Thesis (DTech (Electrical Engineering))--Cape Peninsula University of Technology, 2018. / Industrial processes tend to have very complex mathematical models that in most instances result in very model specific optimal estimation and designs of control strategies. Such models have many composition components, energy compartments and energy inventories that result in many process variables that are intertwined and too complex to separate from one another. Most of the derived mathematical process models, based on the application of first principles, are nonlinear and incorporate unknown parameters and unmeasurable states. This fact results in difficulties in design and implementation of controllers for a majority of industrial processes. There is a need for the existing parameter and state estimation methods to be further developed and for new methods to be developed in order to simplify the process of parameters or states calculation and be applicable for real-time implementation of various controllers for nonlinear systems. The thesis describes the research work done on developing new parameter and state estimation methods and algorithms for bilinear and nonlinear processes. Continuous countercurrent ion exchange (CCIX) process for desalination of water is considered as a case study of a process that can be modelled as a bilinear system with affine parameters or as purely nonlinear system. Many models of industrial processes can be presented in such a way. The ion exchange process model is developed based on the mass balance principle as a state space bilinear model according to the state and control variables. The developed model is restructured according to its parameters in order to formulate two types of parameter estimation problem – with process models linear and nonlinear according to the parameters. The two models developed are a bilinear model with affine and a nonlinear according to the parameters model. Four different methods are proposed for the first case: gradient-based optimization method that uses the process output measurements, optimization gradient based method that uses the full state vector measurements, direct solution using the state vector measurements, and Lagrange’s optimization technique. Two methods are proposed for the second case: direct solution of the model equation using MATLAB software and Lagrange’s optimisation techniques. / National Research Foundation (NRF)