This paper studies the application of reduced models of a distributed parameter system for robust process control and state estimation. We take the approach of integrating model reduction, parameter identification, and model uncertainty analysis, in purpose to find an appropriate trade-off between complexity and robust performance. The application example is the temperature system in a continuous paper pulp digester. Physical modeling of this process results in coupled linearized partial differential equations which are then reduced into low-order nominal process models using an orthogonal collocation approximation method.Two different approaches to obtaining a model uncertainty description are adapted for use on a distributed parameter system with low-order nominal model and shown to produce similar results when tested with measurement data. It is also demonstrated how this uncertainty description, in combination with the reduced model, may be used for robust control design and verification of the control performance on the distributed parameter system.Finally, the possibility of estimating the distributed process state using a state observer for the reduced process is demonstrated. Measurements of the process state in a certain position is available and is shown to agree with the estimated state at the same position.

A physical model of a continuous paper pulp digester is simplified and two subprocesses selected from the digester are modelled by coupled linear partial differential equations. This study focuses on the parameter identification of the simplified linear models. Finite-dimensional approximation of the model is made and a software package developed for identification of distributed parameter processes is applied. This identification system is developed for flexibility to allow identification for different choices of subprocesses and process variables. Unknown parameters of the subprocess models are estimated and the results are illustrated by process simulation and model validation.

A physical model of a nonlinear subprocess in a continuous paper pulp digester is discussed and simplified. Model approximation is carried out in order to produce a simple linear model to be used for unknown parameter estimation of the physical model. The Taylor series expansion and the orthogonal collocation method are applied for the model linearization and model lumping, respectively. The reduced model is expressed as a standard state space form. The model parameters are estimated in the least squares sense, and the parameters retain their own physical meanings. The results of the parameter estimation are discussed and the model is verified using validation data.

The modeling of flotation is a difficult task due to the influences of mineralogical features of ores, floatability of various minerals governed by pulp environments, flotation kinetics and hydrodynamic variables. In the paper the dynamic modeling of flotation is studied. Based on the first order flotation rate equation, the dynamic description of a continuous flotation process is obtained both for a single continuous flotation cell and n cells arranged in series. A dynamic model for the mUlti-component case of continuous flotation is also discussed. The models obtained give the dynamic behaviors when the flotation parameters are changed due to the variation of the chemical and physical environment.

Nonlinear complex multi-input multi-output process is very troublesome to control. It is usually also ill-modeled. The problem of such process both in control and modeling requires a comprehensive utilization of various techniques. The thesis presents the methods for the modeling and control of complex systems. A typical example of complex processes is mineral flotation that characterized by multivariable, nonlinearities, strong interactions, stochastic disturbances, and large and variable delay times. The dynamic nonlinear model of a inverse continuous flotation process is developed based on the first order kinetics. The complexity of mineral flotation in modeling and control is shown by the analysis of the dynamic model and the relation between the process inputs and the process parameters. As an attractive alternative of conventional control technologies, fuzzy logic control is discussed for the control of an MIMO nonlinear flotation system and the simulation of the control system is carried out. LQG optimal control of the pulp level, a subsystem in a flotation process is studied and the robustness is analyzed based on the structured singular value. The control of infinite dimensional systems is known to all a knotty problem. Orthogonal collocation method, which is one of the methods of weighted residual, is employed to reduce the infinite dimensional model of the systems. In a case study a time delay system is approximated using the orthogonal collocation and a robust controller of the delay system is synthesized based on the method introduced by Glover and McFarlane in 1989. The robustness degradation caused by model reduction is discussed. The results show that the strategies studied in the thesis are available to solve the relevant modeling and control problems of complex systems.

The application of fuzzy logic in the control of flotation is studied in this paper. A general description of apatite flotation process is given and a dynamic model is developed. A fuzzy logic controller is proposed for a nonlinear isolated continuous flotation process. The knowledge base of the controller is constructed on the basis of the semi-batch results from the apatite flotation experiments and available knowledge sources. The design of the controller does not need an exact process model. The simulation result shows that the fuzzy logic controller can reduce collector dosage consumption of the apatite flotation process while maintaining the phosphorous content in magnetite concentrate within an acceptable limits less than 0.025% P. Stability of the fuzzy control system is discussed

The application of fuzzy logic in the control of flotation is studied in this paper. A general description of apatite flotation process is given and a dynamic model is developed. A fuzzy logic controller is proposed for a nonlinear isolated continuous flotation process. The knowledge base of the controller is constructed on the basis of the semi-batch results from the apatite flotation experiments and available knowledge sources. The design of the controller does not need an exact process model. The simulation result shows that the fuzzy logic controller can reduce collector dosage consumption of the apatite flotation process while maintaining the phosphorous content in magnetite concentrate within an acceptable limits less than 0.025% P. Stability of the fuzzy control system is discussed