Time delay and model parameter estimation for nonlinear system with simultaneous approach

Time delay is a ubiquitous phenomenon in chemical engineering. In the development of a practical rigorous model for process system, the influence of time delay cannot be ignored. A simultaneous approach for estimating time delays and model parameters is proposed in this work. The critical issue is how to address the approximation for state variable with time delay, which depends on the quotient and remainder obtained by dividing time delay by length of finite element. The strategies for handling the unknown quotient and remainder are designed. Finally, two case studies are considered. The effectiveness of the proposed approach is verified. Moreover, the proposed approach exhibits better performance compared with the gradient-based sequential approach.