimisation is performed using a quadratic performance index and a mathematical model of incorrect structure. Particular emphasis is given to the stability and convergence properties of the algorithm and to the effect of real process measurement errors. Simulation results are also presented illustrating the effectiveness of the technique when applied to nonlinear optimisation problems including a study concerned with determining optimum controller set points to maximise the net rate of return from a chemical reactor plant.

On-line process fault diagnosis using neural network techniques

A neural-network based on-line fault-diagnosis system for industrial processes is presented in this paper. A multi-layer feed-forward neural network is developed and trained with symptom-fault pairs from experience of the operation of a process or from simulation analysis of that process. The trained network can be used to diagnose faults in that it can associate the abnormalities in on-line measurements with corresponding faults. Compared with diagnosis systems based on expert-systems techniques, which have several limitations such as the time consuming nature of developing the knowledge base and the inability to cope with situations not presented in the knowledge base, the neural-network based fault-diagnosis system is easy to develop and performs robustly. The feasibility of applying such a diagnosis system to industrial processes is demonstrated by applying it to a pilot-scale mixing process and in a simulation study of a continuously-stirred tank reactor (CSTR) system. A series of experiments is carried out to investigate the performance of the neutral-network based on-line diagnosis system and it is shown that it can perform satisfactorily with partially incorrect and partially unavailable information. Therefore, to some extent, the system can tolerate measurement noise and model-plant mismatch.

An integrated system optimization and parameter estimation technique for hierarchical control of steady-state systems

This paper presents computer simulation results of an optimal adaptive algorithm (Brdyś and Roberts 1984) and develops a double iterative alternative. Both algorithms are optimal in the sense that Kuhn-Tucker necessary optimality conditions are satisfied. The aim of the latter is to reduce the number of times that information is required from the real system. Simulation results also show that it does not increase the total number of information exchanges during the iteration procedure and may even reduce it.

Convergence and optimality of modified two-step algorithm for integrated system optimization and parameter estimation

This paper investigates convergence and optimality properties of the modified two-step algorithm for on-line determination of the optimum steady-state operating point of an industrial process. Mild sufficient conditions are derived for the convergence and feasibility of the algorithm. It is shown that every point within the solution set of the algorithm satisfies first-order necessary conditions for optimality, and that every optimal solution belongs to this set. It is also shown that there are advantages to be gained by using a linear mathematical model of the process within the implementation of the algorithm.

Joint coordination method for the steady-state control of large-scale systems

Abstract The advantages of several methods for the steady-state control of large-scale systems are combined to give an algorithm which produces optimum solutions for a wide class of processes. It is demonstrated how optimum reality solutions can be obtained even when large model-reality differences exist. The method employs a hierarchical framework where coordination of local decision problems is achieved jointly by price and modifier variables. A three-subsystem process is optimized to illustrate the procedure.

On-line steady-state optimisation of nonlinear constrained processes with slow dynamics

A scheme for on-line optimisation of constrained nonlinear processes with slow dynamics is suggested and applied to a continuous reactor process. A two-model adaptive mechanism, dynamic and steady state, is used in the scheme. The dynamic model is used to approximate the process locally at each working point for the purpose of estimating steady-state derivatives, and the steady-state model is used for model-based optimisation. The performance lost caused by the inaccuracy of the steady-state model is compensated for by derivatives information which is obtained from dynamic data. The correct optimum can be achieved on-line even if both models are very rough. As shown in applications, the scheme is suited to various types of constraints and nonlinearities and is noise-insensitive.

Process fault diagnosis with diagnostic rules based on structural decomposition

Abstract A method for formulating diagnostic rules from knowledge of system structures and component functions is presented. Based on this deep knowledge about a process, diagnosis can be performed hierarchically and structural decomposition is used in the presented technique to narrow the diagnostic focus. In the development of diagnostic rules, the structural and functional knowledge about a process is represented by several Boolean matrices, which describe the relations between subsystems, the relations between measured variables and the relations between malfunctions and measurements. Diagnosis is carried out by searching for the source subsystem where a fault occurred, and locating the fault in this source subsystem. The method is demonstrated in the development of diagnostic rules for a pilot scale mixing process and a simulated CSTR (continuously stirred tank reactor) system, where the diagnosis systems are developed using the ExTran expert system shell.

An extension to the modified two-step algorithm for steady-state system optimization and parameter estimation

This paper presents an extension to the modified two-step algorithm for determining the optimum steady-state operating condition of a system. The new version of the algorithm gives a faster convergent rate and ensures that the optimal condition is achieved in more general cases where system inequality constraints involving system outputs occur. The performance of the algorithm under noisy measurements is examined by simulation. Simple filter techniques are employed to attenuate errors in process measurements.

Steady State Hierarchical Control of Large-scale Industrial Processes: A Survey

Abstract Large scale industrial processes are usually required to operate in a steady-state Manner. The development of hierarchical control of these processes is considered in three stages: static multilevel optimization, steady-state hierarchical optimization and integrated system optimization and parameter estimation. This paper surveys the main achievements in these three stages, and gives the perspective of future developments.