Using Constrained Convex Optimization in Parameter Estimation of Process Dynamics with Dead Time

Abstract

This paper proposes the usage of constrained convex optimization in improving the quality of the parameter estimates of a typical process plant with dead time from its time response data by incorporating system-specific constraints that are not considered in standard estimation methods. As the majority of the process plants are identified as second-order plus dead time (SOPDT) systems, the proposed method uses the same for establishing the optimization process. Traditional methods for parameter estimation in SOPDT systems have often relied on heuristic approaches or simplified assumptions, leading to suboptimal results. The proposed methodology augments the accuracy of the estimated values by leveraging the power of constrained convex optimization techniques, using Newton's Quadratic Model and Sequential Quadratic Programming, which provide a rigorous mathematical framework for parameter estimation. By incorporating system constraints, such as bounds on the parameters or stability requirements, it is ensured that the obtained parameter estimates adhere to physical and practical limitations. The proposed approach is demonstrated using simulations and on a real-time system, and the results show that it is effective not only in accurately estimating the parameters of the underdamped SOPDT systems but also works efficiently for parameter estimation of SOPDT systems in the presence of measurement noise. The efficacy of the proposed algorithm is verified by comparing it with similar published methods.